Thermo-Mechanical Reliability
of Flip-Chip Assemblies
with Heat-Spreaders
Bernhard Wunderle
Technische Universit¨
at Berlin
Fa k u lt ¨
at Elektrotechnik und Informatik
Juni 2003
D83
Thermo-Mechanical Reliability
of Flip-Chip Assemblies
with Heat-Spreaders
von Diplom-Physiker
Bernhard Wunderle
aus Berlin
von der Fakult¨at IV - Elektrotechnik und Informatik
der Technischen Universit¨at Berlin
zur Erlangung des akademischen Grades eines
Doktor der Ingenieurwissenschaften
– Dr.-Ing. –
genehmigte Dissertation.
Promotionsausschuss:
Vorsitzender: Prof. Dr.-Ing. H. Henke
Gutachter: Prof. Dr.-Ing. Dr. E.h. H. Reichl
Gutachter: Prof. Dr.-Ing. E. Meusel
Gutachter: Prof. Dr. rer. nat. B. Michel
Tag der wissenschaftlichen Aussprache: 11. Juni 2003
Berlin 2003
D83
i
Summary
The concept in flip-chip technology, to cool a chip by attaching its electrically inactive
reverse side to the heat-spreading cover of e.g. a controller-housing, represents a very
promising solution to thermal management problems encountered in automotive applica-
tions. However, its technological realization imposes new mechanical constraints on the
flip-chip assembly which have an influence on its thermo-mechanical reliability.
Whereas the unconstrained flip-chip assembly without reverse side cooling has been in the
focus of reliability studies for a long time, the loading induced by additional mechanical
constraints caused by the attachment of the heat-spreader and hence its impact on solder
bump reliability are still largely unknown. To qualify the typical load situation and to
quantify the lifetime as a function of appropriate variables is therefore a fundamental
prerequisite for a reliable design and its optimization by virtual prototyping. Consequently,
there is a need for a comprehensive study to provide adequate design rules.
This thesis comprises analysis, assessment and prediction of solder bump reliability for
flip-chip assemblies on organic board. These assemblies are subjected to various influ-
ential mechanical constraints under periodic thermal load in simulation and subsequent
experiment.
A flexible, modular and parametric finite element model was developed to handle the
required variations as to geometry, material and loads. The required material parameters
were measured and made available to the software. Then the model was calibrated and
optimized with respect to accuracy and speed. This allows a computational analysis of
the reliability of eutectic tin-lead solder bumps, where the accumulated creep strain within
the bump was evaluated as an appropriate failure criterion. For experimental verification
especially designed test-assemblies underwent thermal cycling and were regularly checked
for solder bump failure.
Experiment and simulation are in good agreement when compared within the framework
of the Coffin-Manson low cycle fatigue damage approach. So for the first time a correlation
could be established between lifetime and cooling for flip-chip assemblies.
It was found that flip-chip reverse side cooling represents a thermo-mechanically reliable
option for modern high performance thermal management. However, an attached heat-
spreader results in general in a lower reliability compared to the mechanically unconstrained
flip-chip assembly.
The following variables could be shown to be representative and sufficient for the universal
loading description of the assembly and to determine its reliability. Based on the result-
ing distinct ranking of the individual configurations the influence of the variables can be
obtained:
The thickness of the board (a) has the strongest influence on lifetime, where thick boards
do reduce reliability. This is particularly critical in combination with a fixation (b) of the
board on the heat-spreader for reasons of thermal mismatch. Next, a displacement of the
board (c) reduces lifetime proportionally to its value. Negative values of displacement,
which cause a convex curvature of the chip, can also be realized and do even induce a
small increase in reliability. As far as the thermal interface material (d) is concerned, gap-
fillers yield slightly better results than adhesives. With adhesives a low stress bond at all
ii
temperatures guarantees a higher reliability. The value of a compressive force (e) needed
to displace the board does not have an effect.
Although the individual configurations differ, depending on applied loads and interface
material, largely in chip deformation at low temperatures, this does not influences reliability
to a large extent. Chip and bump are found to accommodate to the applied loads after a
transient response phase. The critical situation for solder bump reliability is a continuing,
enforced or constrained deformation of the chip at high temperatures which differs from
the deformation behaviour of the mechanically unconstrained chip.
A novel set of design guidelines obtained from this study now allows technological real-
ization of flip-chip assemblies with reverse side cooling featuring maximum solder joint
reliability. Moreover, the presented analytical and numerical framework permits its future
simulative prediction. The applied methodology can easily be extended to further configu-
rations and transferred to related problems in microelectronic packaging facilitating their
solution.
iii
Zusammenfassung
Die Entw¨armung von Flip-Chip Aufbauten ¨uber ihre elektrisch inaktive R¨uckseite ist
ein sehr vielversprechendes Konzept f¨ur Chips mit h¨oherer Verlustleistung. Dabei kann
der Chip thermisch an das Geh¨ause angekoppelt werden, wobei dieses gleichzeitig als
K¨uhlk¨orper fungiert. Dies ist besonders interessant f¨ur Anwendungen im Kraftfahrzeug-
bereich (z.B. bei Steuerger¨aten). Durch die technische Realisierung dieses Konzeptes ist
der Chip jedoch neuartigen mechanischen Belastungen unterworfen, welche seine thermo-
mechanische Zuverl¨assigkeit beeinflussen.
Flip-Chip Aufbauten ohne spezielle Entw¨armungsmaßnahmen sind schon seit l¨angerer
Zeit Gegenstand von Zuverl¨assigkeitsuntersuchungen. F¨ur den immer wichtiger werden-
den Fall der R¨uckseitenentw¨armung hingegen ist der Belastungszustand des Chips, her-
vorgerufen durch die Befestigung des K¨uhlk¨orpers, ebenso wie dessen Auswirkungen auf
die Zuverl¨assigkeit der Lotverbindungen (Bumps) noch immer gr¨oßtenteils unbekannt.
Eine Beschreibung der typischen Belastungssituation und die quantitative Ermittlung der
Lebensdauer als Funktion geeigneter Variablen ist jedoch die Grundvoraussetzung f¨ur ein
zuverl¨assiges Design und dessen Optimierung mittels simulativer Methoden. Deshalb
erscheint eine umfassende Untersuchung zur Aufstellung von Designrichtlinien dringend
notwendig.
Die vorliegende Arbeit umfaßt Analyse, Ermittlung und Vorhersage der Zuverl¨assigkeit
von Lotverbindungen f¨ur Flip-Chip Aufbauten auf organischem Substrat unter verschieden
mechanischen Randbedingungen und thermischer Wechselbelastung in Simulation und Ex-
periment.
Um die erforderlichen Variationen bez¨uglich Geometrie, Material und Belastungsmodi ein-
fach handhaben zu k¨onnen, wurde ein flexibles, modular und parametrisch aufgebautes
Finite Elemente Modell entwickelt. Die eingesetzten Materialien wurden charakterisiert
und die gemessenen Daten implementiert. Danach konnten das Modell kalibriert und
bez¨uglich Genauigkeit und Schnelligkeit in der Simulation optimiert werden.
Dies erm¨oglichte eine schnelle und genaue rechnergest¨utzte Zuverl¨assigkeitsanalyse der eu-
tektischen Zinn-Blei Lotverbingungen. Dabei ließen sich die akkumulierten Kriechdehun-
gen im Lotbump als Schadenskriterium bewerten. Zur experimentellen Verifizierung wur-
den entsprechende Testvehikel entwickelt, Temperaturwechselbelastung unterworfen und
in regelm¨aßigen Abst¨anden auf Lotversagen getestet.
Experiment und Simulation konnten innerhalb des Coffin-Manson Ansatzes (Low Cycle Fa-
tigue) miteinander korreliert werden und zeigten gute ¨
Ubereinstimmung. Auf diese Weise
ließ sich zum erstem Mal der Zusammenhang von Lebensdauer und Rckseitenentw¨armung
f¨ur Flip-Chip Aufbauten ermitteln.
Die getesteten Konfigurationen ergaben, daß die R¨uckseitenentw¨armung von Flip-Chips ein
zuverl¨assiges Konzept bez¨uglich der Thermomechanik darstellt. Trotzdem wird generell die
Anbringung einer W¨armesenke, im Vergleich zu einem unbelasteten Flip-Chip Aufbau, zu
einer geringeren Zuverl¨assigkeit f¨uhren.
Es konnte gezeigt werden, daß die folgenden Variablen hinreichend den Belastungszustand
des Aufbaus charakterisieren und deutliche Auswirkungen auf die Zuverl¨assigkeit haben.
iv
Aufgrund der sich ergebenden, deutlich abgestuften Rangfolge der einzelnen Konfigurati-
onen l¨aßt sich der Einfluss der einzelnen Variablen angeben: Den st¨arksten Einfluss auf
die Lebensdauer hat die Dicke der Leiterplatte, wobei dicke Substate die Zuverl¨assigkeit
reduzieren. Dies ist besonders kritisch in Kombination mit einer Fixierung der Leiterplatte
auf dem K¨uhlk¨orper aufgrund der Differenz in den thermischen Ausdehnungskoeffizienten.
Eine gr¨oßere Leiterplattenverschiebung bewirkt eine st¨arkere Reduzierung der Lebensdauer.
Auch negative Verschiebungen, welche eine konvexe Chipkr¨ummung verursachen, k¨onnen
realisiert werden, was sich auf die Zuverl¨assigkeit sogar g¨unstig auswirkt. Bei der Wahl
des W¨armeleitmediums schneiden die Folien geringf¨ugig besser ab als die Kleber. F¨ur
W¨armeleitkleber ist eine spannungsarme Verbindung bei jeder Temperatur Voraussetzung
f¨ur eine h¨ohere Zuverl¨assigkeit. Die Gr¨oße einer kompressiven Kraft,zust¨andig f¨ur die
Durchbiegung der Leiterplatte, zeigte hingegen keinen Einfluss.
Obwohl sich die einzelnen Konfigurationen bei tiefen Temperaturen je nach Belastung
und W¨armeleitmedium stark im Deformationsverhalten des Chips unterscheiden, hat dies
keinen großen Einfluss auf die Zuverl¨assigkeit. Chip und Bumps passen sich nach einer
¨
Ubergangsphase den neuen Belastungen an. Der kritische Bereich f¨ur die Lebensdauer
sind eine andauernde, erzwungene oder eingeschr¨ankte Bewegungsf¨ahigkeit des Chips bei
hohen Temperaturen im Vergleich zum unbelasteten Chip.
Die aus dieser Arbeit resultieren Designregeln erlauben nun die technische Realisierung von
Flip-Chip Aufbauten mit R¨uckseitenentw¨armung bei maximierter Bump-Zuverl¨assigkeit.
Die vorgestellte analytische und simulative Methodik kann leicht auf weitere Konfigura-
tionen ausgedehnt oder auch auf verwandte Probleme im Packaging-Bereich angewandt
werden, um deren L¨osung zu vereinfachen.
v
Danksagung
Zuerst m¨ochte ich meinem Doktorvater Herrn Prof. Herbert Reichl von der Technischen
Universi¨at Berlin f¨ur die Betreuung der Dissertation, stete Diskussionsbereitschaft und die
Schaffung einer sehr motivierenden Arbeitsatmosph¨are danken.
F¨ur die ¨
Ubernahme eines zweiten und dritten Gutachtens spreche ich Herrn Prof. Ekkehard
Meusel von der Technischen Universit¨at Dresden und Herrn Prof. Bernd Michel vom
Fraunhofer Institut f¨ur Zuverl¨assigkeit und Mikrointegration in Berlin meinen Dank aus.
Herr Prof. Bernd Michel hat als Abteilungsleiter die Arbeit von Beginn an fachlich und
organisatorisch begleitet.
Herrn Prof. Heino Henke danke ich f¨ur die Mitarbeit im Promotionsausschuß.
Herrn Dr. Andreas Schubert (†27.1.2003) spreche ich ganz besonders herzlich meinen Dank
aus. Dr. Schubert hat die Dissertation als Gruppenleiter am Fraunhofer Institut betreut.
Ich danke Ihm nicht nur f¨ur seine hervorragende und sehr engagierte Betreuung und die
vielen, sehr wertvollen wissenschaftlichen Anregungen, sondern auch f¨ur seine stete Hilfs-
bereitschaft und sehr freundschaftliche Zusammenarbeit.
Herrn Dr. Wolfgang N¨uchter von der Robert Bosch GmbH danke ich gerne f¨ur die exzel-
lente Betreuung der Arbeit, sein großes Engagement und die Schaffung wissenschaftlicher
Freir¨aume.
Die Einbindung in die Abteilung FV/PLV3 bei Robert Bosch unter der Leitung von Herrn
Dr. Jan Benzler trug zum Gelingen der Arbeit bei. Besonders die Zusammenarbeit mit
Herrn Philippe Jaeckle und Herrn Dr. Wolfram D¨ummler bereitete mir viel Freude. Herr
Dr. Dirk Brinkmann half bei der Umschiffung von Problemen in und um Ansys.
Unterst¨utzung in jeder Hinsicht erfuhr ich von meinen Kollegen der Abteilung Mechanical
Reliability and Micromaterials des Fraunhofer IZM. Besonders danke ich Herrn Dr. Eber-
hard Kaulfersch, Herrn Dr. Rainer Dudek, Herrn Hans Walter, Herrn J¨urgen Hussack und
Frau Astrid Gollhardt. Frau Elke Noack unterst¨utzte mich mit Messungen am Rheometer,
Herr Florian Schindler-Saefkow half mit Bild 4.27.
Ein herzliches Dankesch¨on geht an das Philosophische Quintett! Herr Olaf Wittler, Herr
J¨urgen Keller, Herr Habib Badri und besonders Herr Dr. Ralph Schacht trugen dazu bei,
daß die Promotion zu einer kurzweiligen und intensiven Erfahrung wurde. Einen nicht ge-
ringen Anteil hieran hatten auch Herr Dr. Eckart Hoene und Herr Dr. Gerhard Fothering-
ham.
Schließlich danke ich meiner Schwester Ulrike f¨ur viele aufbauende Worte besonders in
der Endphase der Arbeit, sowie meinem Mitbewohner Jens Heyken, und das nicht nur f¨ur
seinen norddeutschen Humor.
vi
Contents
Summary i
Zusammenfassung iii
Danksagung v
1 Introduction 1
2 Flip-Chip Assemblies under Thermal and Mechanical Load:
Motivation and Conception 4
2.1 Thermal Management of Flip-Chip Assemblies . . . . . . . . . . . . . . . . 4
2.1.1 Maximum Thermal Performance: Flip-Chip Reverse Side Cooling . 6
2.1.2 New Boundary Conditions Through Reverse Side Cooling . . . . . . 9
2.2 Thermo-Mechanical Reliability Issues . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Model Assumptions and Qualitative Considerations . . . . . . . . . 10
2.2.2 Potential Influence on Thermo-Mechanical Reliability . . . . . . . . 11
3 Material’s Characterization, Constitutive Theories,
Failure Mechanisms and Lifetime Prediction 13
3.1 Viscoplastic Creep and Failure of Eutectic Tin-Lead Solder . . . . . . . . . 15
3.1.1 Material Behaviour and Constitutive Equations . . . . . . . . . . . 16
3.1.2 Numerical Implementation of Creep . . . . . . . . . . . . . . . . . . 19
3.1.3 Ansys Data File for 63Sn37Pb Solder................. 22
3.1.4 Lifetime Prediction and Failure Mechanisms for Eutectic Tin-Lead
Solder .................................. 22
3.1.5 Thermally Induced low Cycle Solder Fatigue: Reliability Concept
AccordingtoCoffin-Manson...................... 25
3.2 Linear Viscoelasticity for Thermosetting Polymers . . . . . . . . . . . . . . 29
3.2.1 Material Behaviour and Constitutive Equations . . . . . . . . . . . 30
vii
viii CONTENTS
3.2.2 Experimental Results of Relaxation Tests, Exemplified for an Un-
derfill (Silica-filled Epoxy-Resin) . . . . . . . . . . . . . . . . . . . . 34
3.2.3 ComparisontoFrequencyMethod................... 40
3.2.4 Numerical Implementation of Viscoelasticity . . . . . . . . . . . . . 43
3.2.5 Ansys DataFileforUnderfill ..................... 44
3.3 Characterisation of Thermally Conductive Gap Fillers . . . . . . . . . . . . 45
3.3.1 Ansys Data Files for Gap-Fillers . . . . . . . . . . . . . . . . . . . . 46
4 Finite Element Modelling, Consistency Check and
Experimental Design 47
4.1 Universal FE-Modelling: Modular-Parametric Approach . . . . . . . . . . . 48
4.1.1 Philosophy of Parametric Modelling in Ansys: Combination and
MeshingofStandardModules..................... 48
4.1.2 Model for Flip-Chip with Attached Heat-Spreader: Loads, Con-
straintsandSpecialFeatures...................... 51
4.1.3 Averaging Region for Creep Strain . . . . . . . . . . . . . . . . . . 53
4.2 Guidelines for FE-Model Optimization: Influence of Critical Parameters . . 54
4.3 Characteristic Behaviour, Thermal and Mechanical Load . . . . . . . . . . 60
4.3.1 Response of Flip-Chip and Organic Board to external Load: Dis-
placementandDeflection........................ 60
4.3.2 Verification: Displacement and Deflection . . . . . . . . . . . . . . . 66
4.3.3 Calibration of Organic Board Data: Viscoelastic-Isotropic vs Elastic-
Orthotropic ............................... 68
4.3.4 Critical Displacement and Risk of Die Crack . . . . . . . . . . . . . 74
4.3.5 Response of Flip-Chip with Adhesive: Inhibited Curvature . . . . . 77
4.4 Experimental Design and Procedure: The Test-Specimen . . . . . . . . . . 80
4.4.1 Electrical Layout of Chip and Board: Circuitry for the Detection of
BumpFailure .............................. 81
4.4.2 Design and Assembly of the Test-Specimen . . . . . . . . . . . . . . 82
4.4.3 Extraction of Voids under Vacuum . . . . . . . . . . . . . . . . . . 88
5 Results and Discussion – Simulation vs Experiment 91
5.1 The individual Configurations and Applied Loads . . . . . . . . . . . . . . 91
5.1.1 Mechanical Loads and Characteristic Curves . . . . . . . . . . . . . 92
5.1.2 ThermalLoads ............................. 97
5.2 ResultsofComputationalAnalysis ...................... 98
5.2.1 RankingofConfigurations ....................... 100
CONTENTS ix
5.2.2 Correlation of Curvature and Creep Strain . . . . . . . . . . . . . . 106
5.2.3 Structural Distribution of Creep Strain inside Bump-Volume and
ConsequencesforAveraging ...................... 109
5.3 ResultsofExperimentalAnalysis ....................... 110
5.3.1 General Inspection of Specimens After Thermal Cycling . . . . . . 111
5.3.2 Determination of Bump Failure: Correlation Single Bump and Daisy
Chain Resistance and Verification by Metallographic Means . . . . 111
5.3.3 Ranking of Configurations:
Statistical Analysis and Weibull-Distribution . . . . . . . . . . . . . 118
5.3.4 Solder Bump Failure and Effects of Vacuum Treatment . . . . . . . 121
5.3.5 CheckforDelamination ........................ 123
5.4 Comparison of Experimental and Computational Results . . . . . . . . . . 125
5.4.1 Coffin-MansonPlot........................... 125
5.4.2 Effect of Fixation and Influence of Displacement . . . . . . . . . . . 128
5.4.3 Effect of Board-Viscoelasticity and Orthotropism . . . . . . . . . . 130
5.4.4 Check for Thermal Contact in Gap-Filler Groups . . . . . . . . . . 133
5.4.5 DieCrackinFlexibleFoilGroups................... 134
5.4.6 FailureCriterionforDieCrack .................... 136
5.4.7 Extrapolation by Simulation: Variation of Interesting Parameters . 138
5.5 Conclusions,DesignGuidelinesandOutlook................. 140
APPENDIX 146
A Annotations on Theory 146
A.1 ConventionsandNotation ........................... 146
A.1.1 Units................................... 146
A.1.2 MathematicalRepresentation ..................... 146
A.1.3 Abbreviations.............................. 147
A.2 HeatTransfer .................................. 148
A.3 TimeDependenceofViscoelasticModuli................... 148
A.4 Weibull-Distribution .............................. 149
xCONTENTS
B Annotations on Materials 152
B.1 Dimensions of Dog’s-bone Specimen . . . . . . . . . . . . . . . . . . . . . . 152
B.2 OrganicBoard.................................. 152
B.2.1 Measured Viscoelastic Material Data . . . . . . . . . . . . . . . . . 152
B.2.2 Ansys Data File for Viscoelastic-Isotropic Board . . . . . . . . . . . 155
B.2.3 Ansys Data File for Elastic-Orthotropic Board . . . . . . . . . . . . 156
B.2.4 Calibration of Viscoelastic Board Data (Full Account) . . . . . . . . 157
B.3 Soldermask ................................... 161
B.3.1 Ansys DataFileforSoldermask.................... 163
B.4 Epoxy-Silicone Adhesive . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
B.4.1 Ansys Data File for Epoxy-Silicone Adhesive . . . . . . . . . . . . . 166
B.5 Silicone Adhesive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
B.5.1 Ansys Data File for Silicone Adhesive . . . . . . . . . . . . . . . . . 168
B.6 Linear-ElasticandElastic-PlasticMaterials.................. 169
C Annotations on FE-Simulation and Test-Specimen 170
C.1 FE-Models.................................... 170
C.1.1 Abaqus-Ansys Comparison....................... 170
C.1.2 HEX-TET Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
C.1.3 Variation of the Mesh Density Parameter . . . . . . . . . . . . . . . 172
C.1.4 SliceModel ............................... 172
C.1.5 StatorModel .............................. 173
C.1.6 SolderBarrelModel .......................... 173
C.1.7 PolyimideModel ............................ 174
C.1.8 Quarter Model for Verification of Curvature with Adhesive . . . . . 174
C.2 Delamination and Contact-Mode Simulation . . . . . . . . . . . . . . . . . 175
C.2.1 Small Local Delamination at Solder-Chip Interface (Feature of this
special Bump-Shape) . . . . . . . . . . . . . . . . . . . . . . . . . . 175
C.2.2 Large Local Delamination at Underfill-Chip Interface . . . . . . . . 176
C.3 AnnotationsonTest-Specimen......................... 177
C.3.1 Comments on Technological Constraints and Design Alternatives . 177
D Annotations on Results 179
D.1 Failure Analysis According to Single-Bump Measurements . . . . . . . . . 179
D.2 Tabulated Results of Simulation and Experiment . . . . . . . . . . . . . . 180
Bibliography 181
Curriculum Vitae 191
Chapter 1
Introduction
Thereisplentyofroomatthebottom
1.
Richard P. Feynman
And there still is. Indeed, the trend in electronic industry towards higher integration
densities along with structural downsizing is unbroken. As unbroken as the visionary
impact of Moore’s law which predicts that the number of transistors per chip soars by a
hundredfold roughly every decade [3,4]. And again there is much reason for a continuation
of this trend [5] since the requirements of the next generation of products have always
spun off new technologies and been a challenge for future research. Together with a high
circuit density these requirements are nearly olympic: faster, smaller, lighter and above
all, less expensive than today [6]. At the same time power and power density will also go
up demanding effective heat dissipation and high performance thermal management even
at elevated temperatures. This is for example the case in automotive applications, where
electronic devices are to conquer the space close to the engine.
In this respect the packaging concept of flip-chip on organic board hasbeenthefocusof
renewed interest over the last couple of years which seems to meet most of the described
demands [7]: Due to its high pin count and the possibility for area-array layout renders
it eligible for microprocessors or ASICs with smallest dimensions. Shortest possible signal
paths reduce inductance and enhance signal processing. A big advantage is the compatibil-
ity with in-line SMT production equipment and the inexpensiveness of the organic substrate
and the other materials in application. Then, the electrically inactive reverse side of the
chip offers a unique opportunity: It may be used for most effective heat dissipation and
represents therefore a promising basis for thermal management of flip-chip assemblies. As
there is no insulating encapsulant that blocks the heat path a very direct thermal contact
can be established if only a thermally conductive interface material is sandwiched between
chip and heat-spreader. This is how flip-chip reverse side cooling came into being, an in-
teresting concept which is gradually emerging as recent papers show [8–11]. Therefore this
work is concerned with it.
1This was the title of this famous talk [1] which he gave in 1957 on the potential of increasing the
integration density in microelectronics by going down to the atomic scale. Remarkably, he made an
allusion to the two years earlier published and celebrated novel ‘Room at the top’ by John Braine [2]. In
this piece of literature the protagonist is invited to join the upper class of society by the words: ‘There is
plenty of room at the top.’ As usual, Feynman presents himself visionary yet not quite modest.
1
2CHAPTER 1. INTRODUCTION
However, as the above trends persist, thermo-mechanical reliability of microelectronic com-
ponents – its analysis, assessment and prediction – becomes an issue of increasing impor-
tance [12,13]: Thermally induced deformations and stresses constitute the major contribu-
tion to an elevated failure rate and finite service life of modern integrated circuits as they
cause damage to solder interconnects as well as materials and interfaces [13–19].
Flip-chip technology on organic boards has been made possible by the introduction of an
underfill which translates the thermal shear strains into an overall bending of the assembly
thus reducing greatly the deformation of the bumps which represent the critical point of
the flip-chip assembly [20]. Still at some point during its service life the flip-chip assembly
will eventually fail. In this respect solder bump fatigue cracking represents the main
failure mode if no delamination at various decisive interfaces (e.g. chip-underfill) occurs,
a different failure mode which considerably accelerates bump cracking by eliminating the
beneficial effect of the underfill. The occurrence of failure, however, depends crucially
on the combination of mechanical and adhesive properties of the employed materials as
well as the environmental conditions the component is subjected to. These conditions
manifest themselves in thermal and mechanical loads. In this respect also the flipped chip
with attached heat-spreader will be liable to solder fatigue cracking or delamination as a
function of material properties and loading.
For normal, mechanically unconstrained flip-chip assemblies is concerned, its reliability
has been the object of longstanding research work (e.g. [13,21–33]). As far as the flip-chip
assembly with attached heat-spreader is concerned, this experience and information is lack-
ing: Some authors have addressed the excellent thermal performance of this concept [8] or
emphasized the need for reliability assessment [9,10]. Others have carried out preliminary
design studies by Finite Element simulations in conjunction with sporadic tests [11]. How-
ever, its thermo-mechanical reliability as a function of characteristic (but currently still
unspecified) design variables is, although urgently needed, still largely unknown.
To remedy this, the comprehensive study presented in this work is necessary.
The ability to analyze, assess and predict – then possibly minimize the consequences of
thermal stress is of obvious practical interest: The time to market as well as the cost
for development are crucial ingredients for the competitiveness in industry and so it is of
invaluable advantage to know the reliability of a product already at the design stage.
This need for lifetime assessment has sparked off much activity on the field of micro-
electronic packaging and stimulated a rapid and ever increasing application of advanced
thermal and mechanical simulation methods and tools for the theoretical and practical
treatment of thermo-mechanical reliability [34]. As for solder joint reliability assessment,
Finite Element simulations coupled with thermal cycling tests of test-specimens have been
used to analyze their average lifetime in order to make statements of general validity and to
extrapolate the results to new designs and material combinations [35]. Thereby one draws
upon the principle of inelastic phenomena causing the joints or bumps to accumulate dam-
age before they finally crack. A (mostly) scalar, monotonically increasing failure variable
is calculated and correlated to the mean of cycles to failure recorded in the experiment.
Some authors have used the amount of plastic deformation accumulated within one ther-
mal cycle as failure criterion [36,37]. Others have simulated the creep strain [22,26,38,39]
or dissipated energy [23] within the framework of thermally induced low cycle fatigue and
3
used a Coffin-Manson type of approach [40,41]. All do calibrate the bump as the reliability-
sensitive locus of the assembly to function as a ‘reliability sensor’ for given thermal loads
and a specific solder material. This allows an analysis of influence and comparison of dif-
ferent load and material combinations with respect to solder joint reliability and permits
subsequent lifetime prediction [26, 42, 43]. Alternatively some papers also suggest an ap-
proach based on fracture mechanical means [44–46]. Such a method, although in principle
more universal, was not considered as crack analysis in solder materials requires not only
sophisticated computational methods to allow for the physically correct evaluation of creep
crack growth under periodic loading [47,48], but also experimental investigations concern-
ing the temperature- and rate-dependent fracture toughness, both of which are beyond the
scope of this work.
Under the given service conditions (high homologous temperatures) all inelastic deforma-
tion is essentially creep deformation. Creep induced damage represents the main failure
mechanism of the bump in this regime which makes the creep strain-based approach es-
pecially suitable. Therefore it is preferred over the others and used in this work to de-
scribe low cycle fatigue of eutectic tin-lead solder bumps. Hereby the highly nonlinear and
temperature-dependent response of the material is accurately taken into account.
With the introduction of reverse side cooling the flip-chip assembly is exposed to mechanical
loads and boundary conditions [49] which do influence its lifetime. It is therefore the
objective of this work to analyze, assess and predict the thermo-mechanical reliability of
flip-chip on organic board as a function of the mechanical loads, which are induced by the
attachment of a heat-spreader, under periodic thermal loading.
Different thermal interface materials (sandwiched for efficient heat transfer between chip
and heat-spreader) may significantly alter the state of bending counteracting the beneficial
effect of the underfill [11]. What geometrical and mechanical properties can therefore
be derived for the best thermal interface material? What consequences do the fixations,
deformations and forces the assembly is subjected to bring along for solder bump reliability?
What part does the board’s thickness and inner structure play in the assembly? Which
are other influential factors determining the lifetime of a flip-chip assembly with heat-
spreaders and what are resulting design rules to optimize this package concept with respect
to thermo-mechanical reliability?
These are some of the interesting questions which are to be answered by this work. To
do this, we draw upon a universal, parametric and modular concept of finite element
model generation to handle the large required parameter variations. Thereby the model is
automatically created by a combination of standard modules (e.g. the chip or the bump)
according to previously specified parameters. In parallel performed thermal cycling tests
are used to verify the simulatively obtained results for eutectic tin-lead solder bumps.
As flip-chip reverse side cooling represents a new concept, we start with a brief survey
concerning the boundary conditions brought along with its technical realization.
Chapter 2
Flip-Chip Assemblies under Thermal
and Mechanical Load:
Motivation & Conception
As the technical realization of flip-chip reverse side cooling entails a new state of loading,
a qualitative overview is given concerning the loads and boundary conditions the chip is
subjected to and how it responds to them on a macroscopic level (chip) and how this might
affect solder joint reliability (microscopic level).
2.1 Thermal Management of Flip-Chip Assemblies for
Higher Power Applications
As the trend in the electronic industry to draw towards a higher packaging density is
unbroken and the interest in higher power applications persists one faces the problem of
ever increasing power dissipation in electronic circuits.
In the automotive sector this situation is aggravated by a decrease in headroom up to the
maximally allowed junction temperature (Tmax = 125 oC): Here demands of environmental
temperatures as high as Tenv =85oChave to be met since electronic devices are to conquer
the space close to the engine. So the question of high-performance thermal management
of flip-chips that allows such a small temperature delta arises.
For an illustration of the requirements1of the thermal management for flip-chip assemblies
let us take an average power dissipation of PT=10Wwhich is the interesting order of
magnitude for a power transistor module, an ambient temperature of Tenv =85oCand a
maximum temperature of Tmax = 125 oC.
This results in a temperature delta of ∆T=40Kwhich can be used for heat transfer.
This imposes that the system features a heat path with a total thermal resistance of
RT=∆T
PT
(2.1)
1Specifications by Robert Bosch GmbH, Germany.
4
2.1. THERMAL MANAGEMENT OF FLIP-CHIP ASSEMBLIES 5
which has to be lower than RT=4K/W. This condition will be the knock-out criterion
for eligibility.
I
II
III Heat-Spreader
Thermal Interface
Chip
Underfill
Soldermask
Board
Solder Bump
Figure 2.1. The three ways of cooling a flipped chip. The arrows are to indicate the heat
path. From top to bottom the layers represent heat-spreader (casing), thermal interface
(e.g. adhesive), chip, underfill, soldermask, board,(adhesive and casing again). These dif-
ferent ways of cooling entail new boundary conditions which may affect the reliability of
solder bumps (blue frame). A beginning fatigue crack causing bump failure is indicated.
Some methods of cooling a flip-chip assembly are presented in the following. Their re-
spective heat paths are illustrated in figure 2.1 and their thermal performance compiled
in table 2.1. The values are taken from a computationally verified experimental study [50]
carried out on a 20 mm2chip.
•Cooling by Natural Convection:
This is the situation where no heat-spreader is attached in any way to the chip. This
is the easiest way of cooling. The heat is spread by convection and radiation (smaller
part in this temperature-range). Referring to the thermal resistance evaluated in
table 2.1 below this way is by far not sufficient to rise up to our needs for larger power
dissipation. It may be used for powers up to PT=0.5Wunder the given conditions.
The reason for this is the low thermal conductivity of the organic substrate and
underfill (lower by at least one order of magnitude with respect to thermal interface
materials).
A reduction in thermal resistance may be achieved by enlarging the surface of the
copper fan-out which can then act as a heat spreader, since the solder bumps function
as heat conducting element in this extended heat path. Still RTstays above of what
is needed quite apart from the fact that this measure requires valuable space.
However, the thermal performance of methods relying on natural convection inside
the housing is limited, as no direct thermal contact to the housing is provided. A
heat-spreader inside the housing is not of much use unless there is some additional
ventilation or fan.
6CHAPTER 2. FLIP-CHIP ASSEMBLIES & THERMO-MECHANICAL LOAD
•Cooling Through the Board:
This is the time-honoured way of cooling a flip-chip for situations where higher power
is needed. Here, thermal vias are used to transfer the heat through the board to the
heat-spreader, i.e. the housing, on which the board has to be glued to establish
thermal contact. But as can be seen again from table 2.1 it still does not fulfill
our expectations. The thermal resistance of the heat path is still too large even
if the thermal connection to the heat spreader is improved by thermal vias within
the board [50]. This is due to the low thermal conductivity of the intermediate
layers (particularly the organic board) and the limited number of (thermal) bumps
especially for smaller chips.
•Cooling via the Reverse Side:
In this case the – electrically inactive – reverse side of the flip-chip is used for heat
transfer to a heat spreader which should for thermal and practical reasons be a part
of the housing of the device. Silicon has a comparatively large thermal conductivity
λT= 149 W/mK which assures low thermal resistance by the die itself. In order to
assure perfect thermal contact an interface material (gap filler or adhesive) is put
between the chip and the heat spreader.
Flip Chip Cooling Possibilities
Method and Heat Path # RT[K/W]
FC →Convection →Housing I >70
FC Front Side →Board + Thermal Vias →Housing II >10
FC Reverse Side →Thermal Interface →Housing III <4
Table 2.1. Thermal performance of the three presented methods for cooling a flip-chip
assembly. These values are obtained by experimental test using a chip of area Achip =
20 mm2and were verified computationally [50].
Of these three methods only the last one – flip-chip reverse side cooling – is eligible for high
power applications due to its outstandingly low thermal resistance. Ways have to be found
to facilitate an attachment of the reverse side of the flip-chip to an heat spreader assuring
optimum permanent thermal contact, but also maximum thermo-mechanical reliability.
The thermal performance of the methods presented in the following has very recently been
evaluated by [8] and was found to be exceptional. Thermo-mechanical reliability will be in
thefocalpointofthiswork.
2.1.1 Maximum Thermal Performance: Flip-Chip Reverse Side
Cooling
Working on what has been stated in the last paragraph, we want to look on the flip-chip
reverse side cooling (FC&RSC) in more detail. The principle behind is again depicted in
2.1. THERMAL MANAGEMENT OF FLIP-CHIP ASSEMBLIES 7
figure 2.2. In order to realise the required low thermal resistance technologically one has
to look for the shortest heat path and combine good thermal contact at the surfaces with
thermal interface materials which display a high thermal conductivity. So we go back to
equation 2.1 and rewrite it for insertion of material properties (refer to A.2):
RT=∆T
PT
=1
λT
b
AT
, (2.2)
where bis the thickness of the thermal interface layer, λTits thermal conductivity and AT
the effective or thermally active surface. The latter has been introduced to point out that
there might be ’hot spots’ on the chip (areas which mainly dissipate heat, e.g. a power
transistor) and would thus reduce the active surface. Therefore in general AT<A
chip
should be assumed2, at least this point should be considered when it comes to making
the layout for a specific cooling set-up. (For the following considerations we have set
AT=1
5Achip, which corresponds to the assumptions in [50].)
Thermal
Interface
Housing =
Heat Spreader
Flip-Chip
Heat Path
5 mm
2 cm
Figure 2.2. Principle of flip-chip reverse side cooling: The heat path is symbolized by
arrows as it starts at the flip-chip via a thermal interface medium (gap filler or adhesive)
before it is spread by the housing itself which serves as a heat-sink. The pads around the
chip (white square) demonstrate the area reduction due to flip-chip mounted devices with
respect to electrically equivalent but encapsulated components (e.g. QFP).
Taking into account our upper limit of RT=4K/W (the housing itself is assumed to
be an ideal heat spreader), one may realize reverse side cooling using interface materials
which are commercially available. Thereby, the maximum thickness of the gap is obviously
2It has indeed been shown by thermal simulation [50] that one may severely underestimate the thermal
resistance in such a case. Still the latter depends greatly on λTwhich, when chosen large enough, will in
return result in a more uniform temperature distribution over the chip.
8CHAPTER 2. FLIP-CHIP ASSEMBLIES & THERMO-MECHANICAL LOAD
dependent on the thermal conductivity of the material. Some representative examples are
given in table 2.2. These are also the materials we carry out our studies on in this work.
Therefore, a code letter for future reference is introduced already at this point.
Other criteria for the eligibility3of the materials were on one hand applicability and com-
patibility with production line assembly processes, availability on the market and possibly
an already existing long-term experience with the material. On the other hand they should
be representative examples of their group of materials in order to yield results which may
be extrapolated to similar materials. For a computational treatment they must be charac-
terisable in their physical properties for Finite Element implementation.
Thermal Properties of Interface Materials
Thermal Interface Material Code λT[W/mK]Gapb[µm]
Epoxy-Silicone Adhesive with Silver Flakes E 4.0 320
Silicone Adhesive with Aluminium Oxide Particles S 0.9 72
Carbon Foil C 7.0⊥140.0 560
Gap filler, Silicone with Boron Nitride Particles F 5.0 400
Table 2.2. Examples of typical high performance materials eligible for cooling a flip-chip
assembly. The values are taken from the respective data sheets. AT=20mm2is used for
evaluating the maximum gap for the thermal interface layer. The code letter is introduced
for easy reference throughout this work. The carbon foil displays an anisotropy in the
thermal conductivity.
The given materials do meet all these prerequisites. They are commercially available
interface materials and were tested in their thermal performance for flip-chip reverse side
cooling by [8]. They feature the following properties and can be divided into:
•Gap fillers
Gap fillers (flexible mats or foils) which are usually made of elastomeric binder
(e.g. silicone moulding resin) in compound with a ceramic filler. Generally the ma-
trix material is reinforced by some sort of fibre-tissue. Filler particles employed
are aluminium oxide as well as boron nitride for their high thermal conductivity
λT=1...5W/mK (data sheets). Various thicknesses are available, usually in multi-
ples of 250 µm.
An other material apt for this purpose is carbon foil which displays a very high
thermal (orthotropic) conductivity (see table 2.2). This material has a wax coating
to assure perfect gap closure and thermal contact.
The pros and cons of gap fillers are the fact that no additional curing process is
needed. But on the other hand they require special handling and are not inexpensive.
The thermal conductivity is in general a function of the applied pressure on the
medium. Hereby, a minimum pressure for reliable thermal contact is usually specified
3Specifications by Robert Bosch GmbH, Germany.
2.1. THERMAL MANAGEMENT OF FLIP-CHIP ASSEMBLIES 9
by the manufacturer and lies around pN=0.1MPa for high performance materi-
als. This pressure is needed to make the material conform to surface irregularities
eliminating air gaps.
•Thermal adhesives
Thermal adhesives are based on silicone, epoxy or co-polymeric matrix material and
use besides the above mentioned filler materials also silver flakes as good thermal
conductor. Thermal conductivities are comparable to those reached by gap fillers.
Their advantage is easy application by dispensing. The disadvantage is an additional
curing process which may interfere with the remaining assembly of the device. The
surfaces may need an extra (chemical) treatment to promote adhesion. An applied
pressure is not needed as the adhesive fills potential cavities during dispensing.
2.1.2 New Boundary Conditions Through Reverse Side Cooling
Flip-chip reverse side cooling is the only promising way for high power applications, relying
on standard SMT processes. Yet it brings along new, system-inherent boundary conditions.
For reasons of reliable heat dissipation (thermal reliability) it is essential that the maximum
gap width once determined is never exceeded despite all other tolerances there might be.
This fundamental requirement entails the consequence, that the gap is to be kept close
and its width to be held constant. This can only be ensured by applying a pressure to the
thermal interface.
On imagining the situation in a electronic device one is faced with material imperfections
and manufacturing tolerances which are, although specified, to be compensated for. As
a rough guide to the magnitude in question serves the following contemplation: Typical
tolerances to be taken into account are due to the die itself (±10 µm), the contact (or
bump) height (±20 µm) and the housing (±200 µm), yielding in sum an overall tolerance
of (±230 µm) to make up for.
We want to tackle this problem by bending the board from below by applying a pressure
on a point just below the chip to obtain a displacement which moves the chip so close to
the housing that the specification for the gap is met. This situation is depicted in figure
2.3.
For the case of a gap filler (non-adhesive) this means that this pressure has to ensure
permanent closure of the gap during operation, at the same time keeping up the minimum
force needed to compress the interface material.
This force, in conjunction with geometric boundary conditions such as a local fixation of
the board or a neighbouring component of great stiffness, will subject the flip-chip assembly
to deformation and thus induce an alteration in the state of stress and strain as a function
of temperature.
10 CHAPTER 2. FLIP-CHIP ASSEMBLIES & THERMO-MECHANICAL LOAD
Heat
Path
Board
Thermal
Interface
Force
Flip-
Chip
Housing
= Heat-Spreader
Test-
Region
Fixation
Figure 2.3. Schematic of flip-chip reverse side cooling (‘exploded’ view). Each flip-chip
is pressed against the housing from below the board (black arrows). Thermal contact of the
chips’ reverse side (see red arrows for heat path) can be established to parts of the housing
which are shaped to reach down to the site of the chip and are tipped with a thermally
conductive interface material. The board is fixed at its edges.
2.2 Thermo-Mechanical Reliability Issues of Flip-Chip
Reverse Side Cooling
It is expected that these mechanical loads applied to the flip-chip assembly to facilitate
reverse side cooling do have an influence on its thermo-mechanical reliability with respect
to solder bump failure.
For this reason it will be the task of this work to examine the reliability of the chip under
these novel boundary conditions.
As an approach we want to shed some light on the characteristic qualitative behaviour of
the flip-chip assembly which gives rise to interesting guiding questions and consequences
which will have to be taken into account in the course of this work.
2.2.1 Model Assumptions and Qualitative Considerations
As seen from figure 2.3 we deal with a very complex set-up indeed. But for reasons of
universality of the conclusions we seek concerning flip-chip reliability it is not advisable
to put the whole of such a device to a test, quite apart from the fact that it is beyond
2.2. THERMO-MECHANICAL RELIABILITY ISSUES 11
our means to carry out a corresponding finite element simulation with today’s computers.
So we want to see what constraints are active at the local site of the flip-chip (blue frame
in the quoted figure labelled ‘test-region’), extract the characteristic variables suitable to
describe its behaviour and to condense this situation into a model where the boundary
conditions or loads can be applied and controlled.
F
d
k
Nf
Test-Region
Thermal InterfaceBump
Fixation
b
Board
Figure 2.4. Schematic of test-region for reliability study as stated in figure 2.3. From
there typical loads and boundary conditions must be extracted and controllably applied to
the chip. Depicted is the force Fand the displacement d(with fixation) which may cause,
in conjunction with the properties of the thermal interface and the board thickness b,a
change in the deflection kof the constrained chip and hence influence the reliability Nf
(cycles to failure) of the solder bump.
A set-up well-suited for this purpose is sketched in figure 2.4. An adjustable displacement
dallows to mimic the gap caused by the manufacturing tolerances and a force Fbridges
it by bending the assembly. A rigid or sliding joint (fixation) between plate and board (at
the point of the arrows) can also be considered to mimic the boundary conditions of the
real casing.
The chip, although attached or pressed to an adhesive or gap filler, may alter its state
of bending together with the curvature of the whole assembly. A suitable parameter to
describe this response is a curvature or deflection kof the silicon die. This macroscopic
response may in return have an influence on solder bump reliability which is given by Nf,
the (mean) number of cycles to failure.
2.2.2 Potential Influence on Thermo-Mechanical Reliability
The whole of flip-chip technology on organic board relies on the function of the underfill,
which stiffens the assembly to a degree where it is able to translates the thermally induced
shear strains in the underfill and soldermask into an overall bending of the assembly.
These strains are caused by the mismatch in the CTEs of chip and board as a function of
temperature. Chip and board are the materials which govern this behaviour. So already
at room temperature the chip is in a state of thermally-induced curvature.
12 CHAPTER 2. FLIP-CHIP ASSEMBLIES & THERMO-MECHANICAL LOAD
It has been shown [20, 51] that flip-chip on organic board is not viable without underfill.
For instance, this problem of severe global mismatch does not arise for ceramic substrates
which have a CTE similar to silicon.
So the state of bending is beneficial for the flip-chip assembly and its degree of bending, its
curvature, seems to have a correlation to the lifetime of the bumps as this has repercussions
on the strains the bump will have to comply to [52]. To illustrate this: If no underfill is
used the assembly does not bend under thermal load and the shear strains thus induced
do cause the bumps to fail during a few thermal cycles [53].
Since the ability to curve seems the assembly’s decisive macroscopic behaviour the ques-
tion arises if and to what degree bump reliability may be influenced if this curvature is
altered or constrained by mechanical loads, i.e. an externally applied force. The initial,
thermally induced curvature may be superposed by a mechanical one. In addition to this,
the boundary conditions or fixation may change this response.
Moreover, different kinds of thermal interface materials represent different kinds of con-
straint to the chip and may entail various types and degrees of bending as a function of
temperature.
We may ask further if the reliability may even be enhanced by a particular type of bending.
If the intrinsic concave bending of the flip-chip assembly is vital for its thermo-mechanical
reliability, a further (mechanical) drive promoting this tendency could prolong bump life-
time. Or what is the effect of convex bending which counteracts the intrinsic mode of
bending but could also be a viable technological variant?
For a coupled numerical and experimental approach as we envisage it here the following
topics have to be covered:
•The materials of interest for this assembly have to be characterized concerning their
material properties and made available for Finite Element (FE) input.
•An appropriate failure criterion is to be implemented.
•A FE model is to be created and calibrated to design, simulate and optimize a test-
specimen for numerical evaluation of solder bump reliability.
•The test-specimen has to be constructed and built to undergo a thermal cycling test
for experimental verification of solder bump reliability.
These are key issues for this work. They will be treated quantitatively in the next chapters.
Chapter 3
Material’s Characterization,
Constitutive Theories,
Failure Mechanisms and Lifetime
Prediction
In this chapter we determine the mechanical properties of the materials that make up the
flip-chip assembly with reverse side cooling (see table 3.1) for subsequent Finite Element
implementation. These materials belong to different groups (polymers, alloys, metals,
compound materials) and display, apart form linear elastic material behaviour also non-
linearities and a high temperature- and rate-dependence (elasto-plasticity, viscoelasticity
and viscoplasticity).
We begin with eutectic tin-lead solder and describe its mechanical behaviour and failure
mechanism based on the assumptions of low cycle fatigue (due to large, periodic inelastic
deformation, here: induced by thermal mismatch) at high homologous temperatures. In
this regime creep represents the main failure mechanism of the bump and is evaluated as
failure criterion used for lifetime prediction. As the solder bump constitutes the reliability-
sensitive part of the flip-chip assembly, the correct representation by a viscoplastic law is of
crucial importance: Here we draw upon data from literature [26,43] of strong experimental
support. The respective constitutive equations are discussed and numerically implemented.
Finally, the theoretical framework of lifetime prediction within the Coffin-Manson approach
is motivated and demonstrated.
The second class of important materials comprises polymers. Underfill, thermal adhesives,
organic board do fall among this rubric. They are characterised with respect to their vis-
coelastic properties and the recorded data is subsequently implemented via the respective
constitutive laws. Various measurement techniques are employed to accurately characterise
these materials in the time and temperature domain. These comprise dynamic mechanical
analysis (DMA), thermo-mechanical analysis (TMA), rheometric measurements, tension
and relaxation testing [54].
For the (elastic) characterization of the gap-fillers one has to resort to another experimental
method. Fortunately, material data was provided by the manufacturer, the elastic modulus
couldbemeasuredincompression.
13
14 CHAPTER 3. MATERIALS & THEORY
As far as elasto-plastic material data of metals is concerned we did rely on values taken
from literature on the subject [55].
For the solder and polymers used here it is shown how the material data is made available
for the numerical simulations. In the course of this process the material laws or constitutive
equations were implemented as user-programmable features as Fortran subroutines and
linked to the respective simulation tool. This procedure was necessary since the required
material laws were not available as standard function. The employed algorithms fit the
experimental data very well in Ansys and Abaqus, which were the FE-tools1in use. For
standard material routines we refer to the respective theory manuals for details [56], [57].
To assure readability of this chapter we proceed as follows: Measured data is given as
Ansys input format. This tabular form and nomenclature is explained the first time it
appears for a specific group of materials. Eutectic solder, underfill and gap-filler data is
given at the end of the respective section, whereas all remaining measured data can be
found in the appendix B as also listed in table 3.1.
Table of Employed Materials
Material Behaviour Constitutive Law Application Section
Eutectic SnPb Solder vp Secondary Creep Bump 3.1
Filled Epoxy Resin ve Temperature-time shift Underfill 3.2
Fibre-Epoxy Resin ve Temperature-time shift Board B.2
Epoxy Resin ve Temperature-time shift Soldermask B.3
Epoxy-Silicone ve Temperature-time shift Adhesive B.4
Steel el-pl BISO Fixations B.6
Copper el-pl BISO Traces B.6
Aluminium el-pl BISO Plate B.6
Nickel el-pl BISO UBM B.6
Silicon el Linear Chip B.6
Silicone el Linear Adhesive B.5
Carbon el Linear Gap filler 3.3
Flex-Foil el Linear Gap filler 3.3
Table 3.1. The abbreviations stand for: el-elastic, pl-plastic, vp-viscoplastic, ve-
viscoelastic, BISO-bilinear isotropic hardening. The last column references the section
where the material data (specified for Ansys input) can be found.
The testing conditions of thermal cycling comprise a temperature interval of T∈[−40; 125] oC,
but simulation requires the knowledge of material behaviour up to the highest tempera-
ture encountered in the assembly process, which is the curing temperature T
c= 160 oCof
underfill and thermal adhesive. Therefore the materials had to be characterised within a
temperature range of T∈[−40; 160] oC.
1Ansys, Release 5.7andAbaqus, Release 5.8.
3.1. VISCOPLASTIC CREEP & FAILURE OF EUTECTIC TIN-LEAD SOLDER 15
3.1 Viscoplastic Creep and Failure of Eutectic Tin-
Lead Solder
Viscoplasticity means, that a material starts to flow from a certain stress level on and
deforms irreversibly over time as a function of stress and temperature. The material is also
said to creep for a constant stress experiment. Viscoplasticity is a relevant factor only at
high homologous temperatures, i.e. for T>1/2Tm,whereTmis the melting temperature
on an absolute temperature scale. As eutectic tin-lead solder melts at Tm= 456 K,itis
justified to assume creep as governing mechanism for the deformation behaviour even at
the bottom end of our temperature interval of interest (T>233 K).
Rupture
Primary
Creep
Secondary
Creep
Tertiary
Creep
Creep Strain [arb.u.]
Time [a.u.]
0.1110100
1E-7
1E-5
1E-3
0.1
1
n
IV
III
II
I
Creep Strain Rate [1/s]
Stress [MPa]
Figure 3.1. Left: Creep types typical for alloys at high homologous temperatures. Right:
The stress dependence of the steady-state creep rate for eutectic tin-lead solder can be
divided into four regions [43]. The slope of the graph corresponds to the stress exponent n.
A typical creep curve as depicted in figure 3.1 shows the essential features. Three regimes
of the creep process may be distinguished [58]:
•Primary creep: Under constant load the material undergoes first a transient phase
of creep. It is a dominant part for low homologous temperatures.
•Secondary or steady-state creep: The creep strain rate and microstructure is constant
over time in this regime.
•Tertiary creep: This regime precedes fatal failure of the material due to rupture.
For small strains we can assume an additive decomposition of strain:
εij(t)=εel
ij(t)+εpl
ij(t)+εcr
ij (t)+εT
ij(t)δij, (3.1)
where the total strain tensor is composed of an elastic, a (rate-independent) plastic, a
creep contribution and the thermal strain. The Kronecker-delta reflects the fact that
16 CHAPTER 3. MATERIALS & THEORY
thermal strains have no shear components. Under the given environmental (and hence
testing) conditions the elastic2and time-independent plastic part may be neglected3:This
is justified due to slowly varying loading or drive (as given for low cycle fatigue and service
conditions on the automotive sector [15]). For the same reason we can assume that we
only deal with steady-state creep for eutectic solder under the envisaged testing conditions.
Primary – or transient – creep may be neglected and the high stress regime is not touched
either. It may be assumed that the deformations are, to a good approximation, completely
converted into steady-state creep strain [60]. As can be inferred from figure 3.1 (right) no
yield criterion exists as in conventional plasticity, the material starts to creep as soon as
there is a minor force.
3.1.1 Material Behaviour and Constitutive Equations
The steady state creep regime which is reached when the material has passed through a
phase of transient creep is characterised by a constant creep rate:
˙εij(t)=const. ord2
tεij(t)=0. (3.2)
The steady-state creep rate ˙εij(t) is a strong and highly nonlinear function of stress and
temperature and displays furthermore a dependence on microstructure χ, i.e. phase size
[44,60]. It is, to a first order approximation, assumed not to depend on time [15,43]. This
involves necessarily a dynamic stability in ˙εand χ. Therefore one may write:
˙εij =˙εij(σij,T,χ), (3.3)
where σij and χdenote the stress-tensor and the microstructure respectively. In general, the
microstructure will be itself a function of the load-history and the creep rate, i.e. there is an
interdependence which would eventually entail a self-consistent relationship for evaluation.
χ=χ(˙εij,ε
ij,σ
ij,T,χ
0), (3.4)
Since we do not intend to evaluate the creep strain self-consistently, we merely assume that
the effect of χcan be sufficiently described by the phase size dwhichisthenintroducedasa
structural parameter characteristic for a specific microstructure. This will have to manifest
itself in the respective constitutive equations which have to consider phenomenology and
physical mechanisms.
Steady state creep can be divided into four different creep phases as a function of stress
which are determined each by a different creep mechanism as seen in figure 3.1 to the right
after [43]. All of these mechanisms are assumed to be diffusion controlled due to high
homologous temperatures. Therefore the shear creep strain rate ˙εxy canbeexpressedbya
Weertman-Dorn’s type of equation as a function of shear stress σxy:
˙εxy ∼GbD
kT σxy
Gnb
dp
, (3.5)
2still for FE-input the Elastic modulus need to be measured. This is accomplished with a high-frequency
method or by determining the sound-velocity in the material according to cs∼√E[59].
3It may be argue that the decomposition into plastic and creep strain is artificial anyway. All plastic
deformation is essentially time-dependent, but this dependence is a strong function of temperature which
overcomes the activation energy of rate-dependent mechanisms [43].
3.1. VISCOPLASTIC CREEP & FAILURE OF EUTECTIC TIN-LEAD SOLDER 17
where Gis the shear modulus, bthe absolute value of the Burger’s vector describing
the magnitude of the dislocation orthogonal to a slip-plane and D=D0e−Q/kT is the
temperature-dependent diffusion coefficient for the creep mechanism in question, Qthe
activation energy for the respective thermally activated diffusion process or mechanism
that is rate-controlling, kis Boltzmann’s constant. Further, ndenotes the stress exponent
and pthe grain size exponent, d– originally the grain size – is here to be understood as
interphase spacing according to [43].
These four regions can then be distinguished by different mechanisms, which means stress
exponents, activation energies and microstructural parameters. Hereby the first (I) and
second (II) are based on grain boundary sliding (superplastic deformation at the phase
boundaries) whereas the third (III) features matrix power-law creep (plastic deformation
within the phases) and region (IV) is characterised by a breakdown of the power-law and
could be based on mechanisms like obstacle-controlled glide.
It has been proposed [61], that for eutectic tin-lead solder the creep strain can be described
by two, separately but additively acting mechanisms in the stress domain of interest in
electronic packaging for automotive applications:
˙ε=˙εII +˙εIII . (3.6)
Hereby region (II) is dominated by grain boundary sliding and features a dependence on
microstructure (here characterised by the interphase spacing d), whereas region (III) proves
independent of d. The following constitutive equation is thus formulated, which is based
on strong experimental support by thermo-mechanically driven shear tests carried out on
eutectic solder bumps [43]. It was verified e.g. in tension tests on bulk specimens [26] and for
flip-chip bumps [42] using micro-deformation analysis by gray-scale correlation4[24,62,63]
in combination with FE-analysis. So it can be assured that the measured creep strain in a
bump can indeed be accurately described by this equation. In uniaxial form
˙
¯ε=1
√3
AII
T
1
dp¯σ
√3n
II
exp −QII
kT +1
√3
AIII
T¯σ
√3n
III
exp −QIII
kT . (3.7)
The constants assume the following values after [43] and are compiled in table 3.2.
It should be noted that this equation was originally derived from a fit to experimental data
recorded in shear. For conversion to applicability to tensile (uniaxial) data shear stress and
shear strain have to be replaced by the corresponding equivalent entities ¯σand ¯ε.Thisis
a straightforward calculation5and produces
¯ε=2
√3εxy and ¯σ=√3σxy. (3.8)
In figure 3.2 the simulated creep strain rate is plotted versus the stress in equivalent entities.
Obvious is the extreme nonlinear temperature and stress dependence over many orders of
magnitude. For a correlation to the measured data see [26].
What enters here is the influence of the phase size which should only influence grain
boundary sliding. It was found [43] that when the average phase size in the solder bump
4MicroDAC TM
5Use equations 3.13 and 3.11 taking ν=0.5
18 CHAPTER 3. MATERIALS & THEORY
was considered the postulated relationship (3.5) could indeed be verified although ddoes
not represent a mechanistically correct grain size, but is surely a measure – as long as
it is meaningfully measurable – of solder coarsening. Coarsening in solder alloys occurs
during thermal and mechanical processes towards an energetically more favourable state
of minimised overall surface of the phases [64], since as-cast solder is not in a state of
equilibrium. A coarser microstructure favours deformation due to matrix creep rather
than through grain boundary sliding. So as coarsening proceeds, matrix creep will become
more and more dominating. As a result of this, the creep rate goes down for given values
of stress and temperature, the solder hardens.
Parameters for Creep Law
Parameter Meaning Value
AII Fit constant 1.39 ·10−6
AIII Fit constant 2.38 ·103
nII Stress exponent Grain Boundary Sliding 1.96
nIII Stress exponent Matrix Creep 7.10
QII Activation Energy Grain Boundary Sliding 0.50 eV
QIII Activation Energy Matrix Creep 0.84 eV
kBoltzmann’s constant 8.61 10−5eV/K
dPhase size 2.4µm
pPhasesizeexponent 1.8
Table 3.2. The corresponding elastic properties are given in section 3.1.2 as Ansys input
file.
As has already been mentioned, the microstructure is itself a function of temperature and
creep strain (rate) in a self-consistent relationship. Therefore the grain size of a stable and
periodic cycle depends on the cycle itself, that is T(t) being ramped up and down and held
constant in between. The coarser initial phase size of d=2.4µm was achieved for a cycle
close to the one used in this work. Therefore this value of phase size will be chosen as
stable value for the phase size. This value is larger than for ’as cast’ solder d≈1µm [60],
but microstructure is extremely sensitive to cooling and solidification conditions [44] quite
apart from the fact that it is not homogeneous [60], off-eutectic [65] close to intermetallics
due to depletion, different from bump to bump [64] and difficult to measure as coarsening
goes on. So discrepancies concerning measurement results [38, 66] might be due to the
strong dependence of creep on the microstructure [15].
Due to these difficulties dis usually taken constant and characteristic for a steady-state
creep phase. Then equations (cf. ˙ε(d)↔d(˙ε)) 3.3 and 3.4 need not be solved self-
consistently. Still, work in this direction is being done but not at a stage where it would
furnish conclusive results ( [67] take into account a gradual change in creep mechanism
(II)→(III) with the numbers of cycles).
When the constitutive equation is implemented in an FE-tool and a tension test is simulated
for a consistency check, typical stress-strain curves are obtained as in figure 3.3. This type
of more familiar graphical representation shows that the creep law is indeed correctly
3.1. VISCOPLASTIC CREEP & FAILURE OF EUTECTIC TIN-LEAD SOLDER 19
110100
1E-10
1E-9
1E-8
1E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
100
1000
T = 125 ˚C, d = 2.4 µm
T = 20 ˚C, d = 2.4 µm
T = - 40 ˚C, d = 2.4 µm
T = 125 ˚C, d = 1.0 µm
Equivalent Creep Strain Rate [1/s]
Equivalent Stress [MPa]
Figure 3.2. Constitutive behaviour of eutectic tin-lead solder according to equation 3.7,
[43]. A smaller phase size (dashed line) favours region (II) creep (grain boundary sliding)
at low stresses. The result would be a higher creep rate.
implemented as the values of stress are reproduced in accordance with those of figure 3.2
for a given value of Tand ˙
¯εcr.
Sometimes constitutive equations for solder are proposed which use a hyperbolic sine de-
pendence on stress for the creep strain rate [68,69] according to:
˙
¯ε∼1
Tsinh ¯σ
cn
exp −Q
kT . (3.9)
A law of this type does hence not reflect the physical effect of grain boundary sliding in
the sense of a constitutive equation6(as nis not a stress exponent in the actual sense of
the term) and may therefore underestimate this contribution for small (thus effective or
averaged) phase sizes. It is not considered any further in this work for this reason.
In general lifetime prediction is extremely sensitive to correct representation of the mate-
rial’s response by a creep law. In this respect especially the determination of the correct
stress exponent is very demanding [70], whereas there is less argument about activation
energies of the corresponding diffusion processes.
3.1.2 Numerical Implementation of Creep
For both FE-tools (Ansys and Abaqus) the use of the presented creep law signified a non-
standard use and required an extra compilation, linking and testing procedure of a Fortran
6Based on the constitution of a material and the physical processes which determine its response.
20 CHAPTER 3. MATERIALS & THEORY
0.0000.0020.0040.0060.0080.010
0
10
20
30
40
50
60
70
v = 10
-3
1/s
v = 10
-4
1/s
v = 10
-5
1/s
v = 10
-6
1/s
T=20˚C
Equivalent Stress [MPa]
Equivalent Creep Strain
Figure 3.3. Test: Familiar stress-strain curves for eutectic tin-lead solder as calculated
by an Ansys-implemented Fortran subroutine for a solder-bar in tension, i.e. ¯ε=εzz and
v≡˙εtot
zz .
subroutine. It is instructive to see how creep is treated numerically:
Numerical implementation of the constitutive equation given in the last section follows an
incremental flow rule scheme [56,57]. Therefore, the equations need to be transformed for
equivalent entities first. This enables a simple description of a complex 3D stress state,
not just the well-defined (shear-) stress and strain set up in the experiment. Here, the von
Mises equivalent stress (and strain) is used: It is well suited for the description of plastic
deformation as it characterises the deviation from the hydrostatic state which does involve
hardly any plasticity. As it is evaluated based on the second invariant of the deviatoric
part of the respective tensor it does not depend on the coordinate system. The directional
dependence of the creep strain is subsequently added as the material is assumed to flow
into the direction of the strongest gradient.
The equivalent stress is defined by (see e.g. [58,71]):
¯σ=3
2sijsij1
2
(3.10)
=1
√2(σxx −σyy)2+(σyy −σzz)2+(σxx −σzz)2+6(σ2
xy +σ2
yz +σ2
xz)1
2,
where the inner product extends over sij, the stress deviator given by
sij =σij −1
3σkkδij, (3.11)
where the Kroneker-delta and Einstein’s convention (A.1) has been used.
3.1. VISCOPLASTIC CREEP & FAILURE OF EUTECTIC TIN-LEAD SOLDER 21
Analogously an equivalent strain can be defined:
¯ε=3
2
1
1+ν2
3eijeij1
2
(3.12)
=√2
2(1 + ν)(εxx −εyy)2+(εyy −εzz)2+(εxx −εzz)2+6(ε2
xy +ε2
yz +ε2
xz)1
2.
Here again eij is the strain-deviator calculated in the same vein as in equation 3.11, only
that εij takes the place of σij. The mean volumetric strain is hereby em=1
3εkk.νis
Poisson’s ratio, which for creep strain evaluation is usually set equal to ν=0.5 as creep is
assumed to be volume-preserving, i.e. incompressible [58].
AFortran subroutine calculates now the equivalent creep strain increment (time step)
∆¯εcr
k=tk+1
tk
dt ˙
¯εcr =˙
¯εcr(¯σ,T,χ)∆tk(3.13)
and its derivative with respect to stress (for extrapolation for the next time step) for every
integration point according to a implicit time-integration scheme (unconditionally stable
backward Euler method). (This routine is essentially the same in Ansys or Abaqus and
contains the formulae in their formulation for equivalent entities.)
As already mentioned, the directional material flow follows the gradient nij of the von
Mises stress potential q(σij)=¯σ(can be thought of as a surface in 3D stress space):
∆εcr
ij =∆¯εcrnij where nij =∂q
∂σij
=3
2
1
qsij (3.14)
So for the creep strain increment in three dimensions we obtain:
∆εcr
ij =3
2
∆¯εcr
¯σsij (3.15)
The stress state is in return defined by Hooke’s law based on the fact that only elastic
strains give rise to stress at time tk+1:
σij|tk+1 =Dijmn εmn|tk+1 −εT
mnδmntk+1 −εcr
mn|tk−∆εcr
mn|tk, (3.16)
where Dijmn is the elasticity tensor and use has been made of equation 3.1.
Finally the sum over the individual increments yields the total accumulated creep strain:
¯εcr =
k
∆¯εcr
k(3.17)
This summation is carried out already within the subroutine. Ansys leaves so-called state-
variables for the user to specify. The accumulated equivalent creep strain is as an always
positive quantity put out by either a state variable. Abaqus has this feature already
implemented.
This routine was compiled for both Abaqus and Ansys and produced identical results for
various test cases, only dependent on the used time stepping scheme i.e. creep limit control
(cf. section 4.2). The creep laws were tested for a beam under constant load in tension
and in shear and for a flip-chip bump (results are depicted in the appendix section C.1.1).
The Ansys input data file comprising elastic and inelastic properties is given below.
How this creep strain can be used for lifetime evaluation is the subject of the next sections.
22 CHAPTER 3. MATERIALS & THEORY
3.1.3 Ansys Data File for 63Sn37Pb Solder
In the input file given below first the elastic properties are given in tabular form as a
function of temperature where intermediate values are interpolated linearly.
In the second half of the code file the creep routine usercreep.F7[72] is addressed and the
parameters defining the creep law as given in table 3.2 are transferred to the subroutine.
A state variable sums up the creep strain increments and makes them available to the
program’s post-processor either by etable,svar,4 or by etable,nl,psv. Summing up
the output equivalent creep strain by etable,epcr,eqv is not recommended unless the
values are written to a file after every substep, which may produce quite a bit of data.
The methods are only equivalent for monotonic loading, which is not the case for thermal
cycling. Here, the second method would underestimate the creep strain.
!============================================================================
!-- Eutectic Solder: isotropic, viscoplastic,
!-- Elastic Properties:
MPTEMP, 1, 210, 398, 423 ! Temperature
MPDATA, EX, mat_pb, 1, 36000, 21000, 19000 ! E-modulus
MPDATA, NUXY, mat_pb, 1, .36, .36, .36 ! Poisson’s Ratio
MPDATA, ALPX, mat_pb, 1, .24e-4, .24e-4, .24e-4 ! CTE
!
! -- Calls user-defined subroutine "usercreep.F" for Creep Strain evaluation
TB, CREEP, mat_pb,,,100,
!
TBDATA, 1, 1.39e-6, 1.96, 7.6626e-11, 48157.0, 2.38e3
TBDATA, 6, 7.1, 81239.0,
!-- Accumulation of Creep Strain
TB,STATE,mat_pb,,5
!============================================================================
3.1.4 Lifetime Prediction and Failure Mechanisms for Eutectic
Tin-Lead Solder
In order to correlate bump failure determined during a thermally induced low cycle fatigue
experiment with a computationally accessible damage criterion one needs a theory which
describes this correlation. Based on such a relationship the bump is ‘calibrated’ as a
reliability-sensitive device (in this case the solder bump acts like a reliability-sensor) under
given boundary conditions. Once this is done this relationship can be used to extrapolate
to other tin-lead solder interconnect assemblies, i.e. to predict lifetime for a specific set-up
by simulation.
In order to establish this correlation one draws upon the hypothesis, that damage and its
evolution can be described via state variables which are measurable as well as describable
by a constitutive model, i.e. by numerical simulation of this state [15, 73]. As usual the
argumentation follows the scheme of system, drive and response on various levels. Cor-
relation must ideally be given at each stage, and the better a single link in this chain is,
7Ansys commands are given in typewriter style.
3.1. VISCOPLASTIC CREEP & FAILURE OF EUTECTIC TIN-LEAD SOLDER 23
the better the final result will be. This scheme is depicted in figure 3.4, illustrating this
one-to-one correspondence of simulation (bottom left) and experiment (top right).
Result:
Lifetime
Assessment
&
Prediction
Drive:
Thermal
and Mechanical
Load Cases
Response:
Deformation,
Strain & Stress
System:
FE-
Modelling
Theoretical
Model:
ε
cr
Geometric
Parametres
Material
Data Constitutive
Equations
Appropriate
Failure Criterion
Schematic of Computational
Lifetime Prediction by the
Finite Element Method
Schematic of Experimental
Lifetime Prediction by
Thermal Cycling Test
Drive:
Thermal Cycles
and Mechanical
Loads
Response:
Deformation,
Bump Failure
Statistical
Analysis:
Nf
System:
Test-
Specimen
Detection of
Failure
Correlation via
Coffin/Manson
Correlation and
Consistency
via Set-up
Technological
Aspects
via
Model
via
Deformation
of Chip
Figure 3.4. Schematic representation of the correlation between simulation steps and
their respective experimental counterparts in the framework of the Coffin-Manson approach.
From top left to bottom right the argumentation proceeds and makes use of correlations (ital-
ics, grey arrows) to allow for consistency checks at each stage. Procedures are depicted as
ovals, quantities in rectangles. This figure can also be thought of as a roadmap through the
crucial points of this work.
The system we contemplate is a flip-chip assembly with an attached heat spreader, more
abstractly spoken a multi-layered assembly with small embedded solder interconnections.
This assembly is liable to solder fatigue cracking which proves fatal for the electrical func-
tion of the device. If it occurs, it has to be modelled via an appropriate failure criterion or
parameter which should ideally reflect the physics of the damage mechanism as a function
of a set of state variables [74]. For low cycle fatigue (large periodic inelastic deformation)
of eutectic solder this will involve evaluating the stress and strain states as a function of
applied thermal and mechanical loads.
A word has to be said about possible delamination at various interfaces [12] of the assembly.
If delamination occurs e.g. at the chip-underfill interface, it may severely accelerate bump
failure as it eliminates the beneficial effect of chip bending by the underfill. In any case
a chip has to be checked for delamination (by ultrasound microscopy) and its effect to
24 CHAPTER 3. MATERIALS & THEORY
be accounted for in the model. A fracture mechanics approach to interface delamination
has not been attempted, as it necessitates sophisticated computational effort [47, 48] to
describe stress field singularities at crack-tips or edges of dissimilar materials [75] and a
comprehensive experimental treatment [76] beyond the scope of this work.
Stress and strain state can be appropriately evaluated by nonlinear and rate-dependent
finite element simulation based on constitutive material laws and corresponding data after
input of the respective geometry of the system to be modelled [25, 77]. This correlation
has been established in the last section where the employed materials were characterised
and their behaviour implemented into FE-tools. The appropriate numerical correlation is
established FE-modelling.
The external drive the system is subjected to is the next crucial ingredient. For obvious
reasons one wants the drive to represent the typical load conditions the device is exposed
to in its service life. A standardized thermal cycle [19] is used to this end where the
environmental conditions (e.g. automotive sector with temperatures T∈[−40; 125] oC)
are thought to be controllably and representatively applied in an accelerated manner. This
allows to compare different assemblies to one another and make statements of reliability
based on specified testing conditions. To establish correlation for the drive input loads,
their effect has to be measured and properly mirrored by the simulation (section 5.1).
The response of the system to the imposed drive is subsequently recorded. This involves an
analysis of the strain and stress states within the bump for the simulation and a statistical
analysis of bump failure on the experimental side. Various theoretical approaches exist
to describe the correlation between the two [73]. For low cycle fatigue phenomena one
draws upon the irreversible inelastic (creep-) deformation which is a measure for damage:
Alternate deformation induced by periodic thermal loading causes the solder to creep and
to accumulate creep strain which leads first to the built-up of cavities on a microscale,
then to the initiation and coalescence of microcracks until the bump ultimately fails by
propagation of a macrocrack.
Thereby the approach works on the principle that the amount of accumulated inelastic
strain per converged periodic8cycle is correlated to the statistical mean of a distribution
which can adequately describe bump failure. For this case the Weibull-distribution is best
suited and the mean is calculated for the cycles to failure. A correlation can be established
by the well-known Coffin-Manson relationship which will be explained in the next section.
This relationship which involves free coefficients to be determined as a result of a best
fit procedure may then be used for extrapolation as indicated above. Therefore it will
be the aim to ‘calibrate’ our solder bump – or reliability sensor – by determining these
Coffin-Manson coefficients.
On the way it is advisable to countercheck the correlation on different levels, i.e. to check for
consistency between simulation and experiment by more easily accessible i.e. measurable
quantities. For example the macroscopic behaviour (see again figure 3.4) of the assembly
represents a well-suited starting-point. Deformations (e.g. curvature of the chip) as a
function of mechanical load and, if possible, of temperature can be recorded and simulated
and provide a quantitative statement about the quality of the correlation [24] at this stage.
8The system will usually go through an initial transient phase until the response becomes stably periodic.
3.1. VISCOPLASTIC CREEP & FAILURE OF EUTECTIC TIN-LEAD SOLDER 25
Below we want to deal in detail with the correlation between measured bump failure and
computational inelastic strain in solder fatigue. This works on the principle that the solder
bump is the crucial point of the total assembly and that there is no delamination which
could override solder fatigue as governing failure mechanism.
3.1.5 Thermally Induced low Cycle Solder Fatigue:
Reliability Concept According to Coffin-Manson
The Coffin-Manson relation [40, 41] states that the mean cycles to failure ¯
Nf=N50%,
i.e. the point at which 50 % of the parts subject to cyclic loading have failed is correlated
to a failure parameter evaluated for one cycle ψby a simple relationship
¯
Nf=c1ψc2, (3.18)
where c1and c2are constants which depend on the material and the characteristics of the
cyclic load [73,78]. In low cycle fatigue, i.e. conditions of high periodic stress and strain,
creep represents nearly all of the inelastic deformation at high homologous temperatures
[15,22,64]. Under these conditions eutectic solder failures are due to accumulated creep-
induced damage. Creep is the dominant failure mechanism [17, 43, 68]. Therefore creep
strain [26, 38, 39, 43], (or sometimes also the inelastic, dissipated energy9[23] which is
equal to the area of the hysteresis loop) is taken as failure parameter. Elastic strains are
also negligible in this regime as deformations occur slowly under given test-conditons. So
¯εcr ¯εel is a good assumption and so damage done by elastic strain is also negligible in
this regime. So the accumulated (equivalent) creep strain per cycle ψ≡¯εcr is used in the
Coffin-Manson relaionship, which is written now as
¯
Nf=c1(¯εcr)c2. (3.19)
Empirically it was found that c2∈[−2; −3] for many ductile materials [78] for isothermal
low cycle fatigue. This relation is taken to hold also for thermally induced low cycle fatigue
and for eutectic solder bumps values of c2∈[−1.0; −2.1] are found [11,22,23,38,39,80,81]
under cyclic thermal load. c1is assumed to depend on a variety of material and cycle
parameters [23] showing that a correlation between isothermal and thermal or different
thermal data is still an unresolved question. For this reason it may be argued to compare
only results on a relative scale (for the same type of cyclic load and taking also geometric
features of the bump into consideration) where c1drops out as a parameter. In addition
comparability hinges critically on the correct detection of experimental failure, a correct
statistical analysis and correct computation and reading of the failure criterion.
For eutectic solder bumps under thermally induced cyclic strains creep has been shown
to be the governing damage mechanism. In the course of its fatigue life it accumulates
creep strain in localized, band-like structured zones [15] as a result of an inhomogeneous
9For Coffin-Manson plots the strain produces a higher sensitivity due to a functional dependence ¯ε∼
W1
2and is therefore preferred. Also conflicting, non-monotonic results have been obtained which render
the use of Wquestionable [79]. Still it would have been interesting to consider Wfor comparison, but this
requires further customizing of a subroutine for the specific creep law in use as this currently represents a
non-standard use of Ansys.
26 CHAPTER 3. MATERIALS & THEORY
stress distribution over the bump [42]. These bands act as weakened zones [80] due to an
agglomeration of dislocations which grow by stress-assisted diffusion [73] before microcrack-
nucleation starts. So cracks are assumed to start at a local maximum of strain [24] and
follow a path or band of high local creep strain which has to be taken as its representative
value responsible for the volume damage [38].
It has been discussed [67] if or to what extent the microstructure of eutectic solder influences
its fatigue life as it is well known that it depends e.g. on solidification conditions and its
loading history (annealing, cycling). As already mentioned, creep and its mechanisms
depends also on this microstructure which evolves during cycling and causes consequently
a drift in make-up of the mechanisms. As the solder coarsens its creep rate hinging on
grain-boundary sliding decreases and the overall steady-state creep rate may also. Still it
is undecided if this may be beneficial or harmful for the fatigue life of the joint [44]. There
are indications though [43] that the initial preparation of solder (e.g. by reflow, cooling,
storage) does not have a great effect on its reliability.
As has been pointed [77] out equation 3.19 is based upon a stable creep cycle (closed
hysteresis loop) which displays a constant microstructure (secondary creep) and surely
represents a linear extrapolation: So to a first approximation linear accumulation of damage
is assumed, i.e. ¯εcr =f(N) or for the total failure creep strain ¯εcr
f∼N. Hereby the damage
processes are assumed to start from the point where the stable state is reached as shown
in [43]. It is on the other hand impossible to simulate 1000 cycles or more and actively
incorporate feedback via the phase size into FE-simulations for a flip-chip or a package of
related complexity for reasons of numerical stability (due to nonlinearities) and time.
The Coffin-Manson relationship can be made plausible despite of its empirical origin (see
e.g. [74]) by an approach based on the thermodynamics of irreversible processes without
taking into account a detailed reference to the complexity of microstructural effects. Here
the basis forms the introduction of a damage variable φwhich is sometimes also called a
load-drop parameter (cf. [36] or [43]):
φ=Aφ
A0
=0 (no failure)
1 (total failure) , (3.20)
which describes the ratio of damaged area Aφwith respect to the area A0prior to damage.
The idea behind this is that at regions where the material is damaged (cavity) it cannot
sustain any load any more. This results in a higher effective stress ˜σ,with
˜σ=σ
1−φ≥σ. (3.21)
(In the following paragraph we want to assume that stresses and strains are given in
equivalent entities and leave out the bar over the symbol.) It is postulated that the
respective state-governing equations and kinetic damage evolution laws can be obtained
by differentiation of the thermodynamic potential F(free energy) with respect to the
corresponding associated variables.
F=F(T,ε,φ)fromwhiche.g. Y=ρdF
dφ (3.22)
3.1. VISCOPLASTIC CREEP & FAILURE OF EUTECTIC TIN-LEAD SOLDER 27
the strain energy density release rate Ycan be derived. Analogously a dissipation potential
Dwith
D=D(Y,T,φ)fromwhichby ˙
φ=dD
dY ˙
λ(3.23)
the evolution of damage with time ˙
φcan be obtained where the material’s dissipative
constitutive behaviour has to be incorporated via the viscoplastic multiplier ˙
λ[74], which
for creep entails a strain-damage coupling.
Without going into further detail a general evolution equation for creep damage can be
derived [74] which looks like
˙
φ=Y
S˙εcr =σ2
2ES(1 −φ)2˙εcr. (3.24)
where the damage rate is now proportional to the creep rate ˙εcr.Scan be interpreted
as damage resistance strength and Eis as usual the elastic modulus. All quantities will
depend on temperature and macroscopic (no structural) material properties.
This equation would now have to be solved (in general numerically) taking into account
the interdependence of creep strain rate and damage, i.e. effective stress ˜σ. To renounce a
self-consistent evaluation we make the following assumptions for an extrapolation:
•The damage is constant over the period of one cycle.
•The stable hysteresis loop is approximated by a rectangle symmetric to the origin
and can therefore be described by a constant stress and (creep-) strain amplitude
∆σ/2and∆εcr/2.
•The cyclic stress-strain relationship is given by a Ramberg-Osgood type of equation
∆εcr =∆σ
c(1 −φ)1
m
, (3.25)
where mis the cyclic fatigue ductility exponent [73] and ca constant; both are
material specific.
We can thus evaluate the damage per cycle (of duration t=τ):
dφ
dN =Cycle
dt ˙
φ=2 (∆σ/2)2
2ES(1 −φ)2τ
2
0
dt ˙εcr =c2
4ES(∆εcr)(1+2m), (3.26)
and making use of equation 3.20 for failure
φf=¯
Nf
0
dN dφ
dN = 1 (3.27)
and assume linear aging we obtain an expression
¯
Nf=4ES
c1
2−(1+2m)
(εcr)−(1+2m), (3.28)
28 CHAPTER 3. MATERIALS & THEORY
wherewehavesetεcr =2∆εcr. This equation takes the form of a Coffin-Manson relation-
ship, where the fatigue ductility exponent c2=−(1 + 2m) should be of the order of 2.
Indeed the cyclic hardening exponent mis found to lie within m∈[0.05; 0.2], for higher
temperatures also m∈[0.05; 1] ( [70]). Derivations stating a larger influence of mlike
e.g. c
2=−(1 + 5m) are also found in literature [73].
For thermal low cycle fatigue the above argument would imply a temperature dependence
of all parameters. The integration over one cycle would require a rigorous treatment
of the T-dependence. Although a hysteresis loop for a thermal cycle as measured and
simulated [43,69,81] could still to first order be approximated by a rectangle, the procedure
would become handwaving for the cyclic hardening exponent.
For a simple triangular temperature profile, however, this integration can be carried out:
Let us assume a purely displacement-driven assembly so that to a good approximation
all thermal strain is converted into creep strain for a slow enough temperature variation.
Then we may write:
εcr(t)∼εT(t)=∆α(T(t)−T(0)) ∼T(t)∼t, (3.29)
where we assume a linear time-temperature dependance as in a triangular profile with
∆T=T(τ/2) −T(0). Using again equation 3.26 to evaluate the damage per cycle we
have to properly integrate over one cycle, this time making use of the creep law 3.7 in a
simplified form, written for the effective stress (taking equivalent entities):
˜σ(t)∼T(t)1
m˙ε(t)1
meQ
mkT (t), (3.30)
where mis this time an average stress exponent, which for our creep law is m∈[2; 3] in
the considered stress interval (see figure 3.2).
So we calculate with respect to equation 3.26:
dφ
dN =Cycle
dt ˙
φ=2τ
2
0
dt σ2(t)
2ES(1 −φ)2˙ε(t)∼ε(T(τ/2))
ε(T(0))
dε ε 2
me2Q
mkε , (3.31)
wherewehavemadeuseoft∼T∼εand ˙ε=const.. Using a series expansion of
the exponential function we can easily show that the leading terms of the sum give a
dependance on according to
dφ
dN ∼ε2
m+1 +ε2
m2Q
mkε+ε2
m−11
22Q
mkε2
+···. (3.32)
With the first term governing the functional dependance, we apply equation 3.27 and we
obtain now a Coffin-Manson type of equation as:
¯
Nf∼(εcr)1+2/m, (3.33)
where with m∈[2; 3] we obtain a Coffin-Manson exponent c2=1+2/m ≈2. In this
respect the stress exponent influences the Coffin-Manson exponent. This explains also an
other tendency: Lead-free tin-based solders in general display a larger stress exponent (see
e.g. [42, 82]), which should result in a smaller Coffin-Manson exponent. This is indeed
3.2. LINEAR VISCOELASTICITY FOR THERMOSETTING POLYMERS 29
the case as stated in [83]. Still, this contemplation only serves to make a statement of
plausibility. As the conditions for our case are much more complicated, the integration has
to be carried out numerically by the finite element tool.
An other interesting topic is a deviation from linear aging and how it would alter the
above contemplations. If we take a weak power law dependence with n≈3 as suggested
by e.g. [67] like
d¯εcr
dN ∼N1
n, (3.34)
an evaluation similar to equation 3.27 would yield
¯
Nf∼(¯εcr)n
n+1 c2(3.35)
which reduces the value of the fatigue ductility exponent. This hereby considered slight
increase in creep induced damage per cycle could e.g. be caused by solder coarsening
and hence reduce bump lifetime. So an experimentally found exponent with |c2|<2
could indicate a deviation from linear ageing due to microstructural changes with lifetime
reducing effect as in [67]. In this work, however, we assume linear aging implied in the
Coffin-Manson exponent.
3.2 Linear Viscoelasticity for Thermosetting Polymers
In our assembly we have many materials for which a linear viscoelastic behaviour can
be assumed as they fall among the class of thermosetting polymers. The importance of
the consideration of rate-dependence for FE-modelling of electronic packages has already
been stressed [75,84] or [85]. The significant change in the properties of the material as a
function of temperature and time needs therefore consideration.
A viscoelastic material has a deformation that consists of both an instantaneously recov-
erable part and a time-dependent, mechanically (not thermodynamically) recoverable part
(retarded elasticity). This means, that although the system can reestablish its initial state
of deformation, it has nevertheless dissipated energy which manifests itself in a hysteresis
loop in a stress-strain diagram. Viscoelasticity combines the characteristics of an elastic
body which obeys to Hooke’s law
σ=Eεel (3.36)
and a perfect viscous fluid which features
σ=η˙εvs. (3.37)
Here Eand ηare the elastic and viscous modulus respectively.
Further, these class of materials feature a glass transition temperature Tgbelow which the
material is in a stiffer, ‘glassy’ state and above which is behaves rubber-like. This change
in the material’s behaviour influences the elastic modulus, its rate-dependence and the
CTE. Around Tgthe change of the properties is strongest. Therefore this point manifests
itself in DMA, TMA and relaxation testing [86, 87]. Shrinking of the polymers was not
considered as the manufacturers state a negligible cure dependance in this respect.
30 CHAPTER 3. MATERIALS & THEORY
In the following we will give a brief outline of the theory of viscoelasticity, employed
models and the resulting constitutive equations. Measurement techniques are presented
and exemplified for a filled epoxy resin which serves as underfill. Finally the process of
implementing the data is explained.
3.2.1 Material Behaviour and Constitutive Equations
A simple model to describe viscoelastic relaxation is the Maxwell model (cf. figure 3.5 to
the left). It consists of a spring symbolising the elastic part and a dashpot is meant to
embody viscosity connected in series. When a constant strain is applied to the model, then
the stress relaxes exponentially to zero.
H
V
K
E
(a) (b)
E1E2En
KKKn
V
Figure 3.5. Maxwell-element (a) for viscoelasticity-model composed of a spring (linear
elastic) and a dashpot (viscous). Generalized Maxwell-model (b) is made up of nMaxwell-
elements connected in parallel.
Following this description, one can formulate the differential equation using ε(t)=εel(t)+
εvs(t), ˙ε(t)= ˙εel(t)+ ˙εvs(t) and defining λ=E/η:
˙ε(t)=1
Edt·+1
ησ(t)⇔E˙ε(t)=(dt·+λ)σ(t), (3.38)
where dt·is a differential operator with respect to time.
This differential equation is knowingly solved by a decaying exponential function. This
can be made clear by applying the Laplace-transform L(f(t)) = ˜
f(s)andL(dtf(t)) =
s˜
f(s)−f(0+) [58] and incorporating the boundary condition that the strain has been
applied as ε(t)=εθ(t) to 3.38 (see e.g. [88]):
Es˜ε(s)=(s+λ)˜σ(s)⇔˜σ(s)= E
s+λs˜ε(s). (3.39)
It has been made use of Hooke’s law again in the shape of Eε(0+)=σ(0+). This reduces
the differential equation to a normal algebraic equation. Taking the inverse transform L−1
3.2. LINEAR VISCOELASTICITY FOR THERMOSETTING POLYMERS 31
now we obtain an expression for σ(t) in the form of a convolution integral:
σ(t)=L−1E
s+λ⊗L−1(s˜ε(s)) = t
0
dtR(t−t)dtε(t), (3.40)
where
R(t)=L−1E
s+λ=Ee−λt (3.41)
has been used. R(t) is the relaxation function.
Now the general solution function can be written:
σ(t)=t
0
dtEe−λ(t−t)dtε(t). (3.42)
If we now want to obtain the solution for a special case, e.g. the displacement step-loaded
Maxwell-element at time t=t0this specifies the drive function ε(t)=εθ(t−t0)(withθ(t)
being the Theta or Heaviside-Function) and consequently the derivative with respect to
time ˙ε(t)=εδ(t−t0) yields the Dirac-distribution.
Insertion into equation 3.42 does reduce to
σ(t)=εEe−λ(t−t0)(3.43)
as expected. This behaviour is depicted in the graphs of figure 3.6. The individual strain
distribution can be easily calculated from equations 3.43 and 3.36 and 3.37.
This model, however, does not fully describe viscoelastic behaviour. To describe strain
recovery and convergence (for a creep test) one needs to expand the Maxwell-model (MM)
by putting several of them in parallel. This arrangement, to be seen in figure 3.5 to the
right, is also referred to as the generalized Maxwell-model (GMM).
The mathematical description of the GMM is analogous to the Maxwell-model and will
result in a Prony-series. We start with
σ(t)=
n
i=1
σi(t)andε(t)=εi(t) (3.44)
where the stresses σiof the individual Maxwell-elements add up to give the total stress.
We use the differential equation for each MM (equation 3.38) and take the sum over the
stresses:
σ(t)=
n
i=1
σi(t)=
n
i=1
Ei
λi+dt
·˙ε(t). (3.45)
Again we make a Laplace transform and due to its being linear the sum remains to give
an algebraic equation
˜σ(s)=
n
i=1
˜σi(s)=
n
i=1
Ei
λi+ss˜ε(s). (3.46)
32 CHAPTER 3. MATERIALS & THEORY
0.00.51.01.5
0.000
0.005
0.010
0.00.51.01.5
0
5
10
15
0.00.51.01.5
0.000
0.005
0.010
0.00.51.01.5
0.000
0.005
0.010
Drive
Strain
t [arb.u.]
Stress [MPa]
t [arb.u.]
Elastic Strain
t [arb.u.]
Viscous Strain
t [arb.u.]
Figure 3.6. The axial relaxation response for a step strain loaded Maxwell-model. In this
example, the springs have moduli of 1000 and 500 MPa respectively, the time-constant of
the dashpot has been taken to be τ1=0.5a.u.
0.00.51.01.5
0
5
10
15
0.00.51.01.5
0.00
0.01
0.02
0.03
0.00.51.01.5
0.00
0.01
0.02
0.03
0.00.51.01.5
0.00
0.01
0.02
0.03
Drive
Stress [MPa]
t [arb.u.]
Elastic Strain
t [arb.u.]
Strain
t [arb.u.]
Viscous Strain
t [arb.u.]
Figure 3.7. The axial creep response behaviour for a generalized Maxwell-model. τ1=0.2
a.u. Note the strain recovery and finite strain upon constant stress.
3.2. LINEAR VISCOELASTICITY FOR THERMOSETTING POLYMERS 33
Taking the inverse Laplace transform making use of the distributivity of the convolution
it allows
σ(t)=t
0
dtR(t−t)dtε(t) where again R(t)=
n
i=1
Eie−λts˜ε(s). (3.47)
Taking again the case of a step load as in equation 3.43 we obtain the solution in the shape
of what is called a Prony-series.
σ(t)/ε =E(t)=
n
i=1
Eie−λit. (3.48)
This function is a linear combination of non-orthogonal functions (as long as λremains
a real number) apt to describe monotonously exponential decaying asymptotic behaviour.
Here, λiare the inverse relaxation times τiand Eithe Prony-coefficients for the respective
relaxation process or Maxwell-element.
This, slightly more complex model describes linear viscoelasticity in a better way. The
model includes the extreme cases of missing out a spring or a dashpot. This can then
account for a finite asymptotic elastic modulus E∞and strain recovery, both of which
are features often encountered with polymers. This behaviour is depicted in figure 3.7.
For a real polymer the individual Prony-coefficients Ei,λ
ican be thought of as being
characteristic of internal relaxation processes.
For the sake of completeness it is mentioned, that also other models exist to describe
viscoelastic behaviour (Kalvin-Voigt-Model, Standard-Model, etc. , see e.g. [58]). They
use springs and dashpots in other combinations but can be shown to be equivalent to the
GMM in their generalised formulation.
Equations of the type of 3.45 are also called a hereditary integral equation. The integral
therein describes the stress-history of the system by integrating over all past strain input
dε(t)attimet=t. The bilocal function R(t−t) in the time domain communicates all
time-dependent behaviour to the current or observation time t. The relaxation function
embodies the material system, whereas the remaining functions the external drive applied
to the system to obtain the response which is in this case the stress.
It shall be mentioned that the material is thought not to depend on absolute time. No
aging is taken into account, only rate dependent behaviour on a relative time scale with
respect to to the observation time. Otherwise one would need R(t−t)→R(t, t).
In case of a creep experiment it is more practical to deal with the creep compliancy function
J:
ε(t)=t
0
dtJ(t−t)dtσ(t)where t
0
dtJ(t−t)dtR(t) = 1 (3.49)
is the one to one relationship between the relaxation function and the compliance.
The above equation is also a manifestation of Boltzmann’s superposition principle which
states that a material is viscoelastic if when two stresses are applied a two different times
the strain response at any time subsequent to either of the previous is the same as though
any of the stresses were acting separately.
34 CHAPTER 3. MATERIALS & THEORY
For a real, three-dimensional linear viscoelastic isotropic body one has to consider the full
tensorial formulation for a multi-axial state of stress and strain [58,89]:
σij(t)=t
0
dt2G(t−t)˙eij(t)+t
0
dt3K(t−t)˙em(t)δij, (3.50)
where a tensor decomposition analogous to equation 3.11 for the strain tensor has been
used. The strain deviator interacts with the shear modulus G(t) and the volumetric strain
with the bulk modulus K(t). Special attention has to be paid to the time-dependence,
which imposes [89–91]:
G(t)=L−1LE(t)
2(1 + L˙ν(t))(3.51)
K(t)=L−1LE(t)
3(1 −2L˙ν(t)), (3.52)
where the expected familiar correspondence
G=E
2(1 + ν)(3.53)
K=E
3(1 −2ν)(3.54)
holds for the time independent case or the initial elasticity-dominated instantaneous re-
sponse or the asymptotic case where no rate dependence is active any more i.e. the cases
where G(t0)=G0and G(t∞)=G∞. The same is true for K. The derivation of these
equation is given in the appendix A.3.
3.2.2 Experimental Results of Relaxation Tests:
Exemplified for an Underfill (Silica-filled Epoxy-Resin)
Now we want to measure the viscoelastic behaviour of a polymer which can be assumed
to have a linear viscoelastic response. Two methods of testing are usually used for this
purpose. The first is a relaxation test where a constant strain (within the elastic limit) is
applied at a time t=t0within a certain time (specified is t=1s)andthematerialis
left to relax over the period of one hour. This test seems well suited for materials which
are shapable as dog’s bone specimens (see figure 3.8) to fit into a tension testing machine.
Further, this test is expected to yield suitable results since the data is obtained on a time
scale of one hour which is of interest for a thermal cycling test, which usually use ramp
and hold times of several minutes.
This procedure worked well for the harder thermosetting polymers as the underfill, sol-
dermask and the organic board but the softer elastomers could not be clamped by the
tension testing machine. But these elastomers (silicone-based) were successfully tested by
frequency-driven measurement techniques as there are DMA and rheometre. There, the
viscoelastic properties can be converted from the frequency into the time-domain and be
made comparable to the relaxation data (as is shown in the next section).
3.2. LINEAR VISCOELASTICITY FOR THERMOSETTING POLYMERS 35
(a) (b) (c) (d) (e)
Figure 3.8. ‘Dog’s-bone’ specimens as they are used for the viscoelastic relaxation test.
All depicted materials were characterised: (a) Soldermask, (b) Organic Board, (c) Un-
derfill, (d) Silicone Adhesive and (e) Epoxy-Silicone Adhesive. For dimensions see figure
B.1.
The first method is exemplified for the case of a silica filled epoxy resin. These materials are
of special interest in electronic packaging [17], especially as underfills are concerned which
require matched properties to the employed solder [20]. The filler allows to manipulate the
mechanical properties of polymers. To increase the elastic modulus or reduce the CTE for
instance, one may add micro-particles of a different material, e.g. silica (SiO2). However,
the material will still display a viscoelastic response due to the polymer matrix.
The measurement presented here were conducted at different temperatures on a universal
testing machine (type Zwick 1446). The typical outcome is presented in figure 3.9.
As pronounced temperature dependance, a softening of the material is discernible around
the glass-transition temperature Tg= 125 oC. This behaviour is typical for epoxy-resins.
E(t) does not relax to zero though but to the asymptotic value E∞.
This measured data is now to be made available to the FE-tool. For the incremental
evaluation of viscoelastic stress and strain it is computationally advantageous to have an
analytical and continuous function for the material data. The time-honoured way to do
this is by introducing a temperature dependent pseudo time t=ξ(t), a relationship which
is defined by a shift-function a(T,t). It encompasses the whole temperature and time
scale [89,92].
t=ξ(t)=t
0
dτ a(T(τ)) (3.55)
which reduces to
t=ξ(t)=a(T)t(3.56)
for the simple case of a non explicitly time-dependent temperature (∂τT=0)aswewant
to assume. This shift function is characteristic for the respective polymer and is a man-
ifestation of what is called thermo-rheologically simple. This states the following: There
is a defined correlation between the material’s behaviour at high temperature on a short
36 CHAPTER 3. MATERIALS & THEORY
1101001000
0
1000
2000
3000
4000
5000
Sim.125 ˚C
150 ˚C
125 ˚C
100 ˚C
70 ˚C
T = 0 ˚C
30 ˚C
E(t) [MPa]
t [s]
Figure 3.9. Measured relaxation data E(t)of underfill. Simulated data is printed in
dashed lines for verification.
-202468
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
lg t (T) + Shift-Factor (T)
T
ref
= 303 K
Mastercurve
0 ˚C -> lg t - 1
30 ˚C -> lg t + 0
70 ˚C -> lg t + 1.4
100 ˚C -> lg t + 1.6
125 ˚C -> lg t + 2.8
150 ˚C -> lg t + 4.35
E(t') [MPa]
lg t'
Figure 3.10. Temperature-time shifted data for construction of mastercurve (dashed
line). The individual shift factors are given for each temperature. trefers to the (T-
dependent) time shifted by a factor with respect to the time at Tref measured on a logarith-
mic scale.
3.2. LINEAR VISCOELASTICITY FOR THERMOSETTING POLYMERS 37
time scale and low temperatures at a larger time scale. The respective relaxation or creep
processes occur faster for high temperatures but are of the same nature, i.e. Taffects only
the relaxation times hence allowing a temperature-time superposition principle.
260280300320340360380400420440
-2
-1
0
1
2
3
4
5
T [˚C]
C
1
= 28
C
2
= 778
T
ref
= 303 K
Shift Factor from Data
WLF - Fit, T
ref
= 30 ˚C
log a(T)
T [K]
-13727476787107127147167
Figure 3.11. WLF shift function.
Based on this assumption a so-called mastercurve can be constructed. This is done by
shifting the curves of figure 3.9 on the logarithmic time scale by the shift factor lg a(T
until it produces a continuous function with the next lower temperature curve.
It is easy to see that on a logarithmic scale 3.56 defines a shift factor:
lg t=lgt+lga(T) (3.57)
The result of this process is demonstrated in figure 3.10. The respective values for the
shift function are plotted versus temperature in figure 3.11 and fitted to the so-called
WLF-function10 (William, Landell, Ferry) by two coefficients c1,2.
lg a(T)= c1(T−Tref )
c2+(T−Tref)(3.58)
Hereby the mastercurve is defined for the reference temperature Tref. The last step is
the approximation of the mastercurve by a Prony-series expansion as presented in the
last section. This is possible since the mastercurve is always a monotonously decaying
function with exponential asymptotic behaviour. The fit is carried out for the pseudo-time
t(Tref ). It has been proved suitable to use one Prony element for each order of magnitude
of time τi=1/λi, although this obviously does not reflect any specific material relaxation
10According to theory this function is strictly valid only around Tg. Practical experience has proved
though that it can also be applied to the whole temperature scale. Also other fit-functions are found in
literature [89].
38 CHAPTER 3. MATERIALS & THEORY
mechanism any more. But here we are only looking for a fit-function. This underfill
consequently exhibits a viscoelastic relaxation on a pseudo-time scale of up to ten orders
of magnitude.
As we only measure the relaxation of the stress this has to be translated into a time-
dependent modulus according to equations 3.50 and 3.52. In this respect we have fitted
E(t) by the modified Prony-series
E(t)=
m
i=1
Eie−t
τi+E∞, (3.59)
where we have missed out one dashpot τn=∞and retain as asymptotic E-modulus E∞.
Consequently we get
G(t)=
m
i=1
Gie−t
τi+G∞(3.60)
K(t)=
m
i=1
Kie−t
τi+K∞. (3.61)
Note that the respective relaxation times need not necessarily be the same for shear and
bulk modulus.
-202468
0.30
0.35
0.40
0.45
0.50
Calculated
Poisson's Ratio
lg t'
Figure 3.12. Calculated behaviour of Poisson’s ratio. For high temperatures or very long
relaxation times the material becomes incompressible. This has to be so since Erelaxes
and Kstays constant (see equation 3.54).
To a good approximation [84] we assume that the bulk modulus is not a function of time,
i.e. that there is no volumetric relaxation but only a purely elastic response. So we set
K(t)=K0=K∞. It follows with 3.54 that near Tg,whereEassumes small values the
material approaches the incompressible limit, i.e. Poisson’s ratio assumes the value ν≤0.5
3.2. LINEAR VISCOELASTICITY FOR THERMOSETTING POLYMERS 39
which is experimentally observable. This is indeed confirmed by evaluation of equation 3.52
based on the measured values E(t) (see 3.12). Depending on which quantities are required
by the FE-code (usually E(t), ν(t)orG(t), K(t)) a conversion according to equations 3.52
and 3.52 can (numerically11)bemade.
Once the data has been implemented into the program the relaxation test by which the
data was obtained was simulated for a check. The result is depicted as solid black lines in
the respective diagrams (see e.g. for the underfill in figure 3.9).
The deviation from the measured curves is due to the shift-function which governs now
the time-temperature relationship. As can be seen from figure 3.11, the temperatures for
which the shifted points lie off the curve a computational deviation will appear. Still this
inaccuracy is small bearing in mind that the manually effectuated shift process gives rise
to deviations as well as a temperature drift during measurement. It should hereby not be
forgotten that we do interpolate ten orders of magnitude12 on a time scale!
-6-3036912
0
5000
10000
15000
20000
25000
T
g
= 0 ˚C
T
g
= 120 ˚C
T
g
= 70 ˚C
T
g
= 125 ˚C
150 ˚C
150 ˚C
-25 ˚C
0 ˚C
150 ˚C
25 ˚C
150 ˚C
25 ˚C
Organic Board
Soldermask
Underfill
Epoxy-Silione Adhesive
T
ref
= 30 ˚C
E(t) [MPa]
t' = lg t
Figure 3.13. Mastercurves of all viscoelastic materials determined in this work by relax-
ation testing. Highlighted is the glass transition region and the extremal temperatures for
which the material was characterised. Tref =30oCfor all materials.
Further measurements comprised TMA for determination of the CTE. The result data
can be found in the respective data input files given at the end of this chapter or in
11This conversion can easily made by expert systems featuring a Laplace-transformation like Mathemat-
ica,Maple or Matlab.
12This is 300 years vs 1 second.
40 CHAPTER 3. MATERIALS & THEORY
the appendix for the remaining materials (see also table 3.1). For a brief overview the
mastercurves of all viscoelastic materials treated in this work by relaxation testing are
given in figure 3.13. Note the differences in relaxation behaviour concerning extension and
position of the glass-transition region.
3.2.3 Comparison to Frequency Method
As has already been mentioned it is also possible to determine rate-dependent material
properties by a measurement technique based on a frequency controlled drive as there
are DMA or rheometry. In our case this has been necessary for the softer, silicone-based
materials which did not produce meaningful results in relaxation (cf. appendix B.5).
Frequency-based techniques have the great advantage that the measurements can be carried
out within minutes rather than days as is the case for the relaxation tests but for reasons of
discrepancies between the methods [91] one has so far opted for the relaxation test results
for FE-input. This relaxation test is considered to provide the correct material description,
as it evaluates material viscosity over one hour, which is the same order of magnitude on
a time scale as for the thermal cycle test itself.
Still the frequency-based method gives a qualitative impression how the rate-dependence
changes with temperature (i.e. how pronounced it is at all) and where e.g. the glass-
transition temperature is. For this reason the method came into use for each material used
in this work as preliminary examination.
The frequency based method hinges on the fact that if a viscoelastic material is subjected
to an enforced oscillation, the complex modulus E(ω)=E(ω)+iE(ω) of the material is
frequency-dependent. We apply a the drive, where as usual tis the pseudo-time
ε(t)=εeiωt(3.62)
to the viscoelastic material that is characterised by
R(t)=
k
Eke−t
τk(3.63)
and take the constitutive equation 3.47 to evaluate the stress response of the system:
σ(t)=t
0
dt
k
Eke−t−t
τkε(iω)eiωt. (3.64)
Straightforward integration yields finally
σ(t)=
kEk
ω2τ2
k
1+ω2τ2
k
+iEk
ωτk
1+ω2τ2
kεeiωt−εe−t
τk, (3.65)
where the left brackets signify the complex, frequency-dependent modulus. With the first
term on the right we retrieve the oscillation whereas the second term is just a decaying ex-
ponential representing a tune-in behaviour and can therefore be neglected for our purposes.
Consequently for large t
σ(t)=εeiωt(E(ω)+iE(ω))=|E(ω)|eiωt+iϕ where ϕ= arctan E(ω)
E(ω)(3.66)
3.2. LINEAR VISCOELASTICITY FOR THERMOSETTING POLYMERS 41
with
E(ω)=
k
Ek
ω2τ2
k
1+ω2τ2
k
and E(ω)=
k
Ek
ωτk
1+ω2τ2
k
. (3.67)
The interesting thing now is that if E(ω) is measured by DMA or rheometry then the
above equation can be used to fit a mastercurve on a frequency-scale. The mastercurve is
constructed analogously to the one on the time-scale by a frequency shift function aω(T).
The Prony times and coefficients remain the same. So we compare
E(t)=
m
k=1
Eie−t
τk+E∞(3.68)
E(f)=
m
i=k
Ei
(2πfτk)2
1+(2πfτk)2+E∞. (3.69)
where f=ω
2πaf(T)andt=tat(T)withlgaf=−lg at. For the frequency domain E∞is
assumed for the static limit f=0.
The storage modulus E(ω) of the underfill of the last section was now measured with a
rheometre. The result is to be seen in figure 3.14.
The corresponding frequency-shifted curves is depicted in figure 3.15. For comparison to
relaxation data the mastercurve of figure 3.10 is also depicted. It has been transformed
according to E(t)→G(t)→G(f), Tref =30oC→Tref = 100 oCand lg af=−lg atby
the above equations.
One notices that the rate-dependence extends over a larger time or frequency interval
for the frequency method. For obvious reasons this fact must manifest itself also in the
shift-function in figure 3.16. Worrying is the frequency interval which comprises sixteen
orders of magnitude in frequency (and time) compared to eight for the relaxation test.
Apparently the theoretical equivalence of relaxation processes measured at frequencies
(around f≤10 Hz ↔t≥0.1s) and relaxation times of t≈1000 s, i.e. over four
orders of magnitude seems less obvious in praxi. For lower frequencies the accordance of
the curves is therefore better, although the measurement inaccuracies are higher in this
domain. However, one should not forget that manual shifting of the curves introduces some
degree of subjectiveness.
So assuming correct measurement and time-temperature shifting the outcome seems to
depend on the time scale used for the measurement. Preference should therefore be given to
the relaxation test data when simulation a thermal cycle experiment. Relaxation processes
are then measured on the same time scale as used for lifetime evaluation.
Still, glass-transition zone and extremal values are comparable to the ones obtained by the
relaxation test. Assuming correct measurement, the frequency based result data should
still be viable for the simulation of short-term behaviour, let alone for a qualitative check
for viscoelasticity of a new material in general.
It may be furthermore speculated if the assumptions of thermo-rheological simplicity and
viscoelasticity do not become (at best) vague for an extrapolation on a scale where the
bottom end is marked by the big bang itself. Still extrapolations of this kind are found
42 CHAPTER 3. MATERIALS & THEORY
-1.5-1.0-0.50.00.51.01.52.0
0
400
800
1200
1600
2000
1
2
3
4
56
25 ˚C
50 ˚C
70 ˚C
90 ˚C
100 ˚C
110 ˚C
130 ˚C
135 ˚C
140 ˚C
145 ˚C
150 ˚C
155 ˚C
160 ˚C
165 ˚C
170 ˚C
180 ˚C
1 190˚C
G(f) [MPa]
lg f
Figure 3.14. Measured rheometer data of underfill.
-12-10-8-6-4-202468
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Adjusted Mastercurve
from Relaxation Data
25 ˚C
50 ˚C
70 ˚C
90 ˚C
100 ˚C
110 ˚C
130 ˚C
135 ˚C
140 ˚C
145 ˚C
150 ˚C
155 ˚C
160 ˚C
165 ˚C
170 ˚C
180 ˚C
190 ˚C
T
ref
= 100 ˚C
G [MPa]
lg f'
Figure 3.15. Temperature-frequency shifted data. Note the deviation from relaxation
data.
3.2. LINEAR VISCOELASTICITY FOR THERMOSETTING POLYMERS 43
280300320340360380400420440460480
-12
-10
-8
-6
-4
-2
0
2
4
6
8
c1 = 42.1
c2 = - 478.2
T [˚C]
Shift Factor from Data
WLF - Fit, T
ref
= 100 ˚C
- log a(T), Relax. Tref
= 100 ˚C
log a(T)
T [K]
74787127167207
Figure 3.16. WLF shift function for the above mastercurve. Again a pronounced devia-
tion from relaxation data is found.
in literature (1016 s, [93]) (Palaeozoic) and nicer (1050 s, [31])(!) and are used for lifetime
predictions.
At any rate: Further experimental investigation and data is needed for comparison of the
two methods for a – if possible – general verdict.
3.2.4 Numerical Implementation of Viscoelasticity
The calculation of the viscoelastic strain increment is again performed by a subroutine.
This subroutine does all the logic starting from calculating the thermal strain increment
as well as shifting the time according to the WLF-function and the summation of the
Prony-series of both shear and bulk modulus. At the end of the increment the full tensor
is again assembled as for the viscoplastic case.
To this end a Fortran subroutine which already exists (UsrViscEl.F) and is foreseen as
Ansys user-programmable feature is customized to our needs. Newly implemented was the
WLF-shift function and a different concept for temperature-dependent CTE-input. There-
fore the input variables on the tb,evisc-command given in the Ansys theory manual [57]
have been modified since the number of overall variables is limited. The new relationship
becomes clear from the example input-file given in the next section.
The routine demands a normalised shear g(t) and bulk k(t) Prony-series. Therefore first
the above indicated conversion of E(t)toG(t)andK(t) has to be made. The relaxation
times may be input as they are, but the Prony coefficients need a normalisation according
44 CHAPTER 3. MATERIALS & THEORY
to:
g(t)=
m
i=1
gie−ξ(t)
τi, (3.70)
gi=Gi
G0−G∞
with
m
i=1
gi= 1, (3.71)
k(t) is treated accordingly if needed. The routine allows input of ten Maxwell-elements
which is just about sufficient to describe the polymers of interest in this work.
3.2.5 Ansys Data File for Underfill
After definition of a viscoelastic material by tb,evisc,# the subroutine is called through
the input tbda,5,20. The remaining input is the WLF-coefficients of equation 3.58,
then the CTEs which need to be specified in ascending order of temperature where T1<
Tmin,···,T
5>T
max must be fulfilled. The CTE is then linearly interpolated. It follows
the asymptotic values for the shear and bulk modulus and the Prony coefficients and times
for the shear modulus. Further details can be found in the Ansys-manuals.
!============================================================================
!--viscoelastic constants input for usrve5x.f
!--for underfill ------------------------------------------------------------
tb,evisc,mat_uf ! initialize
tbda, 1, 28.56 ! wlf c1
tbda, 2, 778.84 ! wlf c2
tbda, 4, 303 ! wlf tref
tbda, 5, 20 ! function key, must be 20
!--temperature and cte input-------------------------------------------------
!- follows 5 temp in ascending order covering t-range of simulation
tbda, 26, 210, 273, 393, 413, 440
!- follows 5 corresponding cte values
tbda, 36, 44.4e-6, 44.4e-6, 44.4e-6, 133.0e-6, 133.0e-6
!--prony setup---------------------------------------------------------------
tbda, 46, 2071.15 ! G0
tbda, 47, 11.6768 ! Ginf
tbda, 48, 4487.5 ! K0
tbda, 49, 4487.5 ! Kinf
tbda, 50, 10 ! # g
! -- prony coeff shear-------------------------------------------------------
tbda, 51, 0.0043080, 0.0257507, 0.0277004, 0.0318087, 0.1885794
tbda, 56, 0.3006677, 0.2617653, 0.0582660, 0.0657374, 0.0354158
! -- prony times shear-------------------------------------------------------
tbda, 61, 0.0158398, 0.6288024, 12.542844, 198.67980, 3082.6693
tbda, 66, 30321.403, 171099.06, 883451.51, 3.13087e6, 9.94582e6
!-- end of underfill viscoelastic data input---------------------------------
! an effective nu = 0.3 has been used for data conversion
!============================================================================
3.3. CHARACTERISATION OF THERMALLY CONDUCTIVE GAP FILLERS 45
3.3 Characterisation of Thermally Conductive Gap
Fillers (Foils)
Another type of materials used as thermal interface need to be characterised (see figure
3.17 below). The materials used have been described in detail in section 2.1.1. But it was
difficult to determine their material properties with one of the previously described methods
due to the crumbly, plasticine-like make-up of the silicone-based foil (see figure 3.17 (a)
below) and the paper-like nature of the carbon-foil (b). Fortunately the manufacturer
did provide material data as far as CTE and material composition was concerned. No
viscoelasticity was assumed for either material, since the data-sheet for the carbon foil
stated it and silicone in bulk shape (as cured adhesive) did not display significant rate-
dependence (see appendix B.5).
(a) (b)
20 mm
Figure 3.17. Examples of some comercially available gap-fillers. Of the five ones tested
only the flexible foil (a) and the carbon foil (b) were characterized and came into use in
the experiment.
Since neither of the foils could be fixed without damage by a tension testing machine,
the elastic modulus had to be measured by a different technique. The modulus could
be measured in compression, as both foils are comparatively compliant to deform already
under small forces (see figure 3.18).
Aforcewasappliedonadieofspecifiedsize(10×10 mm2) which compressed the foil.
Through a hole in the foil and the stator plate opposite the die the displacement of the die
and hence the thickness of the foil could be measured very accurately by means of a LVDT
(Linear Variable Displacement Transducer). An apparatus similar to the one depicted in
figure 4.9 later in this work was used for this procedure.
From this data which is graphed in figure 3.18 the elastic modulus can easily be calculated.
As the graphs are curved, a linear approximation in the region closest to the envisaged
work point were used and the elastic modulus was obtained by the slope of the straight
line. The force FN=10Nis the normal force needed to assure thermal contact specified
by the manufacturer. This value is slightly above the lower limit.
46 CHAPTER 3. MATERIALS & THEORY
270265260255250245240235230
-5
0
5
10
15
20
25
30
35
40
E
Flex
= 6 MPa
E
Carbon
= 17 MPa
F
N
F
ext
= F
C2Au
Carbon Foil ("C")
Force [N]
Thickness of Foil [µm]
Flexible Foil ("F")
Poly-Fit
Figure 3.18. Characteristic curves of carbon foil (code ‘C’) and flexible foil (code ‘F’).
The elastic modulus has been determined by taking the gradient in the work point determined
by Fext =FC2Au (see table 5.2 and figure 5.1) of the curves measured in compression.
3.3.1 Ansys Data Files for Gap-Fillers
The data for CTE were not measured but provided by the manufacturer. As for Poisson’s
ratio the value for the carbon foil was provided, whereas for the silicone (a usual value) of
ν≈0.4 was assumed.
The measured E-modulus for the flexible, silicone-based gap filler produced similar values as
the silicone based adhesive in section B.5. This underpins the quality of the measurement.
!============================================================================
!-- elastic constants for Carbon Foil
mp, ex, mat_ad, 17.15 ! Elastic Modulus
mp, nuxy, mat_ad, 0.32 ! Poisson’s Ratio
mp, alpx, mat_ad, 10.5e-6 ! CTE
!============================================================================
!-- elastic constants for Flexible Foil
mp, ex, mat_ad, 6.22 ! Elastic Modulus
mp, nuxy, mat_ad, 0.4 ! Poisson’s Ratio
mp, alpx, mat_ad, 200.e-6 ! CTE
!============================================================================
Chapter 4
Finite Element Modelling,
Consistency Check
and Experimental Design
The objective of this chapter is to show the creation of the finite element model which is
to mirror the flip-chip assembly with attached heat spreader. For reasons of universality
the model is devised in a parametric (scalable) form which furthermore allows to combine
modular entities and merge them into a large FE-model. This model is optimized to
strike a balance between speed and accuracy and is checked for numerical stability and
convergence as to the evaluation of the creep strains which do serve as failure criterion.
Some special features like contact mode simulation are highlighted and commented on. As
the FE-model is parametric, it can easily be adjusted to any real test assembly at a later
stage.
Then the model is checked for consistency with experimental tests by comparing the macro-
scopic behaviour of the flip-chip on board under externally applied loads. Quantities like
displacement of the board and deflection of the die are accessible to measurement. A
special apparatus was built for that purpose. Thereby it is clarified which influences will
act upon a chip in such a configuration and how these constraints of different kind and
magnitude are best applied and varied within a range of technological or practical interest
and physical limit.
The organic board was found to display viscoelastic and orthotropic behaviour, material
properties which can currently not be treated simultaneously by the FE-tools in use. Vis-
coelasticity was eventually given preference over orthotropism, after accordance between
experimental tests and simulation was obtained by the introduction of a calibration factor
for the set of material data.
The considerations made in the previous sections are to manifest themselves in the con-
struction of a test-specimen which is to furnish the experimental correlation to computa-
tional lifetime prediction.
So in the remainder of this chapter the layout of the daisy-chained chip and board is given
to explain how bump failure is to be detected. Finally, the assembly process of the test-
specimen is explained and the problem of voids in solder bumps after reflow is addressed.
Technological difficulties which were surmounted are pointed out.
47
48 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
4.1 Universal FE-Modelling:
The Modular-Parametric Approach
As has been motivated we need to construct a finite element model which has to meet
demands of flexibility concerning size, material and load configuration.
The main geometric features as the size and shape of the individual components, their
position, their connectivity (merged or sliding contact) ought to be variable. The same is
true for the mesh-related properties of each part of the model as mesh-density, mesh type
and application of constraints. The incorporation of modules created by other CAD-Tools1
could become necessary. The inclusion of required constitutive equations has already been
explained in the last chapter.
This are prerequisites for a comprehensive model-parameter study of the intended range
and scope allowing comparability of the results and an automatic model generation.
Another important point is computational efficiency. This implies that the model be as
simple as possible, yet accurate. The question of how much detail is necessary for stable
results concerning our objective, the evaluation of the failure criterion in the solder bump,
needs answering. In order to determine for example the lowest uncritical (result-invariant
that is) mesh-density one has to be able to study the effect of this parameter. One does
not want the result to depend on numerical issues, on the other hand there is little point in
wasting computer resources. It has turned out that this FE-related parameter optimization
helped much reduce the complexity and hence the number of nodes in the model.
This so-called modular-parametric approach to solve this problem is presented below. As
atoolthecommercialcodeAnsys has been used. It is believed that with this approach it
is generally possible to facilitate accelerated model generation and verification for a large
class of electronic components (or microsystems [94]) due to its universality.
4.1.1 Philosophy of Parametric Modelling in Ansys:
Combination and Meshing of Standard Modules
In order to handle the different configurations assuring at the same time an economic and
smart management of elements the parametric approach looks as follows:
All relevant size and shape information is supplied to the program (Ansys, Release 5.7)
via a ASCII file. Here all parameters are identified and mesh definitions given. In a
similar vein material data is read into the program which has been customized beforehand
to provide the required material routines by compiling and linking the respective Fortran
subroutines [72].
The geometry is set up according to a modular system, i.e. each geometric FE-entity (for
example a bump or a chip) is modelled separately and saved to disk. At a later stage it
can be read into the model again at the location where it is needed. This procedure has
the great advantage that one deals with each part at a time and one may create a library
1The shape of the bump can also be crated by e.g. Surface-Evolver, (a program which calculates the
shape according to the surface-tension of the material) and be incorporated.
4.1. UNIVERSAL FE-MODELLING: MODULAR-PARAMETRIC APPROACH 49
of e.g. bumps (see figure 4.1). This is especially practical if these modular subparts require
particular devotion as in this study the make-up of the bumps. So meshing operations can
be tested for the individual modules first before they are integral part of a complex model.
(a) (b) (c) (d)
Figure 4.1. Some bump shapes to be found in flip-chip technology. The one labelled (a)
is the focus of this work (for dimensions refer to figure 4.28), the others represent time-
honoured shapes. This picture illustrates also the capacity of parametric bump-modelling
by alteration of only a few size-parameters with subsequent automatic generation of bump-
geometry.
It has been acknowledged (see e.g. [45]) that meshing a flip-chip assembly is challenging in
terms of economic management of elements and may require some tricks. This is mainly due
to the fact that very small, volume-like regions of interest with non-trivial topology (here:
the bumps) are to be combined with large, area-like regions which require less attention
and are usually of simple topology (the die). This raises the question of which type of
element is expedient for the individual parts taking into account the need for automatic
mesh generation. This latter boundary conditions entails that the model be continuous
and accurate enough for the operations to work flawlessly.
To assure this all submodules were of simple shape (e.g. brick-shape) within which the
non-trivial topological structure is embedded. At the location within the larger entity the
submodules are to be incorporated into a hole of the same size has to be cut out (by
Boolean operations) to create space for the module to fit in neatly. For automatic meshing
the model is ‘glued’ together2at the boundaries to form one single continuous model.
As a rule brick-shaped (HEX) elements are better suited and more economic than tetrahe-
drons (TET-elements) for layered structures of simple topology, whereas TETs should be
used for volume-like structures and have the advantage that volumes of any topology can
be meshed. A continuous mesh transition can be facilitated by pyramid (PYR) elements
when HEX and TETs have already been crated. For largest flexibility and automatic mesh
generation one proceeds as depicted in figure 4.2: The bump geometry is modelled (a) and
clad into a module or box of standard dimensions (b). The second standard module is
represented by the assembly’s layers (c) in which the bump is to be incorporated. At any
desired position in the xy-plane one or more bumps can be inserted (arrows). Therefore
a volume of the size of the module has to be cut from the layers at the specified future
location of the bump (d). The standard bump module is inserted (e) and merged with the
remaining model (f) to form a continuous model. Then the layered structures of simple
2Ansys VGLUE command.
50 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
x
y
z
(a) (b) (c)
(d) (e) (f)
(g) (h)
(i)
Bump Standard
Box
FC-Layers
HEX
TET
HEX
TET
PYR
Complete Model
Desired Bump
Positions
Cut Insertion Merging
Figure 4.2. Exemplification of the modular system: A bump may be modelled individually
(a), clad into a brick-shaped box of standardized (modular) dimensions and saved to disk
(b). At the desired positions (shown for the case of two bumps (arrows)) of the modelled
flip-chip assembly layers (c) a standard box is cut out (d), the bump is inserted (e) and
topologically merged (f) with the model. The bump module is meshed after the main parts
only (g) and remaining space is automatically filled with elements (h) to accurately integrate
it to form the complete model (i).
4.1. UNIVERSAL FE-MODELLING: MODULAR-PARAMETRIC APPROACH 51
topology are HEX-meshed first, followed by the non-trivial topological volumes of bump
and box. Here a TET-mesh is used where appropriate (g). Now a concentric box enclosing
the submodule from all sides is automatically filled with TETs (h). PYRs are formed at
the interface to the HEX-meshed layered structures. This can also be seen in figure 4.3
bottom left.
This procedure has another great advantage: The submodule is integral part of the model
and not just ’sewed’ into it (cf. [10,39]) by additional constraint equations3, which is liable
to convergence problems due to an often ill-conditioned matrix.
4.1.2 Model for Flip-Chip with Attached Heat-Spreader: Loads,
Constraints and Special Features
A FE-model for an unconstrained flip-chip on board may, within the described concept,
look like the one in figure 4.2. But for the FE-representation of a flip-chip assembly
with reverse side cooling one needs to add the thermal interface material and incorporate
mechanical boundary conditions (e.g. a fixation) and loads (e.g. a force and displacement)
as they are to be applied to the chip as in figure 2.2. This model is depicted in figure 4.3,
where the colors signify the different materials as explained in table 4.1.
Element Specifications for individual Materials
Item Code Colour Material Law Element-Type Feature
Plate pl lt. blue Aluminium el S186
Board bd magenta Fibre-Epoxy ve V89
Chip ch lt. green Silicon el S186/187, T174 Target
Interface ad turquoise diverse el, ve S186, V89, C173 Contact
Underfill uf red Epoxy, filled ve V89
Soldermask sm green Epoxy ve V89
Bump bp blue eut. SnPb vp S187, C173 Contact
Footprint fp yellow Copper pl S186
UBM um violet Nickel pl S186
Screw sc dk. blue Steel pl S186
Spacer sp dk. blue Steel pl S186 Birth/Death
Table 4.1. The materials in their FE-representation: The colour code refers to all FE-
figures in this work as does the abbreviation for all formulae. For the material property item
we assign el – elastic, vp – visco-plastic, ve – visco-elastic and pl - plastic. The element
types which support these material laws are given in Ansys-nomenclature (see [57]) and
are quadratic elements in their HEX or TET form.
The model in figure 4.3 exhibits octant symmetry. Via symmetry boundary conditions,
which constrain all displacements orthogonal to the edges, the whole assembly is (numeri-
cally) complemented to a full square.
3e.g. by CEINTF command
52 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
Board
Bump
Chip
Solder-
mask
Plate
Screw
Spacer
Force
Interface Chip
Nut
Underfill
Figure 4.3. The full FE-Model for FC&RSC, regions of equal material have the same
colours. Due to octant symmetry of the assembly only one eighth needs to be modelled.
The details inside the zoomed-out boxes show (from right to left): The interface region
layers, the meshed chip and a bump. Note again the mesh-transition from TET to HEX via
PYR-elements around the bump, which is thus incorporated as a modular entity into the
chip without difficulty. The red arrows symbolize the force acting upon the chip from below.
4.1. UNIVERSAL FE-MODELLING: MODULAR-PARAMETRIC APPROACH 53
A cylindrically shaped meshed region is intended to serve as area for the application of the
external force. Hereby, the force acts as a pressure (red arrows), which is advantageous
since by this means the force acts like a load homogeneously distributed over the specified
area. In order to hold the model fixed in three dimensional space the nodes of the area just
opposite the force application area on top of the plate is fixed in the out-of-plane direction.
In simulating the different configurations one has to take into account the assembly process
and with it the correct order of the application of the individual loads which precede
thermal cycling. So it is e. g. necessary to leave the contact between spacer and nut
undefined as long as this joint does not exist, i.e. as long as the nut is not tightened. This
requires an element ‘birth and death’-capacity.
In praxi this means that underfill and adhesive are cured before a spacer of given thickness
is inserted into the gap between plate and board. Only then the pressure is applied and
the nut tightened, i.e. the contact defined and the elements of all regions have to be active
and merged at the nodes – ‘alive’ as it is called in Ansys. This capability of the elements
allows to build the model in its most comprehensive shape right from the beginning, but
to deactivate elements which are not needed at certain load steps. In the same vein they
can be brought back to life when it is their turn.
The kind of thermal interface material poses an other constraint to come into effect. An
adhesive, as long as the interface area is intact (i. e. no cracks or delamination), may
doubtlessly be modelled as two merged regions and a continuous mesh. In the event of a
gap filler though this is not the case. For this situation the chip-foil interface is layouted
as a contact-target joint. Sliding contact with no friction is used here which is certainly a
good approximation: The chip does not move laterally, only in z-direction. In this case it
is the main task of the interface to allow a gap between the two regions4. This approach
can also be used to include the phenomenon of delamination (e.g. at the bump) into the
model if needed.
A word should be said to dimensional reduction of an FE-model, as proposed by some
authors [33], could not be considered for our purposes. The bumps are at positions where
they can only be taken into account by an octant model. Further, as shown by e.g. [95],
only 3D models can reproduce the true states of stress and strain to the degree of required
sensitivity.
4.1.3 Averaging Region for Creep Strain
For accumulating the failure criterion it is necessary to average the creep strain over a
certain volume in the bump as the value of one single node or a path would not give a
representative result due to local variations of the creep strain. In a 3D-model one has to
take into account a the 3Ddistribution of the strain fields: An averaging region should
include the highly strained part in which failure does occur i.e. the elements below the pad.
Due to the fact that TET-elements do not fill a volume in a regular and reproducible pattern
as HEX-elements would do, a volume adjustable in size and location inside the solder just
4This is also depicted in figure 5.36 where the simulation shows a evolving gap between chip at thermal
interface at low temperatures.
54 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
below the pad has been created. This allows averaging over exactly the same volume for
each bump irrespective of the shape of the elements and hence furnish comparable results.
This feature is depicted in figure 4.4. The averaging itself is done by using Ansys element
table operations5.
Averaging Region for Creep
Strain Evaluation
Figure 4.4. The (adjustable) averaging region for the creep strain.
Important is the location of the averaging region. As a guideline it should be at one ele-
ment’s distance from a material interface [75]. This avoids influences of numerical artifacts
like interpolations or singularities which exist at material boundaries and do not reflect
correct values [10,38]. It can be shown that very close to a sharp edge (as would be found
at the UBM-Solder interface) the creep strain depends on the creep limit (see next sec-
tion). The averaging volume depicted fulfills these criteria and is located close to the pad
where the cracks develop and the creep strains reach a local maximum in a band-shaped
structure.
4.2 Guidelines for FE-Model Optimization:
The Influence of Critical Parameters
As been mentioned before the final results should not depend on FE-related parame-
ters. These shall be understood as all parameters which are of purely numerical nature
(e.g. mesh-density) and do not alter the geometric appearance of the model. There will
usually be a limit value of the respective parameter where the solution converges, i.e. where
the calculated creep strains do not depend on the value of the parameter any more. This
value has to be determined for each so-called ‘critical’ parameter. A list of those is given
in the first half of table 4.2.
There are other – model-related parameters which represent the extent of geometric detail
down to which the solution is convergent. Desirable is a model which can renounce a lot
of detail requiring in detail only the region of interest as is in our case the solder bump for
the correct evaluation of creep strain. They are listed in the second half of table 4.2.
5Ansys ETABLE-Command
4.2. GUIDELINES FOR FE-MODEL OPTIMIZATION 55
In order to determine the influence of the individual parameters the parametric model
described above has been altered accordingly. As load case a full thermal cycle (as fur-
ther carried out in section 5.1) is used for the comprehensive FE-model (figure 4.3) to
yield results apt for quantitative comparison. For some parameter studies other (less com-
plex) models have been used (see appendix C). They underwent a ramped thermal load
(160 oC→25 oCwithin 5 min.), which is the first load step for all configurations as it
simulates the curing of the underfill.
In the following the individual points are illuminated, where some of them may be taken
as guidelines for FE-modelling of flip-chip devices evaluating creep strain in solder bumps.
But some parameters may depend on the employed materials. Still the presented approach
may provide some guidance, as these parameters will have to be checked in any case to
calibrate the model.
Influence of FE-Parameters on Creep Strain & Guidelines
# Parameter (FE-related) Description Influence Guideline
1 Simulation Tool Abaqus to Ansys? N –
2 Element Type (Solder) HEX to TET? Y Use TET
3 Mesh-Density Stable Solution? Y <Lower Limit
4 Creep Rate (Law) Force - driven? Y –
5 Creep Limit Control Stable Solution? Y >Upper Limit
# Parameter (Model-related) Description Influence Guideline
6 Copper traces Necessary? N Leave out
7 External Force Model or BC? N Use BC for F
8 Bump Neighbourhood # of Bumps? N One Bump o.k.
9 Passivation Layer Necessary? N Leave out
10 Bump Position DNP? Y Use Outer Bump
11 Bump Shape Creep Strain? Y Large Pad & Gap
Table 4.2. The label ‘No Effect’ signifies a deviation of less that one percent. For details
refer to the text. The results are given graphically in figure 4.7
1. Influence of Simulation Tool:
In the course of the model generation constitutive laws for secondary creep and visco-
elasticity had been implemented in Abaqus and had to be transferred to Ansys. For an
equivalence check a three-dimensional chip model which simulated one bump in a ‘slice’
(see appendix C.1.4) was created which incorporates all characteristic features to check
our simulations with. Both tools produced identical results (see appendix C.1.1). Ansys
was finally chosen due to better parametric modelling capabilities.
2. Influence of Element Type:
For its non-trivial topology the bump can only be meshed automatically with TET-
elements. The creep strains of the bump may show a sensitivity towards element shape
and density. This must be excluded since creep strain serves as failure criterion.
56 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
To check this a model was created analogous to the one described in point (1) save the fact
that there is a second bump which is this time meshed with TET-elements (see appendix
C.1.2).
The result is that a TET-mesh produces identical results at the expense of more elements6.
A HEX-mesh, however, would be the more economic solution. Differences are to be seen at
the edges which shows a numerical difference (same creep limit). Fortunately these zones
are not averaged over when evaluating creep strain. So TET-elements were finally chosen.
3. Influence of Mesh-Density:
In order to determine the influence of the bump mesh-density on the creep strain the
bump was meshed as described in figure 4.5 (left). (The individual meshes are depicted in
appendix C.1.3.)
It is seen that from a lower limit density the result converges towards a stable value for
equivalent creep strain. This density has been used (>1000 Elements/Bump-Volume).
The influence of the mesh density of the main model (chip and board) was checked, too. No
significant effect on either creep strain (∆¯ε<0.0001) or deflection of the chip (∆k<1%)
was detected. A mesh as is printed in figure 4.3 has been found suitable.
400600800100020004000
0.6
0.7
0.8
0.9
1.0
1.1
1.2
0.1110
0.75
1.00
1.25
Simulation
o.k.
<< fast --- slow >>
6600 Nodes
2100 Nodes
1000 NodesNumber of 10-Node Tet
Elements (Ansys Solid187)
Accumulated Creep Strain [arb.u.]
Elements
Creep Rate
<< low --- high >>
Factor multiplies
creep strain rate
of Creep law
Accumulated Creep Strain [arb.u.]
Factor
Figure 4.5. Left: Influence of the bump mesh-density on equivalent creep strain ¯εcr(t,T ).
The number of nodes and elements refer to solder material only. The creep strain is
normalized to the value for the stable limit. The arrows show the conflicting tendencies.
Right: Influence of creep-rate on creep strain. The factor multiplies the creep-rate given
in equation 3.7.
4. Influence of Creep Rate:
An other issue is the creep rate. Although there are many indications that the flip-chip
assembly is mainly displacement-driven (i.e. the bump itself does not contribute to the
stiffness but has to comply with the applied drive [70]). This could mean that the creep
rate or law is not as important since the solder has to comply to the imposed deformation.
6This corresponds to a factor four in elements and a factor two in nodes. Here, TET-elements have 10
nodes, whereas HEX do have 20.
4.2. GUIDELINES FOR FE-MODEL OPTIMIZATION 57
The results in figure 4.5 (right) show that this is not so. The tested variations of creep
rate display a pronounced deviation from the originally resulting accumulated creep strain
in magnitude and structure. This may be on account of a local interaction between the
solder and its surrounding materials like underfill and soldermask as a result of the elastic
energy still stored in the assembly, since the global curvature is not affected. Obviously
this behaviour will also depend on the solder material which the creep law is characteristic
of.
5. Influence of Creep Limit Control (Creep Criterion):
Ansys allows to specify a creep criterion clmt which controls the maximum creep strain
cmax per iteration and per integration point. It is defined as upper limit for the creep ratio
clmt ≥cmax := max ∆¯εcr
¯εtm t=tn
(Ansys), (4.1)
where ∆¯εcr is the equivalent creep strain increment at time t=tnand ¯εtm is the equivalent
strain of a modified total strain tensor:
εtm
ij t=tn=εtot
ij t=tn−εth
ij t=tn−εcr
ij t=tn−1. (4.2)
As usual equivalent quantities are labelled with a bar. This criterion is different from the
one used by Abaqus7which reads
cmax := max ∆¯εcr|t=tn−∆¯εcr|t=tn−1(Abaqus), (4.3)
where in either case
∆¯εn=tn
tn−1
dt ˙
¯ε(t). (4.4)
There is no obvious relationship between these two criteria which made the investigation
that follows necessary. Simulations have been run for different values of the creep-criterion8
where implicit time-integration was employed. This is shown in the graph of figure 4.6.
If no creep limit is specified, the creep ratio may take on any value which results in a overes-
timation of creep strain despite the implicit time integration scheme which always assures
a numerically stable solution (backward Euler algorithm). As a creep limit is given, the
creep strain converges to a stable value. As a consequence the number of substeps increases
– for small values of clmt anti-proportionally since the limit is reached in each substep. It
is instructive to see that this influence is stronger for the elements at corners than in the
centre (averaging region). From the graph an uncritical value of clmt = 10 can be assumed.
6. Influence of Copper Traces:
It would have made the model much more complicated to model the wiring on the board.
It has been found sufficient just to model the footprint below the solder, the creep strains
7Abaqus-command cetol=0.0005
8Ansys-command cutcontrol,crplimit,value,implicit
58 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
4567891020304050
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
Creep Strain (Corner)
Creep Stain (Centre)
Accumulated Creep Strain [arb.u.]
Creep Criterion
0
20
40
60
80
100
120
140
o.k.
no
limit
<< slow --- fast >>
Substeps
Iterations
CPU - Time [Steps]
Figure 4.6. Influence of creep limit control on failure criterion accumulated equivalent
creep strain. The rightmost value is extrapolated since no creep limit was specified for that
case.
do not depend on the size of the fan-out (‘slice’-model). This largely reduces model com-
plexity.
The whole of the copper on the board may still influence the overall stiffness of the board.
Measurements9have shown no difference between a board with fan-out and one which had
the fan-out removed. This is due to the fact that we deal with only very few tracks on our
PCB10 (printed circuit board). An effective board thickness and E-modulus do account for
this.
7. Influence of Application Mode of External Force:
The external force should be applied to the model as FE-load on a specified surface (see
figure 4.3). In an experiment, however, this would require a stator to hold a spring etc. So
in this respect it is worthwhile checking if the omission of such a stator in the FE-model
has any influence on the result. No influence was found and so further simplification of the
model was possible (cf. figure C.6).
8. Influence of Bump Neighbourhood (Number of Bumps in the Model):
Obviously it would greatly reduce CPU-time to have only a small number of bumps to
model, since they represent the most element-consuming part. For this reason it had to be
checked if it is immaterial for the result if only a small number e.g. two (separated) bumps
are modelled or if the creep strain is affected by an adjacent bump. Therefore a chip was
modelled with two adjacent bumps at the corner (see section C.1.6) and the remaining
part of the soldermask ‘channel’ was filled with a large barrel-shaped bump.
The comparison with the chip with two separated bumps produced no difference. This
9As those described in section 4.3.1.
10Depicted in figure 4.25.
4.2. GUIDELINES FOR FE-MODEL OPTIMIZATION 59
tendency is also stated in [10,39]. Therefore it was concluded that it is sufficient to model
only two bumps at arbitrary positions. Apparently the stiffness of the assembly is large
enough to override any effect of the bumps. This may be different for an other material
combination though.
9. Influence of Passivation Layer (Polyimide):
The active chip surface is protected by a passivation (polyimide) layer of 5 µm thickness.
It was therefore checked if any change in the result would occur if it was missed out.
For this simulation the UBM was taken as thick as the passivation layer (5 µm instead of
8µm) which makes the solder gap between pad and footprint ≈6% larger. This causes the
creep strains to decrease as seen in the corresponding bar in figure 4.7. A slightly greater
value has been chosen to make up for the larger solder gap accordingly in that it can be
assumed that there is no significant difference and that this polyimide layer can be omitted
for our purposes. This furthermore illustrates the large influence of the solder gap width
on creep strain. The model can be seen in the appendix C.1.7.
Test - Bumpshape
Test - Polyimide*
FC - Reference
0.000.010.020.030.040.05
Eqv. Creep Strain
Figure 4.7. The influence of the model-parameters depicted. ∗The slightly smaller value
is due to a slightly higher bump (see test). The strain has been adjusted accordingly. The
abbreviations in brackets refer to table 5.2.
10. Influence of Bump Position and Distance to Neutral Point (DNP):
In some papers [96] the DNP is given as a parameter characteristic for flip-chip reliability.
It states that usually the outermost bump experiences the largest creep strain and con-
sequently fails first, a fact which is not necessarily true for a force-driven package like a
CSP [97].
Here it could be verified that the outermost bump did indeed produce the largest strains
(as will also be shown later in the results chapter). This means that it is sufficient to
simulate bumps close to the corner at maximum distance to the neutral point.
11. Influence of bump shape:
One critical (set of) parameter(s) in the design process is surely the shape of the bump.
This comprises not only absolute size, proportion and pitch but also pad diameter, footprint
height, contact to soldermask etc. This topic is addressed in many papers and represents
undoubtedly a point of interest [98,99].
The simulation tool presented above is able to model bumps of most shapes of inter-
est in flip-chip technology. Some of them are presented in figure 4.1 (a-d). Obviously
60 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
combinatorially-many variations are thinkable and a parametric study focusing on bump
shape is therefore beyond the scope of this work. Furthermore, experimental verification
and analysis, which should always accompany a numerical assessment, are only carried out
for the one set (a).
However, to show the influence of the bump shape on the numerical failure criterion a
comparison between bump (a) and bump (b) has been made. They both exhibit the same
gap (47 µm) but differ in extension and pad diameter. Bump (b) yields slightly lower creep
strain as depicted in figure 4.7, which is accredited to the larger pad. The lateral extension
of the bump seems not relevant. Now our FE-model highlights all features necessary to
evaluate flip-chip reverse side cooling under thermal and mechanical load. As it has been
set up in parametric we can adjust it to any required geometric dimensions. This will be
of interest in the next section.
4.3 Characteristic Behaviour under Thermal and Me-
chanical Loads in Experiment and Simulation
From the last section a FE-tool is now available that functions reliably and the results
of which do not depend on FE-related parameters. We which details are necessary to
obtain numerically correct results and can run our simulations in the shortest possible
time. Furthermore we have recorded the material data and implemented the corresponding
constitutive laws. The model is ready for a consistency check with some measured quantity.
The macroscopic response of the chip such as its curvature and displacement as a function of
the applied loads is well suited for this check. Values of curvature (measured as deflection)
and displacement can be obtained by simulation and are at the same time quantities which
are accessible by measurement.
So in a next step we determine experimentally the characteristic behaviour of the flip-chip
on board assembly for various relevant loading situations. A special apparatus was designed
for that purpose which allows to measure displacement and deflection with a fixation as in
the finite element model. The influence of the adhesive was also examined.
The resulting agreement of simulation and experiment on the macroscopic level are a
prerequisite for the accurate evaluation of creep strain, an outcome which is more difficult to
verify experimentally [63]. It also gives us an idea of a range of interesting or critical values
for experimental adjustment: Interesting in the sense of getting a significant response,–
critical in the sense of upper limits e.g. for die crack.
4.3.1 Response of Flip-Chip and Organic Board to external Load:
Displacement and Deflection
First, the dependence of displacement and deflection (a measure for the curvature) on
the external force is measured. To this end a small apparatus was built which permits
controlled application of a force and simultaneous measurement of the displacement of the
board with the chip mounted on it. This device is depicted schematically in figure 4.8 and
4.3. CHARACTERISTIC BEHAVIOUR, THERMAL AND MECHANICAL LOAD 61
LVDT Stator Board Load Cell Damping Adjustment
Spring Screw
Application Slide Fixation
of Force
Spacers
Figure 4.8. Schematic of apparatus used to determine force - displacement relationship.
d
F
Figure 4.9. Photograph of the apparatus. On the left the LVDT can be seen.
62 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
physically in figure 4.9. To the very right a screw allows to compress a spring which is
sandwiched between two plates which are guided by slides. In collinear arrangement the
tension of the spring is transferred through a load cell to the rear side of the board. (The
spring is only used to enable fine-tuning of the force.) The tip of the load cell is shaped to
make a defined contact zone. The board is supported symmetrically at four points which
form a square in the middle of which the chip is mounted. The distance from board to
stator is adjusted with precision spacers. Now the force can be adjusted by turning the
screw. As a result the board with the chip on it is pressed to the left, in z-direction. This is
called the displacement dof the board. In some sense we are about to conduct a five-point
bending test, the arrangement being reminiscent of the number five on the face of a die in
a game of dice.
The displacement is measured by a linear variable displacement transducer (LVDT) which
is also depicted on the photograph11. This very accurate gauge12(accuracy <±1µm)
touches with a needle the surface of the chip, where the tiny force used to keep up the
contact is negligible. As a display only a commercially multi-meter was needed. The same
applied for the load cell13 (accuracy ±0.5N).
The result of this is seen in figure 4.10. The measurement was carried out for organic
boards of thicknesses of 0.8mm and 1.2mm. One notices, that the force-displacement
relationship is completely linear at room temperature according to
d=pF +d0, (4.5)
where pis the compliance of the respective board (thickness) and Fthe external force, d0
represents the zero offset. The scatter around the origin reflects mainly the fact that the
boards are warped over an area of 41 ×41 mm2(position of fixation screws) after reflow
and underfilling, i.e. after two thermal processes above Tg. The compliance pis not affected
hereby, as the measured values show hardly any scatter for it. Especially the thin board
reveals a great deal of – in some cases even initial – unevenness. In such a case this warpage
was gently corrected by bending the board until it was even again. Still a final warpage
remains which is responsible for the – therefore intrinsic – deviation of δd0=±15 µm (thin
board). This is not bad at all if one considers that we deal with a low-cost material.
Unfortunately these measurements could not be carried out at other temperatures due to
specification limits of the (expensive) gauges. Due to the viscoelastic material properties
of the organic board (cf. section B.2) the curves are expected show some relaxation at
temperatures close to the glass transition temperature Tgas the material displays a rate
dependence.
Then the curvature is measured as the difference in displacement in z-direction (orthog-
onal to the chip plane) of two points: the centre of the quadratic die and the corner (as
e.g. depicted in figure 4.18). This quantity shall henceforth be referred to as the deflection
kof the die, whereas the curvature κ=1/r is defined as the inverse radius (of curvature)
at the centre of the die.
11This apparatus was also used to produce the curves in figure 3.18 by which the foils could be charac-
terized.
12Type: Amos AWM-47-1.5 with amplifier Amos AE-2
13Type: Amos ALM-170
4.3. CHARACTERISTIC BEHAVIOUR, THERMAL AND MECHANICAL LOAD 63
01020304050
0
50
100
150
200
250
Thin Board
Thick Board
Exp
Sim
Gradient Thick Board:
p = 4.93 ± 0.05 µm/N
d
0
= -3.17 ± 9.45 µm
Gradient Thin Board
p = 13.10 ± 0.10 µm/N
d
0
= -3.42 ± 15.12 µm
Displacement d [µm]
F [N]
Figure 4.10. Experimental result for characteristic force Fversus displacement d=pF +
d0curve for thick and thin board. Warpage of the board causes an intrinsic inaccuracy of
δd0=±15 µm for the thin and δd0=±10 µm for the thick board respectively.
010203040
14
18
22
26
30
-
-
-
-
-
d = 200 µm
d = 0 µm
r = 1.11 m
r = 1.00 m
q = -0.34 ± 0.02 µm/N
k
T
= -15.84 ± 0.42 µm
q = -0.62 ± 0.03 µm/N
k
T
= -20.36 ± 0.40 µm
Thin Board
Thick Board
Exp
Sim
Deflection k [µm]
F [N]
Figure 4.11. Characteristic curve force versus deflection k=kT+kFwith kF=qF.The
dotted curves represent the simulated result.
64 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
The deflection is a very accessible quantity and to a very good approximation proportional
to the curvature for all values of force and temperature of interest in this work (see figure
B.6 in the appendix).
k∼κ=1
r. (4.6)
The measurement14 of the deflection was performed using the same apparatus as depicted
above only with the change that instead of the LVDT a curvature gauge was placed to
scan the chip.
The best results15 were obtained using a profilometer16 which made scans of the chip across
its diagonal with a position-sensitive precision probe. Its sub-micron resolution yielded
smooth curves and allowed fast recording of data. The results are depicted in figure 4.11.
Again we find a linear relationship between force and deflection according to
k=kT+kF=kT+qF, (4.7)
where as expected the chip exhibits an initial curvature kTdue to the thermal mismatch
between chip and board. As the force Fincreases the deflection increases by a mechan-
ically induced contribution kF=qF,whereqis the function gradient for the respective
board thickness. The underfill stiffens the assembly to a degree that it communicates this
mismatch. For the thick board the curvature is smaller since there is more board to resist
bending.
Some words have to be said about the fixation of the board. The following type of fixation
was found to come closest to the technological realization of flip-chip reverse side cooling
and was therefore finally used to measure the characteristic curves: First a given value of
force was adjusted, then the nuts were tightened. This assures that these fixations are stress
free and serve only to hold the board parallel to the plate at the location of the screws. This
turns out to be the most stable configuration and comes closest to the assembly process
in a electronic device. Apart from that this has the immeasurable advantage that the nut
joints – which are normally a non-trivial FE-issue – can be simulated as merged regions
and no contact mode is necessary. (For alternatives see the comment in section 4.4.2 at
the end of this chapter.)
Then, the dependence of the curvature of the chip on temperature is measured. The
deflection as a function of Tis measured by speckle interferometry [100]. The speckle
pattern for the deformed chip is depicted in figure 4.12. One had to resort to this less
accurate means since the described precise methods would not work in higher temperature
environment as LVDT and load cell are not specified for it. So these measurements could
only be carried out for the unconstrained flip chip, i.e. for k=kT(T).
The values for the deflection at the corner of the die were measured at various temperatures
for various chips again for both board thicknesses and depicted in graph 4.13. Again the
14The results are based on measurements carried out on a number of samples >20 and includes averaging
over both diagonals. The difference does not exceed a value of 1 µm.
15The values are in accordance with results gained by a laser scanner, but this method proved too
time-consuming and had a lower resolution.
16Type: Perthometer PCV 350 with 59 cm cantilever
4.3. CHARACTERISTIC BEHAVIOUR, THERMAL AND MECHANICAL LOAD 65
0.0
-4.0
-8.0
-12.0
-16.0
-20.0
-24.0
-28.0
-32.0
-36.0
kT
[µm] 10 mm
Figure 4.12. Flip-chip on board as examined by speckle interferometry. Depicted is the
deflection kT(T), i.e. the displacement uzmeasured from the centre of the die at room tem-
perature for the thick board. Note also the intrinsic warpage of the board δd < ±10..15 µm.
-40-20020406080100120140160
-5
0
5
10
15
20
25
30
35
40
concave
convex
T
R
Exp (thin Board)
Sim (thin Board)
T [˚C]
Deflection - kT
[µm]
w
thin
= -0.24 ± 0.010 µm/K
w
thick
= -0.19 ± 0.015 µm/K
T
0
= T
g
Thick
Board
Thin
Board Exp (thick Board)
Sim (thick Board)
Figure 4.13. The deflection kT(T)=w(Tg−T)for T<T
g(wbeing the function gra-
dient) as a function of temperature measured by speckle interferometry. The highlighted
region refers to room temperature. At these points the corresponding values on the lines
represent the precision measurements which the simulations are also based on.
66 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
simulated result is depicted. The temperature dependence is reproduced consistently by
the simulation and is linear. We complete the last formular by writing:
k=kT+kF=w(Tg−T)+qF, for T<T
g, (4.8)
where wis the function gradient (board thickness-dependent). Significant is the fact that
close to the glass transition temperature Tgof the board the curvature changes sign al-
though the stress-free state is reached at Tc= 160 oConly. This is due to the fact that
above its Tgthe board’s CTE drops to a very small value (around αT>Tg≈1ppm/K,
cf. data set for organic board in the appendix B.2.2). This anomaly together with a de-
creasing stiffness above Tgcauses the flip-chip assembly to essentially display hardly any
curvature. A tendency which has also been observed in [18].
Obviously, displacement and deflection are interconnected here, but it is important to
remember that eventually the curvature (deflection) of the chip is the desired local quantity
and that the displacement is dependant on the specific set-up of the device, housing,
component etc. , or as is the case here, the apparatus depicted above in figure 4.9 and only
a means to produce a state of bending.
Still as the displacement is a tangible quantity it will be always stated despite its being
only an auxiliary variable and therefore not universal but only significant for this work. It
can now be written down for this test-setup:
d=d(F, b, Pbd(T,t),fix), (4.9)
k=k(d(F),b,P
bd(T,t),fix), (4.10)
where the quantities in brackets signify force F, board thickness b, temperature- and
rate-dependent material properties Pbd(T,t) (e.g. viscoelasticity of board) and the type of
fixation.
Here the results obtained by simulation have already been shown in the graphs for verifi-
cation. The next section deals with this accordance between simulation and experiment.
4.3.2 Verification: Displacement and Deflection
In simulating the macroscopic response of the flipped chip on board according to the
experimental set-up depicted in figure 4.8 the main model (figure 4.3) was employed. So
in this case we are not interested in any creep strain for the moment but only in the global
behaviour so no bumps were included in the model. This has no effect on either deflection
or displacement as already mentioned.
In a first load step the curing of the underfill was taken into account by cooling down from
the curing temperature TC= 160 oCto room temperature TR=25oC. This results in a
thermal deflection kTof the chip due to the thermal mismatch of chip and board.
In a second load step the boundary conditions which hold the board parallel to the xy-plane
where the spacers touch the board (fixed uz-displacements) are activated. The respective
nodes are thus allowed to move freely in the directions orthogonal to it, thereby mirroring
the experimentally prescribed situation. The external force is then applied, too. As a
4.3. CHARACTERISTIC BEHAVIOUR, THERMAL AND MECHANICAL LOAD 67
Displacement d [µm]
100
200
0
k
d
F
Chip
Figure 4.14. Visualisation of displacement (d) of the board and deflection (k) of the chip
as a function of the externally applied force (F). No adhesive is present for this case.
The scale refers to the displacements din zdirection. This model was used to verify the
experimental results stated in figures 4.10 and 4.11 by dashed lines.
result, chip and board experience a displacement din out of plane direction. In addition to
that, the chip reacts again by bending and produces the second, mechanical contribution
to the deflection kF. This behaviour is illustrated in figure 4.14.
When not only an octant but the whole device is modelled the perfectly spherical displace-
ment field around the chip is clearly visible (cf. figure 4.15 to the left). The effect of the
non-circular fixation by four screws is thus neutralized by the stiffness of the board. This
indicates that our set-up may indeed be used to make statements of more general validity
as the kind of fixation seems not important. Even if a non-symmetrical fixation is used
the state of bending is to a good approximation spherical (cf. figure 4.15, right) as can be
inferred by the insets which show the deflection kof the die under combined thermal and
mechanical load (the force is applied directly below the die). For obvious reasons we do
not want to have our lifetime evaluation depend on any special position or fixation: So
both figures feature similar kinds of local bending at the site of the chip although globally
their fixation is completely different.
It can therefore be concluded that it is sufficient to study a symmetrical set-up and we
may concentrate on interesting parameters like materials, mechanical loads and constraints.
Further it allows easy, reproducible and controllable application of boundary conditions
and loads and represents an invaluable advantage for FE-simulations as only one octant
needs to be considered.
68 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
F
T
k
d
0 d [µm] 330 0 k [µm] - 19
T
F
k
d
0 d [µm] 100 0 k [µm] - 25
Figure 4.15. Left: Symmetric set-up suitable to study effect of ’five-point bending’: At
four points (arrows) the board is fixed, at the centre point the force is applied). The dis-
placement field close to the chip is perfectly spherical. Right: Arbitrary set-up of a flip-chip
on board with a force Fapplied from below. Despite its eccentric position the chip still bends
spherically as seen from the deflection k.
4.3.3 Calibration of Organic Board Data:
Viscoelastic-Isotropic vs Elastic-Orthotropic
In comparing the experimental results discussed in the last section with the simulative pre-
diction for displacement and deflection, a discrepancy was found which has to be attributed
to the numerical representation of the organic board.
One reason for this is that in carrying out simulations one is forced to make a choice as
to rate-dependence (elastic-viscoelastic) and symmetry (iso-orthotropic): Ansys supports
only isotropic viscoelasticity or orthotropic elasticity. The material, however, exhibits both
features and both ought to be simulated: viscoelastic relaxation as a function of time and
temperature was found and is depicted in section B.2. Possible viscoelastic behaviour of
compound materials consisting of a fibre-reinforced epoxy resin have already been pointed
out in [101]. Then the material is orthotropic which is obvious from its layered structure.
So the question is: Which behaviour is more important for the description of the board,
orthotropism or viscoelasticity, and which material parameter is responsible for the devi-
ation? Then: How can agreement between experiment and simulation be obtained? To
answer these questions the following parameter study was made. Thereby first the influence
of the material parameters on the result is clarified before a physically justified calibration
is made to reach agreement (by introduction of a calibration factor). Some quantities had
to be remeasured with greater accuracy as they have a stronger influence on the result
4.3. CHARACTERISTIC BEHAVIOUR, THERMAL AND MECHANICAL LOAD 69
than previously assumed.
In the following the decisive steps are presented and the results given in table 4.3 and figure
4.16. A complete protocol of the study can be found in the appendix B.2.4.
Cornerstones of the calibration process:
To countercheck the experimentally obtained data (quoted in lines (1a,b)17 of table 4.3)
the measured viscoelastic set of data was used to carry out the simulation (lines (2a,b)).
A distinct discrepancy was found. The board appeared to be too stiff; The applied loads
did not yield a high enough displacement of the board.
Board Data: Elastic versus Visco-elastic
Cnfg # bLaw βF k
TkFdComment
Units [mm][N][mm][µm][µm]
Exp 1a 0.78 ? - 7.7 20.3 4.6 100 kFand d linear in F
1b 1.15 ? - 20.3 15.8 6.9 100 kand dlinear in F
Sim 2a 0.82 ve-iso 1.0 7.7 20.5 4.3 70.3 measured ve-data:
2b 1.18 ve-iso 1.0 20.3 14.9 5.4 70 dtoo small
3a 0.82 ve-iso 0.7 7.7 21.1 5.2 99.9 best solution:
3b 1.18 ve-iso 0.7 20.3 15.7 7.05 98.5 closest set visco
4a 0.82 el-ort 1.0 7.7 20.6 4.5 85 derived el-data:
4b 1.18 el-ort 1.0 20.3 15.2 5.9 83 dtoo small
5a 0.82 el-ort 0.85 7.7 20.8 5.1 99 no effect on kT
5b 1.18 el-ort 0.85 20.3 15.5 7.0 97.5 but closest set elastic
6a 0.82 el-iso 0.85 7.7 20.6 4.9 90.7 isotropic and elastic
7a 0.73 ve-iso 1.0 7.7 22.3 5.3 97 beff for 0.8mm
7b 1.045 ve-iso 1.0 20.3 16.7 7.0 97 beff for 1.2mm
7c 1.38 ve-iso 1.0 43.8 12.7 8.4 100 beff for 1.6mm
Table 4.3. Cornerstones of calibration process; The discussion is in full given in appendix
B as well as the elastic-orthotropic and visco-elastic-isotropic material data used. As usual
bis the board thickness, βis a calibration factor for the elastic modulus of the board. Applied
loads are: T= 160 →25 oCwithin t= 300 s. The abbreviations signify: ve-viscoelastic,
el-elastic, ort-orthotropic, iso-isotropic.
It was then tried to adjust the material data of the board in that as good as possible an
agreement of experiment and simulation could be established. As criterion the values of
the two board thicknesses have to coincide in the tree variables kT,k
Fand das a function
of F.
17These values are taken from figure 4.10. As in the experiment, simulations were carried out for the
thin (a) and the thick (b) board.
70 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
A calibration factor β<1 introduced to ‘soften’ the board by multiplying the elastic
modulus of the board. Thereby an effective E-modulus (tensor) is given by
Eeff =βE0. (4.11)
This measure did not affect kTbut only d(lines (3a,b)). The change in the modulus is not
the crucial variable to dominate the deflection of the chip. Also a viscoelastic change in
time does not enter significantly. kTis mainly influenced by Tgand αT<Tg(T)asshownin
the appendix.
Still an effective modulus does affect the displacement of the board. Taking βve =0.7 (rows
(3a,b)) produces the best fit to all considered quantities when compared to the experiment
(again lines (1a,b)). It is important to point out that also the thickness bof the board
influences dand k. This quantity has to be measured carefully.
dFk_Tk_F dFk_Tk_F
0
5
10
15
20
25
30
Force [N]
Deflection [µm]
Thin Board Thick Board
elastic-ortho
viscoelastic-iso
Experiment
0
50
100
150
200
250
300
350
T = 25 ˚C
Displacement [µm]
Figure 4.16. Visualisation of the main statement of table 4.3: Both viscoelastic-isotropic
and elastic-orthotropic material data achieve good agreement with the experiment in all
measured quantities. Here, as driving quantity is the displacement is given, not the force.
Both sets of data are calibrated to optimum fit by their respective factor βgiven in the
table.
Then for comparison to the viscoelastic-isotropic board, an elastic-orthotropic set of data
is needed. This represents the time-honoured way of simulating an organic board. This
set was obtained from the measured viscoelastic data by simulation: A pull-test (as it
would have been performed for the measurement of the elastic modulus in tension) was
modelled and computed by simulation. For this purpose the pull-test was performed on this
‘virtual’ dog’s bone specimen for various temperatures with a speed of v=0.1mm/s.The
thereby obtained values for the elastic modulus Ex,y lay close to the initial modulus of the
viscoelastic data. The remaining orthotropism parameters shear modulus and Poisson’s
ratio (Gij,ν
ij) are now tensorial quantities and came in through a calibration factor derived
from an already existing orthotropic data set [102] and subsequent adjustment.
4.3. CHARACTERISTIC BEHAVIOUR, THERMAL AND MECHANICAL LOAD 71
The simulations were carried out with this set, assuming βel = 1 as an initial value (rows
(4a,b)). Again this yielded too large values for dand was corrected by taking βel =0.85
(rows (5a,b)).
So a very good accordance as to the displacement and both types of deflection can be
established with either set of data when a calibration factor βis used. This fact is illustrated
once more in figure 4.16. There the values are calculated for a given displacement d=
100 µm which makes it easier to analyze the values for kFwhich should only be compared
at equal values of d.
Row (6a) shows the influence of the material’s symmetry: The board was simulated elastic-
isotropically. A deviation of 10 % is the result, the inclusion of orthotropism softens the
board for this set-up. This is a consequence of a more complicated load situation due to
the fixation and the presence of the chip which deviates from a state of pure bending for
which no deviation is expected.
Influence of Organic Board Material Parameters
Increase in Parameter Symbol Influence Response
E-Modulus Eii,G
ij ++ d
−kT
+kF
Board Thickness b++ d
Glass-Transition Temperature Tg++ kT
0d
CTE (in-plane) below Tgα,T <Tg++ kT
0d
CTE (in-plane) above Tgα,T >Tg++ kT
0d
CTE (out-of-plane) α⊥,T>Tg0d,kT
Poisson’s Ratio (in-plane) νij −d
0kT
Cooling Time tcool +kT
0d,kF
Table 4.4. Qualitative effect of an increase in a material parameter on the macroscopic
response. Legend: ++: strong increase; +:weakincrease;0: no influence; −:weak
reduction; −−: strong reduction.
Now the aim is reached and the simulation describes accurately the experimentally ob-
tained data for the global quantities. Also the dependence on temperature is accurately
reproduced by both sets of data as counterchecked by speckle interferometry in figure 4.13.
Eventually the viscoelastic set of data was given preference for carrying out the simulations
although is seems not to be responsible for the accurate description of bending of the
chip. It may still have an influence on the remaining assembly and stress relaxation may
become important at other points and over the period over one or more complete cycles,
72 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
where temperatures close to Tgare encountered over a significant span of time. In view
of (6a) the influence of the material’s symmetry can – at this point – be assumed to be
compensated by a calibration factor, whereas this is not possible for rate-dependence. The
graphs in figures 4.10, 4.11 and 4.13 have been calculated with this set of data. Finally
the qualitative influence of the material parameters varied in the study on the response
quantities is summarized in table 4.4.
The system is now ready for the evaluation of creep strain!
Several comments need to be made:
First of all, an organic board represents an multi-layered, orthotropic, inhomogeneous low-
cost material. It consists of a fibre-reinforced epoxy matrix, where the fibres mainly fill
the middle layer of the board and the epoxy makes up the surface. The fibre tissue extents
only in the xy-plane, therefore it is undoubtedly orthotropic. Fibre and matrix are not
interwoven regularly, and they do not interchange on a microscopic scale but are of the
order of magnitude of e.g. a bump or a pad, therefore the material is inhomogeneous. The
board is neither perfectly plane nor is its thickness constant over our region of interest.
In other words, a material model for an organic board is bound to make assumptions and
simplify. So an introduction of calibration factors seems justifiable.
To determine orthotropic data of a quasi two-dimensional material is difficult, let alone for a
visco-elastic case. Many parameters – such as Poisson’s ratio – have to be extrapolated from
the bulk material or taken from literature. Then material parameters do vary. Especially
the glass transition temperature Tgand the CTE αmay diverge a good deal18 from the
values measured for this special material employed in this work and do have a relevant
influence on the results as shown in table B.1. This variety is also reflected in literature
(see e.g. [68] or [29]).
Further, it has been mentioned that not all material models are available in FE-tools. Vis-
coelasticity in Ansys allows only isotropic symmetry. In the adjustment process calibration
factors were introduced in order to establish accordance. This indicates further that it is
not trivial to model these composite material.
But the calibration factor β<1 can be physically motivated: The set-up of the flip-chip
on board involves a different kind of loading of the board than the one its material data
was measured with. Dog’s bone specimens were loaded in tension and left to relax in
the in-plane direction only. The stiff fibres determine most of the elastic modulus before
relaxation starts which means that material inhomogeneity and orthotropism are not ‘seen’
in this measurement. In our set-up which resembles a ‘five-point bending’ experiment (for
its being reminiscient of the number ‘five’ on the face of a die in a game) the board is
loaded in bending and also in shear (at the spacers). Hereby the zone of loading is shifted
from the central layer (fibres) to the outer layers (epoxy-resin). This thesis is supported by
a three-point bending experiment of a dog’s bone specimen (no shear(!)). The measured
elastic modulus dropped19 by a factor β≈0.83 which would justify the elastic-orthotropic
calibration factor. So this can account for a smaller stiffness but entails that our material
18Own investigations have shown Tg∈[115 oC,135 oC]andαT<T
g∈[11.5,13.5] and αT>T
g∈[0.0,4.5]
for material provided by different manufacturers.
19Tension: Ex,y =23GP a; Three-point bending: Ex,y =19GP a
4.3. CHARACTERISTIC BEHAVIOUR, THERMAL AND MECHANICAL LOAD 73
data is to a certain degree load-case dependent and that for a universal material model a
more elaborate, composite description has to be found.
0.70.80.91.01.11.21.31.41.5
2
4
6
8
10
12
14
16
18
20
22
b
0
= 0.82
b
0
= 1.18
Equivalent:
b = b
eff
and E = E0
or
b = b
0
and E = Eeff
Equation:
f(b) = 8.43 b-2.87
µm/N
Char. Board Constant
Fit
Char. Board Constant
d/F [µm/N]
Board Thickness b [mm]
Figure 4.17. Simulated values for the board constant d/F as a function of board thicknes.
The graph is valid for the board data and experimental set-up of this work.
But both data sets need a calibration factor. A 10% increase in stiffness due to the
incapacity to simulate the material’s orthotropism would nearly account for the visco-
elastic βve =0.7. Still there remains a general measurement inaccuracy in determining the
modulus. The correlation between the viscoelastic and elastic data as was described earlier
depends on the correct numerical representation of the simulated pull-test in the time
domain, a discrepancy which could make up for the remaining difference in the calibration
factor.
As far as the thickness of the board plays a role, the copper fan-out (see layout of the
circuit board in figure 4.25), is not considered on board level due to its fineness. It is
thought condensed in the overall thickness of the board and elastic modulus.
The measured board thickness (as stated in lines (1a,b)) does not include the soldermask
layer on either side of the board. Since the board is not uniformly covered with soldermask,
an averaged value was added to yield a working thickness of bu=0.82 mm for the thin
board and bx=1.18 mm for the thick one. Here, the nominal value provided by the
manufacturer (0.8mm and 1.2mm) respectively were not accurate enough.
It ought to be mentioned that instead of introducing an effective elastic modulus as in
equation 4.11 one might have introduced an effective board thickness like:
beff =γb0. (4.12)
This equivalence as to the board is illustrated in figure 4.17. The diagram is either valid
for E=E0and b=beff with γ=0.87820 or E=Eeff and b=b0with β=0.7.
20cf. figure B.5
74 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
The equivalence prevails as long as there is no chip mounted and only the pure board
is considered. As seen from lines (7a,b) the effective modulus produces better results
concerning the thermal deflection and therefore Eeff is finally given preference.
4.3.4 Critical Displacement and Risk of Die Crack
In determining the save parameter range for our experiments it is necessary to rule out the
risk of die crack and therefore to determine the maximally allowed values for the applied
loads. To this end the displacement was further increased until the die finally cracked. The
maximally attainable curvature was recorded experimentally by gradually increasing the
force in edging towards the critical point and recording the curvature at each step until
the die did crack.
Deflection
Exp Scan
Asym Fit
Sym Fit
y [µm]
x [mm]
-2 0 2 4 6 8 10121416
-10
0
10
20
30
40
rc
rm
Chip Diagonal
k
y [µm]
x [µm]
12 13
14
19
24
x [mm]
Figure 4.18. Illustration of Deflection k: Profile as scanned along the diagonal of the
chip and fitted by a polynomial. At the peak the radius of curvature assumes the theoretical
minimum rm, but due to non-ideal conditions (asymmetry), this chip has an eccentric
minimum radius rc. It is assumed that this radius is the critical one for die fracture.
The radius of curvature has been evaluated by fitting the experimental (see figure 4.18)
data to a polynomial function of sixth order comprising only even powers (to get the
theoretical minimum radius rmin the middle of the die) and by taking the inverse of the
second derivative. This obviously assumes, as the simulation always does, that the die
bends symmetrically and that the point of greatest stress is in the exact centre of the die.
This is not always true, but a polynomial of the above kind can make up for this deviation
if it is not too large. For with a large asymmetry this method would predict a larger radius
than there really is thus underestimating the risk of fracture.
Therefore the measured data were fitted to a ninth degree polynomial with all powers
allowed. This curve produces a very close fit (cf. the inset in figure 4.18) which is then
not necessarily centred about the middle of the die. The eccentric minimum radius rcthus
4.3. CHARACTERISTIC BEHAVIOUR, THERMAL AND MECHANICAL LOAD 75
obtained by the asymmetric fit is always slightly smaller or similar to the one obtained by
the symmetric fit rc≤rmbut has to be taken as the correct critical value for fracture,
whereas rmis evaluated and correlated to the simulation. This asymmetry may be due
to an eccentric force application or inhomogeneities within the assembly (the effect is,
although smaller, also visible if no force is applied).
This precision deflection measurement could only be performed at room temperature, but
since the curvature is also a strong function of Tit is important to know the highest stress
in the die which should coincide with the smallest radius of curvature. This situation is
aggravated as the temperature decreases. Diverse values for the radius were recorded at
TRand extrapolated via simulation to the lowest temperature of interest (T=−40 oC)
for our cycle tests. The result is given by the graphs in figure 4.19.
Here the (inverse) radius is printed versus the deflection and displacement for room tem-
perature TRand T=−35 oCwhich is close the minimum temperature for the thermal
cycle test. For each board thickness the radius has been measured for various values of
force at TR(red symbols and lines). Averaged values for the critical radius rcjust before
die crack (red stars) and the corresponding symmetric radius rm(red square below) are
marked. Then rcdefines a borderline for each board thickness, i.e. the minimum radius
found under a given load in the experiment. Beyond this line die crack is likely to occur.
Then these values are simulated and the extrapolation to low temperature is made. For
TRthe simulated values (green lines) slightly underestimate the curvature and thus the
risk of die crack. This should be due to a systematic feature of the simulation concerning
e.g. material data: We see that as expected, deflection and inverse radius increase with
decreasing T(blue lines). The relationship between kand 1/r is linear which means that
for an unconstrained die (no adhesive, see next section) either variable is fit to describe its
behaviour. Mechanical and thermal load do contribute to rto equal parts and in the same
fashion (see figure B.6 in the appendix where this is depicted for a larger range of values).
Still the proportionality is not exact, as (we quote from this reference):
r(k)=c1
1
k+r∞>c
1
1
k, (4.13)
where c1=−2.08 10−4m2and r∞=0.055 m. The deflection is reproduced correctly
as it was used to calibrate the simulation, whereas for the radius there remains a slight
overestimation by r∞.
The results are correlated to the displacements in figure 4.20 and we obtain an upper limit
of dc≈300 µm whichiswhatwewerelookingfor. Thisisthoughttobeagoodvalue
despite the slight underestimation of curvature by the simulation: The measurement of the
crackpoint is a very delicate procedure and depends on how careful the force is increased.
In the test-specimen during thermal cycling the adjusted curvature increases further due
to the slowly varying thermal load and unlike in the test without sudden effects. This
means that the die could tolerate even a smaller radius, rc=0.46 mgiven in the graph
would then have to be considered too large and therefore conservative enough to make up
for the computational overestimation of rm.
Under the given boundary conditions a save upper displacement should not exceed a value
of d≈200 µm.
76 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
15202530354045505560
0.6
0.9
1.2
1.5
1.8
2.1
2.4
0.46
Exp. T = 25 ˚C
Exp. Fit, T = 25 ˚C
Sim. T = 25 ˚C 0.49
F = 0
d = 0
Radius [m]
1/Radius [1/m]
Deflection -k [µm]
1.6
1.4
1.2
1
0.8
0.6
0.4
Critical
Radius r
c
Critical Deflection kc
Full Lines & Symbols = Thick Board
Dashed Lines & Symbols = Thin Board
Sim. T = -35 ˚C
Exp. Crackpoint
r
c
Figure 4.19. The radius of curvature rm(k,T)at the centre of the die measured along its
diagonal versus the deflection k: The experimental values are recorded at room temperature,
the computational ones are based on the simulations presented in the last section. Uncritical
values of rare below the dotted line. rmand rcare defined in figure 4.18.
0100200300400
0.6
0.9
1.2
1.5
1.8
2.1
2.4
Critical Radius rc
0.49
Exp. T = 25 ˚C
Exp. Fit, T = 25 ˚C
Sim. T = 25 ˚C0.46
F = 0
Radius [m]
1/Radius [1/m]
Displacement d [µm]
1.6
1.4
1.2
1
0.8
0.6
0.4
Full Lines & Symbols = Thick Board
Dashed Lines & Symbols = Thin Board
thick
thin
d
c
> 300 µm
Critical Displacement
Sim, T = -35 ˚C
Figure 4.20. Radius r(d, T)versus displacement d. A critical displacement can be derived
as dc>300 µm.
4.3. CHARACTERISTIC BEHAVIOUR, THERMAL AND MECHANICAL LOAD 77
4.3.5 Response of Flip-Chip with Adhesive:
Inhibited Curvature
An other important topic in FC&RSC is the reverse side attachment of the die by a thermal
adhesive. Thereby it is expected that the movability of the die is further constrained in
comparison to the ’free’ case which should have repercussions on its curvature and later
on its reliability.
In order to measure the curvature of an attached chip the method described in the last
section cannot come into effect. One had to resort to another, unfortunately much less
accurate means. The chip was glued to an aluminum plate where the thickness of the
adhesive was adjusted by precision spacers between the board and the plate. Then it was
cut in half parallel to the edge21. A line cut along the diagonal did break the chip at the
corner. These specimens were subsequently polished and can be seen in figure 4.21.
500 µm 500 µm
Plate
Adhesive
Chip
Figure 4.21. Left: Set-up for measuring the curvature: Cross section through the chip
attached by a (medium-hard) epoxy-silicone based thermal adhesive (’E’). From top to bot-
tom the different layers are: Aluminium plate, adhesive, silicon die, underfill, solder mask,
organic board. The coarse structure of the adhesive is due to silver flakes. Right: Cross
section with (very soft) silicone based thermal adhesive ’S’.
The deflection (as defined above or in figure 4.18) of the die was determined by repeat-
edly measuring the thickness of the adhesive (the distance from chip-top to plate-bottom)
with a special microscope at three points (left edge, centre, right edge of the die). From
this information it is easy to calculate the curvature of the chip. A mean value of three
measurements was taken and the whole procedure carried out on at least 5 chips for each
type of adhesive and board thickness. We optimized this method in order to come down
to an error of within ±3µm which was the best result for this not very accessible value.
(A laser scan over precision bolts which reached down through the plate to touch the chip
surface [103] did show the effect of curvature but the results were not reproducible due to
preparation effects.) Great care had to be taken not to cause the die to crack or splint
since all attempts to clad the specimen into any kind of mold-mass leaving the adhesive
21This has to be taken into account when comparing it to the results of the last section!
78 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
intact and thus rendering it machineable failed. In the end it turned out best to do all
steps manually. By the same method the thickness of the adhesive layer could be checked.
The adjusted value of had = 265 ±20µm was retrieved with a large deviation reflecting
the known warpage of the board mentioned in section 4.3.1.
On analyzing the behaviour of the attached chip (cf. figure 4.22) one can distinctly discern
the effect of the harder epoxy-silicone based adhesive which inhibits the curvature of the
die significantly. Thus, it neutralizes to a certain extent the stiffening effect of the underfill
which tries itself to curve the chip. The correlation of k∼1/r (equation 4.6) may surely
be lost at this point, but there is no possibility to measure rnow.
0
2
4
6
8
10
12
14
Board: Thin Thick Thin Thick Thin Thick
Epo-Sil Silicone Free FC
Deflection -kT
[µm]
(along Edge)
Experiment
Simulation
Figure 4.22. Juxtaposition of simulation and experiment for the deflection kTat TR=
25 oC. For comparison the corresponding value for the unconstrained flip-chip assembly
is also given (rightmost column). Curing conditions of the adhesive were tc=15min at
Tc= 160 oC, the size of the chip used was 10 ×10 ×0.375 mm. It should be noted that for
technological reasons these values of kTare measured along the edge, not the diagonal as
in the previous section.
For the pure silicone adhesive there is hardly any effect as can be inferred from the nearly
equal values for the free chip22 depicted in the right column. The standard deviation of
±3µm is mainly due to blurred edges at the aluminium-adhesive and adhesive-silicon
interfaces. An other contribution to this could derive from the deviations in the thickness
of the adhesive due to already mentioned intrinsic warpage of the board.
22The curvature along the polished edge of the free chip could not be measured meaningfully by any
of the presented techniques. Here the simulated value (approximately half of the curvature along the
diagonal) is given.
4.3. CHARACTERISTIC BEHAVIOUR, THERMAL AND MECHANICAL LOAD 79
The simulated value of the curvature along the edge is slightly smaller than half the value
along the diagonal. The error bars show the standard deviation of the measurements
according to which the simulation has been calibrated. The curvature along the cut for
the unconstrained (pure) chip was not measured.
In analogy to equations 4.10 the dependence on variables can now be complemented by
the properties Pad(T,t) and gap width had of an adhesive material:
k=k(d(F),b
bd,P
bd(T,t),h
ad,P
ad(T,t),fix). (4.14)
To model what had been done in the test required a quarter-model of the flip-chip assembly
with adhesive and plate (the model can be seen in the appendix C.9): In a first load step
the assembly was cooled down from curing temperature. At this point we still deal with
a full chip and consequently the symmetry boundary conditions are set to complement
the quarter model to a full one. This can be seen in figure 4.23 (a): The chip bends as
expected, but much less compared to the unconstrained chip (no adhesive). The result is
identical – as it must be – to a simulation with octant symmetry. Now the system is left
to relax for a twenty-four hours – just as was done in the experiment.
uz [µm]
-4.0
0.0
x
y
x
(a) (b)
Measurement Path
Figure 4.23. The displacements uzin the simulation of the quarter model after cooling
down from Tc(a) and after cutting in half and having the system relax (b). The adhesive
and plate are not depicted to permit view on the chip surface. Symmetry boundary condi-
tions are indicated by dashed lines and the path for measuring the deflection of the chip is
printed as a red line.
In a third load step the assembly is ‘cut in half’ (as is to be seen in figure 4.21) by removing
the symmetry boundary conditions along the y-direction (see figure). The assembly is left
to relax for a load step lasting one week and the result can be seen in (b): The chip takes
on a different state of bending, its centre moves to the centre point of the remaining –
now rectangular – chip. This means that the adhesive complies with the much stiffer rest
of the assembly. The deflection is now recorded along the printed path (red line in figure
4.23) as was done in the measurements. From the bars in figure 4.22 it can be inferred
that the simulation can reproduce the measured values to a fair degree of accuracy. The
simulation underestimates the deflection thus overestimating the stiffness of the assembly.
There may be several reasons for that: First it could be a systematic measurement error
80 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
since all values measured with this method are slightly higher than the ones measured with
the profilometer (cf. figure 4.22). For the silicone adhesive in any case a value smaller than
for the free chip is expected.
For the case of the epoxy-silicone adhesive there might be other explanations. Any crack at
the interface caused in the separation process or any tiny bubble in it would have the effect
of an increase in k. Another reason for the discrepancy might be found in a particularity
of the material. In chapter 3 we have worked on the principle that our polymeric materials
behave thermorheologically simple, i.e. that their short-time behaviour at high temperature
is correlated to their long time behaviour at low temperatures. A small deviation from this
assumption may cause an underestimation of the viscoelastic relaxation at low T.
Now the correlation between experiment and simulation has been established on a macro-
scopic level, it remains to tackle the experimental evaluation of solder bump reliability for
the flip-chip assembly with reverse side cooling.
4.4 Experimental Design and Procedure:
The Test-Specimen
This part is concerned with the experimental verification of solder bump reliability. Its
objective is to furnish a statistical statement about the average lifetime of a flip-chip
assembly as a function of the mechanical loads prescribed. Therefore specially prepared
test-specimens have to undergo thermal cycling under specified conditions in a thermal
cycling chamber.
To this end a test-specimen was designed which allows reproducible and precise adjustment
of loads in the range of interest. This specimen permits a statistical analysis of bump
failure accomplished by computer-controlled high precision measurements of the electrical
resistance of selected bumps as a function of the number of thermal cycles.
In the construction and preparation of the test-specimens we draw upon the experience
gained in the previous chapters. On top of this, some other guidelines or boundary condi-
tions were considered for the design:
•Comparability: All test-specimens have identical dimensions.
•Reproducibility, identical process parameters: For each test-group i.e. parameter
configuration the samples should be in the same state, in the ideal case they should
be identical. This imposes that all processes to which the samples are subjected
during their assembly should in return produce reproducible states. Therefore high
precision and low tolerances were assured by qualified standard flip-chip processes
wherever possible.
•Series-conditions: Production steps are carried out under series conditions with pro-
fessional equipment. For future impact on the market integrability into existing
processes is important. Further it helps keep tolerances down.
4.4. EXPERIMENTAL DESIGN AND PROCEDURE: THE TEST-SPECIMEN 81
•Realistic and economic design: The design which most realistically models the envis-
aged application should be tested and the materials most likely employable for this
technology should come into use.
•FE-compatibility: The specimen complies to the FE-model’s specifications.
•Low complexity and standardized parts.
All these requirements are met for the test-specimen which is presented in the following.
4.4.1 Electrical Layout of Chip and Board:
Circuitry for the Detection of Bump Failure
In order to yield information about bump failure the electrical resistance of the bumps
must be measurable. The chip in use provided two kinds of possibilities for this:
•Single-bump measurements at selected bumps (#2 and #6 as seen from each corner).
This feature permits position-sensitive and four-point currentless (therefore very ac-
curate) determination of the electrical resistance of a single bump (see 4.24). This
possibility exists for sixteen bumps, where 8×2 are located at statistically equivalent
positions due to the octant symmetry of the chip.
•So-called ‘Daisy-chain’ measurements. Hereby the resistance of all bumps plus the
wiring on the chip and board as depicted below is measured. This kind of mea-
surement considers all electrically connected bumps save the ones involved in the
four-point wiring. It is therefore not position-sensitive but serves as an indicator for
overall bump-failure. It is much less accurate since it is not wired as a currentless
measurement and the resistance is not purely due to the solder.
The individual connections for the single-bump (SB) as well as the daisy-chain (DC) mea-
surements respectively are linked to pads on the circumference of the board as shown in
figure 4.25. They can be connected via a needle-pin adaptor to a computer-controlled
Ohm-meter.
The region to the left and the right of the chip are not covered by solder-mask on either
side in order to attach the fixation directly to the board.
To reduce the warpage of the board after reflow the identical layout is again found on the
rear side. This measure had indeed the desired effect as did show the comparison to the
boards used for the set-up and had the circuits on one side only.
A slit decouples the two specimens per test-board mechanically. The twin-layout facilitates
handling of the specimens when it comes to place and measure them.
82 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
B u m p # 2
B u m p # 6
W i r i n g o n B o a r d
W i r i n g o n C h i p
A
B
U + U - I- I+
Figure 4.24. ‘Daisy-chain’-circuit on chip (red) and board (black). It is connected via
the pads labelled (A,B). In addition, currentless four-point-resistance measurements can
be performed at 8×2geometrically equivalent positions (arrows) due to octant symmetry.
One four-point circuit is highlighted (green) and magnified (centre).
4.4.2 Design and Assembly of the Test-Specimen
The test-specimen essentially comprises the features of the apparatus used for the set-up
experiments (cf. section 4.3.1) only in less universal but standardised and most compact
form. The outcome is to be seen in figures 4.26 (as built) and 4.27 (schematic, ‘exploded’
view ). The dimensions used are compiled in table 4.5 for the specimen and in figure 4.28
for the bump.
Flip-Chip Processes and Quality Checks
The qualified standard processes23 employed under series conditions24 were accompanied
23We will not go into any detail for any of these processes. Here we refer to the standard textbooks on
flip-chip technology [4,51].
24Most steps were carried out in the Robert Bosch production site in Ansbach/Germany or in the
laboratories in Waiblingen and Schwieberdingen (Germany)
4.4. EXPERIMENTAL DESIGN AND PROCEDURE: THE TEST-SPECIMEN 83
162 mm
80 mm
41 mm
Figure 4.25. The circuit board for the test-specimen. The circuits on two chips may be
contacted via pads.
by frequent quality checks25 as to UBM (bump shear strength), bump hight, underfill air-
enclosures etc. All samples which did not pass one of the checks were sorted out and not
considered any further (less than 1 %).
Anon-standard process became necessary due to the occurrence of voids (next section) in
the bumps on board level: The voids were extracted under vacuum.
Reproducible Application and Curing of the Adhesive
The chips have to be glued to the plate before any of the other boundary conditions or
loads are applied. This corresponds to the series-conditions where the last step would be
the closure of the housing under pressure and hence the application of external loads. The
chip must then already adhere to the heat-spreader. Moreover, any load applied to the chip
at curing temperature could do irreversible damage to the bumps and alter our required
identical initial state preparation26.
The following procedure furnished the best and most reproducible results for the adhesive-
filled gap width bgap =had = 265 ±20 µm27:
•The adhesive is dispensed in x-shape onto the chip. Then the board is put chip-down
onto the plate where the spacers at the four holes adjust the specified gap width bgap
for the adhesive according to:
bgap =bsp −(bsm +buf +bch), (4.15)
25This test-programm was absolved according to the quality standards specifications of the Robert Bosch
GmbH / Germany
26The underfill cannot stiffen the assembly as required at TC>> Tgwith the consequence that the
bump is strained.
27The scatter is due to the warpage of the board and one of the reasons why the gap width was increased
to hold the error down to less that 10 %. See also section 4.3.1 or 4.3.5
84 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
10 mm
Figure 4.26. The test-specimen as it was built 220 times. One aluminium plate is de-
mounted to permit view on the chip. Despite the plate the sample still fits in the needle-pin
adaptor in figure 5.17.
Nut
Backplate
Screw
Spring
Centering Slide
Bolt
Spacer
Board
Chip & Adhesive
Plate
Figure 4.27. ‘Exploded view’ of the test-specimen and its individual components.
4.4. EXPERIMENTAL DESIGN AND PROCEDURE: THE TEST-SPECIMEN 85
Dimensions of Test-Specimen
Item Dimensions
Plate 50 ×50 ×4mm
Nuts M4
Spacers M4,8mm φ ×b
Screws M4×50 mm
Bolt 6 mm φ
Screw Positions 41 ×41 mm
Board 82 ×82 mm ×b
Chip 10 ×10 ×0.375 mm
Pitch 250 µm
Footprint 230 ×125 (btm),100 (top)×45 µm
Bump (Height) 100 µm, see also figure 4.28
Underfill (Thickness) 65 µm
Soldermask (Thickness) 35 µm
Thermal Interface (Thickness) 265 µm
Back-plate 50 ×50 ×1.5mm
Table 4.5. Constant dimensions common to all test-specimens. bsignifies a variable
thickness (parameter) of the respective item, φa diameter.
where the thicknesses of soldermask, underfill and chip are subtracted from the spac-
ers’ thickness bsp. The amount of adhesive material is just enough to fill the whole
gap without bubbles up to the edge of the chip and forms a fillet as depicted in figures
4.21. The exact quantity is important, since an encapsulation is to be prevented as
it could severely crack down on the lifetime of the chip as pointed out in [11].
•Four small screws are inserted and gently tightened to keep the chip in position as
the adhesive is cured.
•Either of the two adhesives is cured for fifteen minutes at the cure temperature of
the underfill TC= 160 oC. (Both adhesives are specified for this process.) This has
the following advantage: The flip-chip assembly reaches again its stress-free state it
had when the underfill was cured. This puts us in the comfortable situation that
we deal with a defined state at this temperature to start from in our computational
lifetime prediction. Shrinkage of underfill and adhesive is negligible according to the
manufacturer’s specifications.
•The assemblies are left to cool down to room temperature and the screws and spacers
are removed.
Application of Loads and Boundary Conditions
In the next step the individual groups had to be configured i.e. their set of parameters
adjusted.
For the non-adhesive groups there is no problem and the test-specimen can be assembled
as pictured in figure 4.27:
86 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
7 5 µ m
1 6 2 µ m
1 2 5 µ m
4 5 µ m
1 0 0 µ m
1 0 0 µ m
4 7 µ m
2 3 0 µ m
Figure 4.28. Dimensions of the bump as seen along the PCB track. The skew arrow
indicates the length.
•The gap filler (sticky side) is attached to the plate and the four screws are put
into their holes and fixed. In the order depicted, the spacers which specify the
displacement dof the respective group are put in their position. The total thickness
of the spacers btot now measures:
btot =bsp +d, (4.16)
where bsp is the thickness of the spacers from equation 4.15 to which the displacement
which represents the load is to be added.
Then board, spacers again (here they serve only as washers), nuts and plates are
added. The nuts on board and steel plate are not tightened yet.
•The steel plate labelled ‘centering slide’ serves to hold a bolt (well defined contact
surface where it touches the board, identical for all samples) centered at the position
of the chip. It is only held by the force of the spring and is not fixed anywhere. Is
other function is to cage the spring. A force of F≈50 Nis not to be trifled with.
•Now the force is applied. To increase precision and reduce assembly time, small-scale
production equipment driven by a pneumatic cylinder was designed (see figure 4.29
(right)): A very important feature represented the in-situ measurement of the applied
force for each sample.
•As the cylinder compresses the spring with the correct force, the nuts at the backplate
are fixed. The force can not change any more now.
•As a last step the nuts at the board are tightened. The board is now in the intended
position: parallel to the plate at the four points as in our set-up experiments (section
4.3.1). So no in-plane forces which could cause the board to slide are active – as
would have been the case if the board was fixed before the application of the force.
4.4. EXPERIMENTAL DESIGN AND PROCEDURE: THE TEST-SPECIMEN 87
Figure 4.29. To the left: All test-specimens (440 chips in 24 configurations) just before
they go to the thermal cycling chamber. They are taken out and checked for bump failure
in periodic intervals.
To the right: Small-scale ‘production’ equipment: Pressure application device for assembly
process. An air pressure cylinder allows precise compression of the spring as the resulting
force is adjusted and measured by a load cell (cable).
(Other washers with grip did not perform as well but put some inclination on the
board.)
For the adhesive groups the procedure is a bit more complicated but follows in principle
the same steps. Here it is important that the spacers are inserted before the screws are
added (it does not function otherwise). Then the rest of the sample is put together, the
force applied and then all nuts tightened, the ones on the board last.
Automatized Recording of Bump Failure
through measurement of electrical bump resistance was used. At specified intervals all
specimens were taken out of the cycling chamber to be checked for their bump resistance.
An in-situ measurement (permanent electrical check for bump failure) was beyond every
means due to the immense number of contacts (see 4.29). To this end each sample was
put into a needle-pin adaptor (see figure 5.17) and a program28 was run which performed
all necessary steps.
28The program was written in HP-VEE.
88 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
4.4.3 Extraction of Voids under Vacuum
Voids were found in the bumps after reflow on board level as is to be seen from the pictures
in figure 4.30. As can be seen also from X-ray photographs in figure 4.31 (a), the voids
do emerge in a wide range of size from b=5..50 µm and are distributed over the bump
neither deterministically (always at the same position) nor randomly (small bubbles all
over the bump, sponge-like): Voids tend to gather around and below the pad where they
stay pinned after they float upwards during reflow. There they reduce the effective cross
section which may also reduce their compliance to withstand fatigue cracking and therefore
the lifetime of the bump. Above all it is the task of the bump to resist fracture rather than
exhibit a large load carrying capability [15]. Voids are classified to be harmful depending
on their size and location [12], [104]. They were reported to cause major concern if they
are situated close to the connecting surfaces like pad or land [105]. On the other hand it
has been reported [106] that voids may have the ability to stop already propagating cracks
thus prolonging the lifetime of bumps.
In any case: Irrespective of whether voids do prolong or reduce the reliability of a bump the
configuration in which they occur here disturbs the preparation for statistical equivalence
of the bumps and the whole assembly: The bumps are not in a well-defined initial state
identical for all bumps and so it is unlikely that the average lifetime for bumps with voids
will only differ from a scaling factor from an impeccable configuration. This could cause a
blurring of the statistical mean value for the cycles to failure. Moreover there is no typical
void-configuration which could be modelled and simulated.
Pad Ø:
75 µm
Pad Ø:
125 µm
(a) (b)
Figure 4.30. Voids just below the pad as they appear after reflow on board level. The
chip and UBM have been removed to permit view on the solder bump. On the right the
‘shoulder’ is to be seen which is typical of this bump shape due to the small pad diameter.
For this reason the voids had to be eliminated.
A succinct parameter study was conducted in order to try to eliminate this phenomenon.
Varied parameters were: The reflow profile (temperature and time above liquidus), the
flux (tackiness, activity, volume), solder paste (manufacturer), the type of passivation on
4.4. EXPERIMENTAL DESIGN AND PROCEDURE: THE TEST-SPECIMEN 89
chip and the UBM (different companies) [107]. Here it is important to point out that the
aluminium trays the chips were reflowed on had no influence on the creation of voids.
It turned out that none of the parameters varied in this study could account for the prolific
occurrence of voids and that it was beyond the scope of this thesis to optimize this process
which would constitute a time- and resource-demanding technological development. A
decision was therefore made to eliminate the voids by a vacuum process.
(a) (b)
250 µm 250 µm
Figure 4.31. X-ray pictures of the same group of bumps before (a) and after vacuum
treatment (b).
0100200300400500
0
50
100
150
200
250
Temperature
Time [s]
1E-5
1E-3
0.1
10
1000
Liquidus
T = 183 ˚C
Pressure [mbar]
Figure 4.32. Process parameters of vacuum treatment on a hot plate used for obtaining
the above depicted void reduction. The curves depict only a qualitative behaviour, but
extremal values are to scale.
This vacuum process29 was carried through on a hot-plate according to the scheme depicted
in figure 4.32 for four chips at a time. This process step was optimized according to the
following guidelines:
First, obviously, it should eliminate the voids to a satisfactory degree. Then the treatment
itself should be as short as possible using as low a vacuum as possible not to cause any
29Employed was a computer controlled hot-plate with vacuum-pump, a special design by SRO-Systems.
90 CHAPTER 4. FINITE ELEMENT MODELLING AND EXPERIMENTAL DESIGN
harm to the organic board. The result is depicted in the X-ray photographs in figure 4.31
to the right: The size and number of voids was greatly reduced by the vacuum process.
Now the preparations for the simulative and experimental study are all done. A numerically
optimized and calibrated parametric FE-tool is set up to accurately evaluate the creep
stain in the solder bumps and thus make a predictive statement about reliability. For the
experimental part a test-specimen has been designed which is able to verify the numerical
results in a thermal cycling test. The results of either of the two and their correlation will
be the subject of the next (and concluding) chapter.
Chapter 5
Results and Discussion–
Simulation vs Experiment
In this chapter the results of the finite element simulations are stated and interpreted
for the individual load configurations. Therefore a ranking is drawn up according to the
varied input quantities. Then the FE-results are compared to the statistical outcome of
the experiment for verification.
Within the framework of the Coffin-Manson approach a correlation is established which
enables lifetime assessment and extrapolation to other, not explicitly tested but interesting
parameter and load configurations for the flip-chip assembly with attached heat-spreader.
Some configurations could not be analysed with respect to bump reliability as die crack
did occur. A fracture criterion was applied to explain and predict this phenomenon.
At the end of this chapter we draw some conclusions, summarize the functional dependence
of solder bump reliability on the varied parameters, give design guidelines and an outlook.
5.1 The individual Configurations and Applied Loads
The test-specimens are now to undergo the thermal cycling test. The available chips were
divided up in 24 configurations, most of which containing 20 samples, a number which is
considered sufficient for a Weibull-based analysis of solder bump failure. The chips were
distributed according to the following philosophy and list of priority:
•All samples should undergo the same thermal cycling test, i.e. they should all be
thermally equivalent. No variation according to the thermal loads is to be tested.
•The mechanical loads should be applied in a way which allows a variation of the
value in the required range as well as a cross check to see the effect of force and
displacement independently.
•Both a thick and a thin organic board are to be tested.
•Of the thermal interface materials the two gap fillers and two adhesives of different
physical properties (soft, hard) are to be employed.
91
92 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
•Some configurations should be tested without loads to serve as reference to an uncon-
strained flip-chip assembly. For the same reason a group featuring only an attachment
by an adhesive without further loads should be tested.
As there was a limited number of chips, the testing-scheme drawn up exhibits several
preferences. So not the full program for the whole matrix was conducted. Some parameter
variations have to be limited to one type of interface-material. The choice which was taken
is explained in the next section.
5.1.1 Mechanical Loads and Characteristic Curves
All necessary information is now given to develop a distinct picture of what loads are
present in a housing in reality. Each board thickness gives rise to a set of characteristic
curves by which one may determine – as for a transistor – the characteristic parameters
for the work point.
Classification of Load Configurations
#Item Code Meaning
1Letter: KPure flip-chip (no attachment)
Kind of reverse side attachment L FC with voids (no attachment)
(thermal interface material) FFlex foil
CCarbon foil
S Silicone adhesive
EEpoxy-silicone adhesive
2Number: 0 No displacement
Displacement 1d= 100 µm
2d= 200 µm
3Letter: G Gap closure
Force AWork point
BOverload
Mby negative Displacement
– Zero Force
4Letter: uThin board
Board thickness x Thick board
Table 5.1. These abbreviations or encodings are used to specify the loads and materials
of the individual configurations. See also table 5.2.
These characteristic curves are depicted in figure 5.1 and are to be read as follows: From
section 4.3.4 it is known that the critical limit for the displacement is dc= 300 µm. Beyond
this value die crack is likely to occur. For this reason let us specify d2=dG= 200 µm as
maximum gap width, encoded by the number ‘2’ (for 200). To bridge this gap the board
has to be pressed from below by the external force F=FG(x-axis) and follows a linear
relationship up to the point where the chip touches the thermal adhesive. This linear
5.1. THE INDIVIDUAL CONFIGURATIONS AND APPLIED LOADS 93
0510152025303540
0
50
100
150
200
250
T = 25 ˚C
f = 0f <f >
k >
k <
"G" -
Gap
Closure
Specified Gap Width [µm]
F
SPEC
F
N
"2" =
Max.
Gap
"1" =
Med.
Gap
"B" -
Over
Load
"A" -
Work
Point
Risk of Die Crack
@ d > 300 µm
Exp.
Displacement [µm]
External Force [N] (Thin Board, b = 0.8 mm)
0
100
200
Figure 5.1. Force vs Displacement: Characteristic curves for thin board.
behaviour and the error-bars have been derived in figure 4.10. At this point the chip exerts
no pressure (internal force) f=0Non the interface material yet.
Now the extra normal force FNis applied to compress the interface material for optimum
thermal contact. FNis specified by the manufacturer. Throughout this work FN=10N
has been taken, a value which is for both gap fillers above the specified minimum force.
This force cannot displace the board any further, therefore the curve flattens out parallel
to the x-axis. The compression of the interface material is negligible compared to the
accuracy the gap-width can be specified (δd ≈±15 µm from figure 4.10). This applies
for the adhesives in any case, but also for the gap-fillers (figure 3.18). This point is called
the work point ‘A’ for the given displacement at room temperature. It is furthermore
characterised by a curvature kand an internal force f=FN. Its external force is thus
Example: F=F2Au =FG+FN=1
pbb=‘u’
dG|G=2 +FN, (5.1)
where pbis the thickness-dependent board compliance defined in section 4.3.1 and b=‘u’
stands for the thin board. The same scheme is true for a medium-sized gap of width
dG=d1= 100 µm. This curve is depicted below the first one and is characterised by a
smaller deflection k.
Let us assume that a chip has to be specified to function for a work point Fspec =F2Au,then
the situation may arise where the tolerance of the housing causes the gap to be smaller and
the work point gets shifted down to lie on the lower curve. This represents an ‘overload’
situation denoted by ‘B’. The internal force fis increased, since there is less force needed
to displace the board. It assumes the value of f1Bu =f2Au +1/cb∆dG,where∆dGis the
94 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
020406080
0
50
100
150
200
250
T = 25 ˚C
f = 0f <f >
k >
k <
"G" -
Gap
Closure
Specified Gap Width [µm]
F
SPEC
F
N
"2" =
Max.
Gap
"1" =
Med.
Gap
"B" -
Over
Load
"A" -
Work
Point
Risk of Die Crack
@ d > 300 µm
Exp.
Displacement [µm]
External Force [N] (Thick Board, b = 1.2 mm)
0
100
200
Figure 5.2. Force vs Displacement: Characteristic curves for thick board.
difference in gap width, which is chosen half the maximum gap width in expectation for a
good resolution. This situation has to be managed by the chip also in reality. Therefore it
is incorporated in the test-program.
These are the two points of practical interest for the design of a real housing situation.
But we need to cross-check if it is the smaller displacement or the higher effective force on
the chip that now affects bump life if it does at all. To this end the points F1Au and F2Bu,
which represent the lowest and highest loads respectively, are also checked for. The same
is true for the thick board and is depicted in the second diagram, figure 5.2.
Following this philosophy a test plan was drawn up which is depicted in table 5.2. For
better visualization the main categories which the test-configurations can be divided into
are illustrated in figure 5.3. So the line-up of the groups presents itself (table 5.2):
•K0u, K0x
The unconstrained chips ‘K’ are tested for both boards to serve as reference group.
For thermal equivalence to the other samples they need to be connected thermally to
the aluminium plate via their reverse side. This is accomplished by a very soft gap
filler which merely touches the flip chip and does therefore not represent a mechanical
load. This situation is depicted in figure 5.3 (a).
•L0x
The group ‘L’ consists of chips which did not undergo the vacuum process. Therefore
their bumps do still contain voids (figures 4.31 and 5.3 (a)).
5.1. THE INDIVIDUAL CONFIGURATIONS AND APPLIED LOADS 95
Test-Configurations and Applied Loads
Group and Material Code d F b Type
Units [µm] [N] [mm]cf. Fig. 5.3
Flip Chip, no BC K0u 0 - 0.8 (a)
K0x 0 - 1.2 (a)
FC with Voids, no BC L0x 0 - 1.2 (a)
FC, Flexible Foil F1Au∗(200); 100 17.7 0.8 (c)
F1Bu∗(225); 100 25.4 0.8 (c)
F2Au 200 25.4 0.8 (c)
F2Bu 200 33.1 0.8 (c)
F1Ax 100 30.3 1.2 (c)
F1Bx 100 50.6 1.2 (c)
F2Ax 200 50.6 1.2 (c)
FC, Carbon Foil C1Bu 100 25.4 0.8 (c)
C2Au 200 25.4 0.8 (c)
FC, Silicone, no BC S0x 0 - 1.2 (b)
FC, Epoxy-Silicone, no BC E0x 0 - 1.2 (b)
FC, Epoxy-Silicone E1Au 100 17.7 0.8 (c)
E2Au 200 25.4 0.8 (c)
E1Ax 100 30.3 1.2 (c)
E2Ax 200 50.6 1.2 (c)
FC, Epoxy-Silicone, neg. Displ E2Mu -200 15.4 0.8 (d)
FC, Flexible Foil, neg. Displ F2Mx∗(-100); -200 20.3 1.2 (d)
FC, Silicone S1Au 100 17.7 0.8 (c)
S2Au 200 25.4 0.8 (c)
S1Ax 100 30.3 1.2 (c)
S2Ax 200 50.6 1.2 (c)
Table 5.2. Overview over the individual configurations. The code refers also to the values
for the applied loads (see table 5.1). The groups marked with an asterisk feature different
loads (given in brackets) as originally specified due to a reduction of foil-thickness dur-
ing thermal cycling. For Configurations with negative displacement (‘M’) the force is not
externally applied by a spring but by the bending of the board itself.
•F1Au, etc.
The flexible foil ‘F’ seems a promising solution for thermal management. Therefore
it undergoes (nearly) the full program depicted in figures 5.1 for both board thick-
nesses. Unfortunately die crack occurred in most configurations due to an unforeseen
reduction of the foil-thickness. The remaining groups (asterisk) are still incorporated
in the analysis. Above this situation is depicted in (c).
•C1Bu, C2Au
The carbon foil is only tested for the points of practical interest. The off-line values
96 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
(a) (b)
(c) (d)
Void
F
d
Fix
b
Figure 5.3. The main test categories depicted schematically (cf. table 5.2 and explana-
tions below). Displacements dare depicted as black arrows which denote concave (c) or
convex (d) bending of the board. An external force is symbolised by a bold black arrow.
C1Au and C2Bu are not tested for lack of chips. The cross-check is expected from
another configuration. Again this situation is the one depicted in (c).
•S0x, E0x
The adhesives ‘S’ and ‘E’ are put to a test without any mechanical loads save their
reverse side attachment (see figure 5.3(b)). In the first place they are incorporated as
a less complex configuration for comparison to the computational results. Although
these groups do not reflect the boundary conditions for flip-chip reverse side cooling
in a casing (cf. figure 2.4), they still mimic the situation of a small, chip-sized heat-
spreader attached to the chip.
•E1Au, etc.
The Epoxy-Silicone ‘E’ groups are tested for the two work points only (for lack of
chips). The remaining two configurations can be evaluated by simulation if needed.
This configuration is represented by (c).
•E1Mu, F2Mx
This principle is depicted in figure 5.3(d) and tested to see if a curvature which
counteracts the tendency of the concave thermal bilayer1bending of the flip-chip on
board. These groups have no external force applied but the chips are only pressed
against the adhesive or foil with the reaction force of the board caused by a negative
displacement of the board. At room temperature this compressive internal force is
readily evaluated as F2Mu,x =f2Mu,x =1/cbdG>F
N,whichis,asithastobe,
always greater than the normal force FNneeded for sufficient thermal contact.
•S1Au, etc.
The same as for the E1Au groups, only with Silicone adhesive ‘S’.
1Chip and board determine the sense of curvature due to their difference in the CTE.
5.1. THE INDIVIDUAL CONFIGURATIONS AND APPLIED LOADS 97
5.1.2 Thermal Loads
The test-specimens finally undergo air-to-air thermal cycling in a two-chamber system. As
a check we have recorded the temperature over the duration one (stable) cycle, since due
to the large thermal mass represented by the aluminium plates it is expected that the
given temperature profile of the chamber does not coincide with the one measured at the
test-vehicle.
0.0 33.0 66.0
Time [min]
120
100
80
60
40
20
0
-20
-40 0 min, -38 °C
#1
#2
#3
#4
#5
#6
7 min, 90 °C
16 min, 120 °C
33 min, 125 °C
40 min, -10 °C
49 min, -38 °C
#2#3
#5 #4
#1 (Air)
Figure 5.4. Temperature as recorded during thermal cycling at different positions on the
test-specimen. The chamber was fully loaded during the measurements. Below: Position of
the temperature sensors.
This is depicted in figure 5.4, where the individual graphs correspond to different loca-
tions of the temperature sensors on a representatively positioned test-specimen. First one
notices indeed the retardation with respect to the chamber temperature (#1). But then
it is important to see that there seems to be hardly any temperature gradient within the
assembly since plate (#4,5) and chip (#3) show nearly the same profile, whereas the board
(#2) follows with some distance the chamber air due to its small heat capacity and low
98 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
thermal conductivity. It is therefore a good assumption to assume a homogeneously dis-
tributed temperature across the chip where the creep law for the solder bumps displays a
very sensitive temperature and rate dependence.
This outcome necessitates indeed the attachment of a heat-spreader also to the normal
flip-chip test groups K0u,x as they would otherwise ‘see’ cycle (#2) instead of (#3) as all
other samples do.
The dotted, linearised temperature versus time function is taken to serve as thermal load
input for the simulation.
5.2 Results of Computational Analysis
The simulation starts at the stress-free point which is assumed to be identical to the curing-
temperature of underfill and adhesive respectively (see also [31,32]). Here, Tcure =Tref =
160 oC. At this point all ‘layers’ are assumed to be parallel to one another, even after a
second heat-up to this temperature for the curing of the adhesive this initial condition is
assumed to be reestablished since Tref is well above Tgof both underfill and soldermask.
The results obtained by speckle interferometry in section 4.3.1 underpin this assumption.
According to information provided by the manufacturers shrinkage of the adhesives is
negligible.
For these reasons it is enough to simulate both of these curing processes simultaneously as
the multi-layered assembly is cooled down to room temperature. This is depicted in figure
5.5 (first load step LS1).
In a second load step LS2 the mechanical loads are applied. This corresponds to simulating
the assembly of the test-specimen. The model is then left to relax and to accommodate to
the loads for some time before the actual thermal load cycle begins in the third load step
(arrow).
This preparation is important to model the correct initial state of the different configura-
tions and follows the steps conducted in the experiment as explained in the last chapter.
In this respect figure 5.5 represents the drive and response functions of the physical system
we are about to observe. The graphs describe the loaded group C1Bu, i.e. an assembly
using a carbon foil, medium loads and a thin board. The creep strains are recorded from
the point where the thermal cycle starts since our model considers no singular (initial)
events but only the creep strain accumulated over one cycle as required by the Coffin-
Manson approach. As expected, the bumps exhibit the largest rise in creep strain during
changes in temperature at high temperatures where large thermal strains and can cause
maximum creep deformation of the solder due to a high creep rate. The outer bump (#22
in figure 5.6) accumulates more strain induced damage than the inner one (#6). So for
a flip-chip assembly under these mechanical loads bump creep strain increases with the
bump’s distance from the neutral point (DNP). This may indicate a dependence on chip
size, too.
2The selection of bump #2 and #6 was imposed by the electrical chip layout (figure 4.24).
5.2. RESULTS OF COMPUTATIONAL ANALYSIS 99
0200040006000800010000
-50
0
50
100
150
200
Start of
Simulation
T
R
= 25 ˚C
T
C
= 160 ˚C
Temperature
Temperature [˚C]
Total Simulation Time t [s]
0.00
0.02
0.04
0.06
0.08
2.
1.
2. Creep Cycle:
Start End
LS 2
LS 1
1. Creep Cycle:
Start End
Group: C1Bu
Equivalent Creep Strain
Outer Bump (#2)
Inner Bump (#6)
Figure 5.5. Drive and response: Temperature cycles as measured (cf. figure 5.4) and
simulated as sequence of load cases. The resulting creep strain accumulates monotonically
right from the beginning (t=0) and is recorded for each bump over a sequence of cycles.
#2
x
y
z
NP
750 µm
1000 µm
3250 µm
250 µm
#6
Axis of
Symmetry
Figure 5.6. Schematic of flip-chip model with bump-location and orientation (not to
scale). The bumps are numbered starting from the outermost bump, i.e. bump #2 is the
second bump from the corner (cf. figure 4.24). The lower left corner represents the neutral
point (NP). Due to the specific symmetry it suffices to model only one octant.
100 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
Remarkable in figure 5.5 is the fact that the creep strain per cycle seems to show a conver-
gence behaviour as it changes (in this case decreases) for the second cycle. Apparently the
flip-chip assembly accommodates to the external loads after the first cycle and ¯εcr becomes
stable. This will also be explained below in the course of the next sections.
5.2.1 Ranking of Configurations
The results of the simulations of the configurations tested in the cycle experiment are
depicted in figure 5.7 for the first cycle and in figure 5.8 for the second cycle. The ranking
is determined by the equivalent creep strain averaged over both bumps.
Figure 5.7. Ranking of configurations for the first simulated cycle sorted by equivalent
creep strain ¯εcr. Depicted are also the accumulated normal εzz and shear components εxz
and εyz of the creep strain tensor εcr
ij for outer and inner bump. The numerical values are
also given in table D.1. During the first cycle the system goes through a phase of transient
response before convergence is reached in the second cycle. The asterisk refers to table 5.2,
the colours/letters (a-d) to the categories of figure 5.3.
In the diagram the dominant strain tensor components are depicted individually for inner
(#6) and outer bump (#2). For reference see again the schematic of the chip in figure 5.6.
5.2. RESULTS OF COMPUTATIONAL ANALYSIS 101
The first observation is that there is a distinct difference as to the individual configurations,
i.e. there is a ranking and a dependence on the mechanical loads which cause an increase
in equivalent creep strain in all configurations. Hereby the values range from ¯ε>0.03 for
the best configuration up to ¯ε<0.06 for the worst. This is nearly an increase by a factor
two for the first cycle! Apparently mechanical loads do have a significant and harmful
influence on lifetime, a tendency already indicated by [11] who considered chips attached
to a heat-spreader by an adhesive (comparable to the groups E0x or S0x) without fixation.
Figure 5.8. Ranking after the second (stabilized) simulated cycle.
On simulation of a second cycle the system relaxes and there is a creep strain redistribution
to the effect of a smaller equivalent creep strain for all constrained chips. The order of
the ranking changes, too, i.e. the degree of relaxation depends upon the constraints. From
figure 5.8 we find:
•The most reliable configurations are the unconstrained flip-chip assemblies K0u,x
together with the adhesive groups without displacement E0x and S0x, followed by
groups featuring displacement and fixation.
•For the groups without displacement and fixation on a thick board: The silicone-
epoxy adhesive group E0x shows a slightly better reliability than the corresponding
102 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
unconstrained chip K0x. This is a quite unexpected result. The silicone adhesive
S0x, however, comes last for the considered configurations.
•A displacement (with simultaneous fixation) considerably increases bump creep strain
and hence reduces reliability.
•For the same interface material the larger displacement produces the lower reliability.
•Board thickness is a dominant factor. Thin boards prolong lifetime throughout all
configurations.
•Groups using a gap-filler (foil) prove slightly more reliable than those with an adhe-
sive. The epoxy-silicone adhesive yields slightly better results than the silicone-based
one. A distinction between the gap-fillers is hardly possible.
•A convex curvature of the chip (E2Mu) seems to produce slightly better results
(cf. E2Au). This, however, is changed when a thick board is used (cf. F2Mx).
•The influence of a force cannot be judged at this point yet. We will come back to do
this later in this work.
The influence of the individual parameters is extracted and again depicted in figure 5.9.
The dominance of the board thickness and fixation after the transient response of the
first cycle indicates that eventually flip-chip reliability is again mainly governed by the
mismatch between chip and board. Additional mechanical loads like a displacement or the
type of interface material do exert a smaller influence, but their effect is amplified by a
fixation or a thicker board.
The increase in creep strain of the constrained groups with respect to the normal flip chip
is largely due to an increase in shear strain εxz and εyz. The latter component assumes
smaller strain due to a more favourable position (less close to the chip edge as seen in figure
5.6) of the bump within the chip. The same argument applies to the always smaller shear
strains of the inner bump, an effect which is stronger for groups with mechanical loads
and most pronounced for the foil groups, then the silicone groups and least for the epoxy-
silicone groups. This tendency is correlated to the movability of the die during cycling
which is constrained most for the epoxy-silicone adhesive as depicted in figure 5.14. The
normal component εcr
zz shows the inverse behaviour. The inner bump yields slightly higher
values. This illustrates that the die does not deform exactly parallel to the board but that
its centre has a higher out-of-plane amplitude than the corners. Still the differences are
only minute. As far as the equivalent creep strain is concerned though, ¯εcr
#2 ≥¯εcr
#6 from
figures 5.7 and 5.8).
Further, the εzz component hardly shows any dependence on the applied loads and is
mainly caused by the comparatively large thermal mismatch between bump and underfill
(αUF(T<Tg)=44ppm/K) and solder (αSnPb =24ppm/K). For the unconstrained chip
K0u,x this contribution is the dominant part, a tendency which has already been pointed
out by [24]. As the soldermask with an even higher CTE of αSM(T<Tg)=72ppm/K fills
one third of the gap between chip and board this tendency is even aggravated [30]. In
5.2. RESULTS OF COMPUTATIONAL ANALYSIS 103
Cu
Eu
Su
Ex
Sx
200 µm
100 µm
-200 µ
m
3.4
3.6
3.8
4
4.2
4.4
0x
1u
2u
1x
2x
Silicone (S)
Epo-Sil (E)
Carbon (C)
Flex (F)
3.4
3.6
3.8
4
4.2
4.4
K0
E1
E2
S1
S2
Thick (x
)
Thin (u)
3.4
3.6
3.8
4
4.2
4.4
K0u
K0x
E2Mu
C1Bu
E1Au
E2Au
S2Au
E1Ax
S1Ax
Alle (Fix, d, F)
3.4
3.6
3.8
4.0
4.2
4.4
All: Fix, d, F
Adhesive only
Normal FC
Attachment Board Thickness
DisplacementInterface Material
Load (Group)
Variation
ε
cr
[%]
ε
cr
[%]
ε
cr
[%]
ε
cr
[%]
+
_
Figure 5.9. Ranking according to individual parameters. Creep strain is averaged over
both bumps.
figure 5.10 the effect of underfill-solder mismatch is illustrated for the assembly used in
this work and a matched system for comparison.
In figures 5.11 and 5.12 the evolution of the creep strain components over the period of the
first and second cycle is again depicted for two representative groups, the unconstrained
chip K0u and a carbon-foil configuration with medium loads C1Bu. For the sake of clarity
the strain is zeroed after the first cycle.
Here we see that the application of external loads does indeed manifest itself in a large
increase of the shear strain components with respect to to the unconstrained case K0u.
This is true for all loaded groups (figure 5.7): Shear stain becomes the ranking-governing
tensor component for all groups with displacement and fixation. For the unconstrained
flip-chip assembly on the contrary the normal strain represents the governing part for the
equivalent creep strain. This tendency prevails also for the second cycle (figure 5.8).
But from the first to the second cycle a convergence or relaxation behaviour is observable
resulting in a redistribution of creep strain as follows: First, all creep strain components
104 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
01000200030004000
-50
0
50
100
150
T
Time [s]
0.00
0.01
0.02
0.03
Outer
bump
Group: K0u
CTE
UF
> CTE
SnPb
Eqv.
zz-Comp
xz-Comp
CTE
UF
= CTE
SnPb
Eqv, etc
Temperature [˚C]
Equivalent Creep Strain
Figure 5.10. Effect of the underfill CTE on creep strain. A thermally matched solder-
underfill system largely reduces (normal) creep strain thus improving reliability.
display an increase at low temperatures (cf. figures 5.11 and 5.12) irrespective of the group.
Second, at high temperatures the normal component εcr
zz still rises for all groups, and
largest values of this component are obtained for the unconstrained chip (cf. figure 5.8).
All loaded groups, however, feature lower values of normal creep strain. Third, groups with
a displacement d= 0 display shear strain components which relax to lower values (see again
figure 5.12). For groups with no displacement, however, there is no such relaxation as the
graphs in figure 5.11 show. This is also true for groups which only feature a reverse side
attachment by an adhesive like E0x or S0x.
This redistribution of strain might be due to the viscoelastic properties of the underfill
and soldermask as it appears in any group irrespective of loads and board-properties (elas-
tic/viscoelastic). It is furthermore in accordance with the respective stress components
plotted in figure 5.13. Higher stress goes along with less creep as the solder displays more
elastic behaviour at this point at low Tand does not transform the stress into inelastic
deformation. The slight increase of creep strain at low temperatures for the second cycle
might be due to local plastic deformation of the pad. Interestingly the stress does not go to
zero not even at high temperatures. The movements have not come to rest in the package.
Due to the mismatch in CTE with the underfill, the bump is always under compression
during the cycle.
Still the unexpectedly good result of the epoxy-silicone adhesive group without loads E0x
needs explaining: All loads and constraints increase the shear components of bump creep
strain, but slightly reduce the normal component with respect to the values for the un-
constrained chip K0x (see figure 5.8). Due to the underfill-solder mismatch, this normal
component is extraordinarily high (εcr
zz ≈0.03) and dominates in this case the equivalent
creep strain on which the ranking is based. So although the constrained group E0x fea-
tures larger shear strain and should therefore be less reliable, this is compensated by a
larger normal component for the free group K0x. Interestingly, the constrained group can
so outdo the free chip K0x with respect to reliability.
5.2. RESULTS OF COMPUTATIONAL ANALYSIS 105
0200040006000800010000
-50
0
50
100
150
Outer bump
T
Group: K0u
Time [s]
0.00
0.01
0.02
0.03
0.04
0.05
Temperature [˚C]
Eqv.
zz-Comp
xz-Comp
Creep Strain Component
Figure 5.11. Creep strain components’ evolution for unconstrained chip K0u,bump#2.
0200040006000800010000
-50
0
50
100
150
Outer bump
T
Group: C1Bu
Time [s]
0.00
0.01
0.02
0.03
0.04
0.05
Temperature [˚C]
Eqv.
zz-Comp
xz-Comp
Creep Strain Component
Figure 5.12. Creep strain components’ evolution for loaded chip C1Bu,bump#2.
0200040006000800010000
-50
0
50
100
150
200
Total Simulation Time [s]
-120
-100
-80
-60
-40
-20
0
20
40
60
80
Ts
xz
Stress-free
Points
eqv
s
zz
C1Bu
K0u
Temperature [˚C]
Stress [MPa]
Figure 5.13. Corresponding evolution of stress, bump #2.
106 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
This result for E0x, however, cannot be generalized, as for a (normally used and technically
relevant) matched solder-underfill system the shear strain part would dominate and the
ranking would favour the unconstrained chip K0x as expected.
5.2.2 Correlation of Curvature and Creep Strain
The curvature (measured as deflection k) has been used as tangible and accessible quantity
for the global or macroscopic behaviour of the flip-chip assembly to determine its current
state under mechanical and thermal loading. Its measurement did serve for fine-adjustment
of the simulations. For this reason it is again used in the following to examine if there is
a correlation between the curvature itself and the creep strain. The next two pages show
the simulated movement of the chip diagonal over the first two cycles. Each curve (figure
5.14) corresponds to a certain T(t), where the full cycle is divided into seven load cases,
i.e. we deal with eight curves. The corresponding accumulated creep strain averaged over
both bumps per load step is given by the graphs in the lower right diagram. Chosen were
five groups, the unconstrained chip K0u and the groups having the same displacement of
|d|= 200 µm and the same board thickness and external force (save E2Mu – due to convex
bending), but feature different thermal interface materials. A red arrow marks beginning
and end of the cycle. All graphs do have the same scale.
First of all the qualitative difference is remarkable. Different materials constrain the move-
ment of the chip to a different extent. The ‘free’ chip K0u (a) moves as predicted since
it has been the object of study and calibration in the preceding chapters. As expected,
the harder epoxy-silicone adhesive allows hardly any movement, whereas softer adhesive or
gap-filler do. The directional tendency to curve is prescribed by the sign of the displace-
ment: For the group with negative displacement (b) the curvature results in a convex state
of bending at nearly all temperatures, whereas for the group with positive displacement
the chip bends concavely (d). Here it is evident that the curvature is not proportional to
kany more as was supposed for the chip without adhesive (cf. section 4.3.5 or figure B.6).
For the carbon foil group (c) the mechanical load causes a large increase in curvature with
respect to to (a). The silicone adhesive (e) displays an interesting reaction: At high tem-
peratures the chip hardly ‘feels’ the adhesive due to its very low E-modulus. This changes
at low Tsince the silicone adhesive exhibits a rise in Eand develops considerable strain
due to a very high CTE (α= 175 ppm/K) during cooling down. This flattens the chip.
This extra movement the chip has to undergo each cycle reduces its reliability with respect
to groups with similar loads as can be seen for the interval in which the temperature is
ramped up (f). This effect is even larger in combination with a thick board.
As can be seen in all graphs save (a) the chip does not return to its initial state. This ‘open’
loop is indicated by red arrows and is typical for all groups with a non-zero displacement
d= 0. Only the movement of the unconstrained chip K0u (a) and E0x in figure 5.31 (e),
both of which do not feature a displacement, has converged after the first cycle (green
arrow).
Therefore a second cycle is simulated and its results presented in figure 5.15. After the
second cycle the movements of the chip diagonal do indeed form closed loops and become
periodic as is to be seen again from the green arrows. This is also true for the creep
5.2. RESULTS OF COMPUTATIONAL ANALYSIS 107
-1012345678
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
-1012345678
-0.04
-0.03
-0.02
-0.01
0.00
0.01
-1012345678
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
-1012345678
-0.04
-0.03
-0.02
-0.01
0.00
0.01
-1012345678
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
K0u (1): FC,
d = 0 µm, F = 0 N, b = thin
25 ˚C
-10 ˚C
-38 ˚C
-38 ˚C
90 ˚C
120 ˚C
125 ˚C
25 ˚C
u
z
[mm]
E2Mu (1): Epo-Sil Adhesive
d = -200 µm, F = 15.4 N, b = thin
Key to Arrows:
-> High-T creep
-> Open cycle
-> Converged cycle
S2Au (1): Silicone Adhesive
d = 200 µm, F = 25.4 N, b = thin
(f)
(e)
(d)
C2Au (1): Carbon Foil
d = 200 µm, F = 25.4 N, b = thin
u
z
[mm]
E2Au (1): Epo-Sil Adhesive
d = 200 µm, F = 25.4 N, b = thin
(c)
(b)
(a)
c [mm]
c [mm]Eqv. Creep Strain
u
z
[mm]
S2Au
E2Au
C2Au
E2Mu
K0u
0.000.010.020.030.040.05
25..-10 ˚C
-10..-38 ˚C
-38 ˚C
-38..90 ˚C
90..120 ˚C
120..125 ˚C
125..25 ˚C
Figure 5.14. Movement of chip diagonal over the period of first simulated cycle. The
corresponding equivalent creep strains (averaged over both bumps) per load step are added
up in (f). Note the large effect of loads (b) and interface medium (c-e) with respect to
(a). A red arrow indicates beginning and end of an ‘open’ cycle, a green arrow a converged
cycle. Black arrows denote the critical creep phase at higher T.
108 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
-1012345678
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
-1012345678
-0.04
-0.03
-0.02
-0.01
0.00
0.01
-1012345678
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
-1012345678
-0.04
-0.03
-0.02
-0.01
0.00
0.01
-1012345678
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
S2Au
E2Au
C2Au
E2Mu
K0u
0.000.010.020.030.040.05
K0u (2): FC,
d = 0 µm, F = 0 N, b = thin
25 ˚C
-10 ˚C
-38 ˚C
-38 ˚C
90 ˚C
120 ˚C
125 ˚C
25 ˚C
u
z
[mm]
E2Mu (2): Epo-Sil Adhesive
d = -200 µm, F = 15.4 N, b = thin
C2Au (2): Carbon Foil
d = 200 µm, F = 25.4 N, b = thin
(f)
(e)
(d)
u
z
[mm]
E2Au (2): Epo-Sil Adhesive
d = 200 µm, F = 25.4 N, b = thin
(c)
(b)
(a)
c [mm]
c [mm]
Key to Arrows:
-> High-T creep
-> Open cycle
-> Converged cycle
S2Au (2): Silicone Adhesive
d = 200 µm, F = 25.4 N, b = thin
Eqv. Creep Strain
u
z
[mm]
25..-10 ˚C
-10..-38 ˚C
-38 ˚C
-38..90 ˚C
90..120 ˚C
120..125 ˚C
125..25 ˚C
Figure 5.15. The same configurations but for the second simulated cycle. Again green
arrows indicate closed loops now and hence a stabilized, converged system for all groups.
5.2. RESULTS OF COMPUTATIONAL ANALYSIS 109
strains which assume lower values for the constrained groups. This is an important result:
The system has relaxed and accommodated to the given loads, although the characteristic
differences due to the interface material are still prominent.
However, these differences in deflection amplitude seem not to influence the creep strain
of the solder to an expected extent. Apparently, the low-Tphase of the cycle, where there
is most difference in the curvature of the contemplated groups, is of no relevance for the
creep strain. Creep needs high temperatures to be activated. This phase is crucial for the
accumulation of creep and hence damage.
At high temperatures the chip essentially assumes a state of lower curvature and differences
due to the different interface materials are not as pronounced as at low T. Therefore the
identically loaded groups (c-e) do display similar creep strains, small differences are may
depend on the way the interface material constrains the curvature of the die. Thereby the
sign of the curvature seems not to play an important role (b).
This leads to the following observation: Large creep strains are caused by a continuing
movement of the die (black arrows in first cycle) or remaining (constrained) curvature at
high temperatures which differs from the unconstrained case (a), i.e. the unconstrained
chip which yields the highest reliability. Here only chip and board determine the curvature
of the chip.
Every external influence seems to increase creep strain. Thereby also the sense of bending
(concave or convex) seems to be of no importance. This is not intuitive at first glance,
but due to the viscoelastic properties of underfill and soldermask which allow a relaxation
and consequent convergence of the cycle at high temperatures T≈Tgthe chip and with
it the bump may deform until they assume a new equilibrium position (green arrows)
about which they oscillate driven by the thermal cycle T(t). The bump’s creep strains
develop eventually only through a relative, thermally induced deformation. This is evident
also from a mathematical point of view: The strain depends only on the derivative of
the deformation, not on the deformation itself. In order to assume this new equilibrium
though, the bump has to undergo this transient period of larger creep of the first cycle.
5.2.3 Structural Distribution of Creep Strain inside Bump-
Volume and Consequences for Averaging
This large increase in shear strain for the mechanically loaded groups manifests itself also
in the structural distribution over the bump volume. This phenomenon is shown in figure
5.16. For a mechanically unconstrained chip K0u a well-known structure (a) [25] evolves.
This structural distribution of strain, shaped like an X, develops as the chip bends down at
low temperatures and up again at high temperatures, each time giving rise to one ‘leg’ of
the X. This particular structure is obviously characteristic for a situation where the normal
strain dominates over the shear strains.
However, this structural feature is lost when mechanical loads are applied to the chip and
shear strain wins over normal strain. Again we use group C1Bu (carbon foil, medium
loads, thin board) for comparison. A rather layered structure develops (b). As the creep
strains per cycle become stable, the equivalent creep strain assumes lower values and a
110 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
more X-like band structure reappears (c) due to the earlier mentioned redistribution of
strain (see also figure 5.12).
K0u, 3.21 % C1Bu (1), 4.45 %
Crack Avg. Disc
(a) (b) (c)
C1Bu (2), 3.93 %
1.0 5.0 % 1.0 9.0 % 1.0 7.0 %
Figure 5.16. (a): Typical X-shaped structure after one thermal cycle for a bump within
an unconstrained chip K0u. (b): Flip-chip bump with reverse side attachment exemplified
for C1Bu: The X-band structure is overlaid by a layered structure due to an increase in the
out-of plane shear components. Creep strains are averaged over a disc-shaped region (red
box, cf. figure 4.4) where fatigue cracking occurs. (c): Stabilized creep strains of second
cycle.
When it comes to evaluating the creep stain, the need for averaging over a certain volume
has already been stressed (see section 4.1.3). In order to capture the points of maximum
creep strain and its local variations in the region where the crack develops (red frame), the
averaging region has to extend over the diameter of the pad at a certain thickness. At the
same time numerical artifacts at corners have to be excluded. The best shape to accomplish
this is an oval disc as depicted in figure 4.4. Its dimensions have been obtained in order
to yield the maximum value for the case of the unconstrained flip-chip figure 5.16(a). The
creep-strain distribution in the volume is still found to be reasonably homogeneous.
For comparability of the results, the averaging region has been chosen identical in all
configurations as also in all cases the bump cracks below the pad. This has been confirmed
by experimental investigation (see e.g. figure 5.24). So the red framed region constitutes
the zone of the damage path across the bump.
5.3 Results of Experimental Analysis
Now the results predicted by the simulation are now to be verified by the experiment.
The analysis of the experiment consists mainly in detecting bump failure as a function of
the numbers of cycles. This is done by electrical resistance measurement and verified by
cross-sectioning of the respective bumps by metallographic means. The recorded values
are shown to obey a Weibull-distribution and the individual groups do show a ranking
as a function to the applied loads. Analysis techniques like ultrasound microscopy and
5.3. RESULTS OF EXPERIMENTAL ANALYSIS 111
metallographic sectioning again were employed to check for delamination and local defects,
voids or microstructure coarsening.
5.3.1 General Inspection of Specimens After Thermal Cycling
A general inspection after each stop during thermal cycling was carried out. This meant
disassembling the test-specimens to look for delamination of the adhesives, die crack, tight-
ened nuts and overall integrity of the samples. At each stage of cycling (every ∆N= 250
cycles) one sample per group was held back to perform this check.
Here it was found that nearly all flexible foil groups ‘F’ had a large number of dies cracked
due to a unforseen reduction in the thickness of this thermal interface material. As a
consequence the critical displacement load was exceeded which caused too large a curvature
of the chip and then die crack. This could be confirmed by FE-simulations making use of
the surface stress as fracture criterion. Only three groups remained with enough samples
to yield statistically meaningful results to be included in the analysis. They are henceforth
marked with an asterisk. Die crack was not observed in any other group.
All adhesive groups were impeccable in that no delamination of the adhesive at either
interface, plate or chip, was found. This was detected by optical inspection under tensile
load and finally by twisting off the die from the plate where the silicone adhesive still stuck
to either surface and the epoxy-silicone left a homogeneous mark on the aluminium plate.
The remains of the adhesive were removed and the chips underwent a ultrasound exam-
ination to look for delamination. Here only minor, very localized delamination at the
solder-passivation interface was found. As for the nuts which are to secure a tight joint
between the board and the plate no decrease in strength was noticed.
5.3.2 Determination of Bump Failure:
Correlation Single Bump and Daisy Chain Resistance
and Verification by Metallographic Means
A computer-controlled resistance measurement was carried out on all chips at regular
intervals. Therefore the test-specimen is inserted into a needle-pin adaptor (see figure
5.17) which conducts single bump and daisy-chain measurements, each of which featuring
advantages and disadvantages as described in section 4.4.1.
A program (MS-Excel Macro) automatically measures the resistance of sixteen single
bumps and the daisy chain. Failure is detected according to a certain threshold value
scheme which is explained in table 5.3. This reflects a consistent relationship between the
two measurement types and is underpinned by metallographic sectioning confirming the
through-crack in the bumps.
In order to carry through a correct statistical analysis for the failure behaviour of the bumps
a maximum of information is needed from both kinds of measurements. However, there
is some difficulty in determining the exact point of failure for the daisy-chain as it repre-
sents an overlay of the failure of many bumps connected in series. Therefore it is first of all
112 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
Figure 5.17. Computer-controlled measurement of bump resistance. To the left the multi-
meter and the relay box for switching between the individual bumps can be seen. Inset:
Needle-pin adaptor. The plate fits in neatly between the needles.
important to establish a correlation. This is done in a self-consistent way as outlined below.
Single Bump Failure
The evolution of the resistance is illustrated graphically in figures 5.18 and 5.21 for the
single bump and the daisy-chain respectively. Here arrows mark the points of failure and
the evolution of the resistance at failure is illustrated. The single bump resistance rises
gradually by ∂RSB per ∆N, an effect which is attributed to gradual ageing: Growing
intermetallics, accumulating crystal defects and coalescence of microcracks caused by low
cycle fatigue (cf. section 3.1.4 and [108]) may contribute to a slight increase in electrical
resistance through reduction of the current carrying volume in the sense of equation 3.20.
Only a ‘catastrophic’ event can be counted as failure where the resistance rises sharply by
nearly one order of magnitude. Hereby the failure sometimes announces itself by an earlier
rise is resistance which proves not fatal yet. It usually stays below around Rl≈20 mΩ
then. An open circuit seldom exceeds an upper value of Ru= 1 Ω at failure (as to be seen
in figure 5.18) at room temperature due to the bump being under compression. Still, the
best way to detect a fatal damage unambiguously is by making use of the increase with
respect to to the last measured value (see table 5.3). This criterion traps the fatal event
best. The subsequent number of cycles is then taken as number of cycles to failure. This
is in agreement with the analyses presented in [37] or [109] which use an absolute value
of R>100 mΩ as failure criterion for SB failure. In our case, however, bumps could be
shown to have failed already at absolute values above Rc≈25 mΩ.
5.3. RESULTS OF EXPERIMENTAL ANALYSIS 113
0500100015002000
10
-3
10
-2
10
-1
10
0
(a)
(b)
R
0
N
f
o.k.
Failure
Single Bump Resistance
R
SnPb
= 1.6 mOhm
R
Al
= 1.4 mOhm
Resistance [Ohm]
Cycles
Figure 5.18. Single bump resistance vs cycles: Bump failure (a) at Nf=Ni
SB cycles is
unequivocally detectable by a sharp rise in electrical resistance which signalizes a ’catas-
trophic’ event (arrow). Usually this is preceded by a steeper slope of the curve than for an
intact bump (b). This rise in resistance can be experimentally correlated to crack propaga-
tion. The inset shows the composition of the resistance: solder vs Aluminium (leads).
Correlation Between Single-Bump and Daisy-Chain Measurements
Item Single Bump Measurements (SB) Daisy Chain Measurements (DC)
Number of Bumps nSB =8×2 at statistically equiv-
alent positions
nDC = 112 out of 148 (save SB)
bumps contacted in series
Resolution Very good due to measurement
of single bump. Therefore locally
sensitive.
Smeared out due to overlay of
failure of many bumps. Not lo-
cally sensitive but evaluates inte-
gral value over chip.
Sensitivity Ratio RSnPb
Rtot =0.53 Ratio RSnPb
Rtot =0.083
Accuracy Very good due to four-point cur-
rentless resistance measurement.
Error δRSB <1µΩ (Resolution
of Gauge)
Blurred. Error δRDC <100 mΩ
due to two point resistance mea-
surement affected by drift in relay
contact resistance.
Normal value ∂RSB ≈0.5mΩ→∂RDC ≈nDC∂RSB +δRDC
Threshold value ∂RSB >5∂RSB →∂RDC >5∂RDC
or ∂RSB >∂R
C
SB =25mΩ; →∂RDC >n
DC∂RSB +δRDC +
+nDC
nSB ∂RC
SB = 375 mΩ
Table 5.3. The single bump results are used to establish a correlation to the daisy-chain
values. We define: ∆N= 250 (Cycles); The increase in resistance per ∆N;∂R =RN−
RN−∆N;∂R=RN−∆N−RN−2∆N.
114 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
This fact can be confirmed by intersections through the bump as depicted in figure 5.19.
Bumps (a) shows no cracks whereas (c) and (d) show a clear crack accompanied by many
micro- and mesocracks across the entire cross-section of the bump. Bump (b) is just
becoming critical and its crack is already half the way through.
K0u008b_ola_2000
R = 3 mOhm
E1Ax060a_lra_1000
R = 32 mOhm
K0x_005a_lla_2000
R = 53 mOhm
E1Au037b_lla_750
R = 8 mOhm
(a) (b)
(c) (d)
20 µm
40 µm
20 µm 20 µm
Figure 5.19. Different bumps from various test-groups and their resistance. The bump
is specified by the notation: GROUP/CHIP/POSITION/CYCLE. Magnification is 500×
and 1000×respectively. Red arrows indicate cracks.
Another test supports this threshold value Rc: The samples were measured, heated up to
T= 125 oC, measured again, and remeasured an other time at room temperature. The
resistance went up and returned to exactly the same value if the bump was intact. A
cracked bump did not so once it exceeded this value of Rc≈25 mΩ. Interestingly pure
mechanical unloading of the chips (disassembly of the test-specimen) did not show this
effect. This is due to the fact that at room temperature the solder bump is always under
compression (see figure 5.13).
The dependence of the resistance on the cracked area is simulated and sketched in figure
5.20. For a single bump of height Hand initial cross-section A0(= area of the pad) the
overall resistance is composed of a solder RSnPb and a non-solder fraction RRest which are
calculated to account each for nearly half of the total resistance. Based on the assumption
that a crack zone of area Aφand height hreduces the effective current carrying solder
5.3. RESULTS OF EXPERIMENTAL ANALYSIS 115
0.00.20.40.60.81.0
1E-3
0.01
0.1
1
Calculated:
R
SnPb
= 1.6 mOhm
R
Rest
= 1.4 mOhm
Localized Damage
Volume Damage
R
0
= 3 mOhm
Bump Resistance [Ohm]
Damage Parameter
Figure 5.20. Calculated single-bump resistance as a function of crack zone extension
given by a damage parameter φ=Aφ/A0. The upper curve assumes a large damage zone
of extension hequal to the solder gap width H=47µm (cf. figure 4.28) whereas the lower
represents a local cracking (h=0.1 H) of the solder bump below the pad.
volume of the bump the resistance rises as a function of the extension φ(or damage
parameter as in equation 3.20) of this zone according to:
R(φ)=SnPb h
A0(1 −φ)+H−h
A0+RRest, (5.2)
where the specific resistance for eutectic solder was taken to be SnPb =16µΩcm [65] at
room temperature.
As one can derive from the curves, however rough a guideline they may seem, a soaring
resistance means in any case a severe damage in the bump. As can be seen from the inter-
sections the cracks are multiple and microscopic encompassing an extended damage process
zone around them before they finally merge to cause fatal rupture. This is in accordance
with the damage hypotheses of thermally induced low cycle fatigue in ductile materials
where a weakened, coarsened zone precedes fatal failure [64] as presented earlier in this
work. There may be, however, other metallurgical changes contributing to the increase
in resistance prior to fatal failure of the bump by fracture. Multiple cracks, oxidation at
crack faces, point contacts or grain boundary effects can add to the effective decrease in
area and increase in electrical path length.
Daisy-Chain Failure
When considering a typical daisy-chain response like those graphs in figure 5.21 the diffi-
culty in determining the point of failure becomes obvious: Bump failure produces much less
an effect in the overall resistance. In this respect graphs (b) and (d) do present no prob-
lem since they clearly testify a ‘catastrophic’ event. But many chains produce curves like
116 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
(a) and (c). This is due to the low sensitivity (i.e. solder resistance to overall resistance
ratio) and the considerable measurement inaccuracy caused by the two-point measure-
ments which are unfortunately affected by the non-constant contact resistance of needle to
pin and also the relays in the switching box. This is responsible for an intrinsic error of
δRDC =±50..100 mΩ.
0500100015002000
0
2
4
6
8
10
12(d)
(c)
(b)
(a)
Failure
Daisy Chain Resistance
R
SnPb
= 180 mOhm
R
AL
= 2 Ohm
Curves are each y-shifted
by +1 Ohm w.r.t the previous
R
0
Resistance [Ohm]
Cycles
Figure 5.21. Some representative examples (chip a−d) for daisy-chain measurement
results: The number of cycles to failure (arrow, Nf=Ni
DC) is more difficult to detect but
consistent with the experiment and correlated to single bump results.
Therefore the insights gained with the single-bump measurements are now used to develop
a threshold criterion for the daisy-chain that is consistent with experimentally verified
bump cracking. This is in principle a straightforward extrapolation from the single bump
criticality criterion to a larger number of bumps connected in series as is described in table
5.3. It was made use of the fact that a critical state must account for the gradual increase
and – as experience from the single bump measurements shows – on average one bump
in sixteen goes up by ∂RC
SB which means failure of one bump. The error δRDC has to be
added.
The criterion given in the table is in good agreement with experimental results. Sectioning
showed unequivocal fatal damage to at least one bump in every case. The value Ni
DC thus
obtained for the daisy-chain is usually smaller than the number of cycles to first single-
bump failure per chip Ni
SB (cf. figure 5.18) by a number Ni
c(cf. figure 5.21) for each chip
where iis a chip-index. This result seems reasonable, since with a much larger number of
bump involved the daisy chain is more likely to display bump failure.
Determination of Chip-Failure
A chip has failed when the first bump has failed. The corresponding number of mean cycles
to failure ¯
Nffor this particular event has to be found. A bar on top of the symbol signifies
ameanvalue ¯
Nf=N50 %.
5.3. RESULTS OF EXPERIMENTAL ANALYSIS 117
A purely daisy-chain based evaluation can be ruled out for various reasons: First, the
daisy-chain usually fails for all chips of a group within two or three subsequent measuring
intervals ∆N. Two points do not produce a Weibull-fit and three produce a very vague
result with a large scatter. It did not give rise to a meaningful and well-resolved ranking
when put up. Second, the daisy-chain value ¯
NDC provides no local information which
makes it difficult to correlate it to the computational strains of a specific bump which
depend very much on bump position (distance to neutral point).
The next possibility to rigorously evaluate ¯
Nfwould be to determine ¯
NSB based on all
single bumps per group n=nSB ×nch and evaluate the probability for the above event ¯
Nf
for the number of bumps in the daisy chain nDC (nch is the number of chips in the group)
according to
¯
Nf=¯
NSB 1
nDC 1
β
(5.3)
This is derived in the appendix A.4. The method, however mathematically correct it may
be, has several practical shortcomings. First, the number of single-bump failures is small3
which requires far-reaching extrapolation to N50 % which produces a large uncertainty and
is not recommended [110]. This is further aggravated as it is difficult to fit the single bump
failure data to a straight line (cf. figure D.1 in the appendix). Then, our contemplation
requires that necessarily all bumps display equal ageing behaviour which is of course not
true: Bumps closer to the corner fail earlier. This manifests itself in a lower effective
number of bumps neff ≈30 nDC = 112 which has to be introduced to bring ¯
Nfto
a meaningful value of the order of ¯
Nf= 1000 which is at any rate postulated by the
daisy-chain values for the normal flip-chip group K0u4. Further, neff may vary from group
to group and so this again is no tenable approach and furnishes only a tendency but no
conclusive result.
Taking this into account the following approach is finally adopted: The first single-bump
failure per chip is counted as chip failure. For chips where no single-bump failure occurred
a group-averaged value for single-bump failure ˜
NSB based on the corresponding daisy-chain
˜
NDC value of the chip in question was calculated:
˜
NSB =˜
NDC +˜
Nc, (5.4)
where a mean shift ˜
Nc>0 is evaluated for each group according to:
˜
Nc=1
nf
nf
i
Ni
SB −Ni
DC, (5.5)
where the tilde signify averaged quantities over all samples nfin the group which have a
single bump failure and iis an index. This self-consistent evaluation of ˜
Ncper group takes
into account that the failure behaviour of the bumps differs from group to group and its
values are printed in table D.1.
3The group K0x shows the greatest percentage of single bump failures with nf/n < 20 %. The average
is nf/n ≈10 %.
4K0u happens to produce unambiguous daisy-chain failure. For comparison: ¯
NSB = 4806 ±900,
¯
NDC = 1020 ±200.
118 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
This has great advantages: All chips of the group do contribute to the statistics and we
obtain a well defined mean. The percentage of failure is defined for many values of N
(usually 5 up to 10) which allows a good Weibull-fit. The statistical evaluation is carried
out for bumps at specified locations which enables a direct reference to the corresponding
bump in the FE-model. This method proved successful also in that it produced the best
Weibull fit as can be seen in figure 5.22.
5.3.3 Ranking of Configurations:
Statistical Analysis and Weibull-Distribution
We assume the fatigue data to be Weibull-distributed. Therefore we take the data obtained
for bump failures as percentage of first single bump failure per chip of the total number
of chips in the group. Here we do not distinguish between inner and outer bump, since
the slight domination of the outer bump was not deemed significant enough. This value
was then plotted versus the corresponding number of cycles to failure according to the
Weibull-Distribution as reviewed in section A.4
F(N)=1−e−(λN)β(5.6)
where λ−1=N63 % is the characteristic number of cycles to failure and βis the Weibull-
exponent and function gradient in the (y-axis double-logarithmic, x-axis logarithmic) di-
agram. Therefore Weibull-distributed data appears as a straight line in the diagram
[110,111].
This can be seen in figure 5.22 where the plot is depicted for some representative groups.
The characteristic lifetime N63 % can be read from the graph.
This is done for all experimental groups. The mean value of cycles to failure ¯
Nf=N50 %
needed for the Coffin-Manson relationship is then calculated by (see appendix A.4).
¯
Nf=N50 % =N63 %Γ(1−1/β), (5.7)
where Γ is the Gamma-Function.
When ¯
Nfis plotted for all groups the ranking to be seen in figure 5.23 is obtained. The
results are also summarized in tabular form in section D.2 in the appendix.
Also the experiment shows a dependence on the mechanical loads. Although the ranking
is not as clearly resolved as for the simulative results, the outcome is for the most part
consistent with the computational results quoted in section 5.2:
•Thin boards seem more reliable than thick boards, although with increasing loads
this tendency becomes blurred.
•All mechanical loads and constraints reduce reliability.
•Foils seem better than adhesives. Thereby epoxy-silicone seems better than pure
Silicone adhesive.
5.3. RESULTS OF EXPERIMENTAL ANALYSIS 119
5
3
2
99
95
100 200 300 500 1000 2000 4000
Cycles to Failure
Percent Failure [%]
63 %
β
1
70
50
30
20
10
F1Au
C2Au
E1Ax
S0x
K0x
L0x
Figure 5.22. Weibull-plot for some representative groups. Highlighted is the characteris-
tic lifetime at 63 % failure. The fit to a straight line indicates one single failure mechanism.
Note the steeper slope (of gradient β) for the group containing voids (L0x).
•There is no significant dependence on the sign of the displacement (convex or concave
bending).
•There is no significant dependence on the value of the displacement.
•There is no significant dependence on the force.
•A vacuum process has a negative influence on reliability or voids do have a positive
effect (compare L0x (voids) to K0x (extracted voids)).
•There is no significant dependence on a second curing process.
The simulation resolves an effect concerning the displacement, whereas this result is blurred
in the experiment. And unfortunately, many cross-relationships – especially those concern-
ing displacement and force – were lost due to the die crack in most flexible foil groups . So
in this respect one has to rely on the computational result.
This low resolution is a consequence of the remarkably early overall failure of the config-
urations. All values of ¯
Nfdo lie within one order of magnitude. This may be due to the
following points:
•The solder gap between pad and land is very small b=47µm. So the bump
experiences more creep strain which strongly depends on b.
120 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
L0x
K0u
K0x
F2Mx**
C1Bu
F1Bu*
S0x
F1Au*
E2Au
E1Ax
E0x
E2Mu
S2Au
C2Au
S1Ax
E1Au
S2Ax
E2Ax
S1Au
0
200
400
600
800
1000
1200
1400
1600
Colours:
Main Groups
Patterns:
Fabrication Processes
Standard FC
Vacuum
Vacuum, 2.Curing
N
50%
Figure 5.23. Experimental ranking of configurations. ∗Due to a shrinkage of the foil (see
later in section 5.4.5) these two ‘F’-groups actually support a higher displacement load than
specified. ∗∗This displacement load is actually lower than specified.
•There is a prolonged creep phase due to the heat capacity of the attached heat
spreader during thermal cycling.
•The underfill-solder mismatch (αUf ≈2αPbSn) for this specific underfill cf. figure 5.10
is quite large. This induces additional normal creep strain in the bump which reduces
reliability.
•A potential initial damage (e.g. pre-crack) caused by non-standard processes during
assembly as there were the extraction of voids under vacuum (or a second curing
process).
•Last but not least the geometric features of the bump, a small pad and the resulting
‘shoulder’ could be a reason for faster fatigue cracking along the pad or earlier crack
initiation around this shoulder.
This might also be an explanation for the unexpectedly low reliability of the adhesive
groups without mechanical load S0x and E0x for which a value close to the unconstrained
chip K0x was predicted by simulation.
The best group is undoubtedly the unconstrained assemblies L0x, K0u, K0x. As expected,
the thin board (-u) produces higher reliability than the thick board within a group [52].
Still, L0x, K0x should produce identical results. Let us therefore have another look on the
preparation of the samples, which differ in two points:
5.3. RESULTS OF EXPERIMENTAL ANALYSIS 121
Not all chips have seen the same fabrication processes during the assembly. A potential
dependence may exist and therefore this difference is encoded in the patterns of figure 5.23.
L0x has undergone the standard flip-chip processes and incorporates voids (cross-hatched).
All other groups have seen a vacuum treatment described in section 4.4.3 and are depicted
without hatching. The singly hatched groups are all adhesive groups which have therefore
seen a second curing process.
There is also an indication that L0x displays an ageing behaviour different from the others
since its Weibull-exponent βL0x=7.55 (see table D.1 in the appendix) is about twice the
ones of the remaining groups. If this is caused due to the presence of voids or due to
an absence of a vacuum treatment is impossible to say since there exists no cross-check.
Values for β∈[2; 4] have also been reported in [23] to by characteristic for thermal low
cycle fatigue of eutectic tin-lead solder. Values in this range signify on average a quadratic
failure rate λ(N)∼N2. For all groups though the values lie to a very good approximation
on a straight line from which it can be concluded that there is only one single failure
mechanism (a second would cause a kink in the curve).
For this reason a second curing process is not likely to have caused any harm. The respective
groups are not conspicuous among the others in figure 5.23 and their failure-rates lie among
the others. It remains to verify if the vacuum treatment did induce any initial damage. In
order to explain this deviation one has to look on some intersections of the bump.
5.3.4 Solder Bump Failure and Effects of Vacuum Treatment
In figure 5.24 bumps representative of their configuration have been chosen for comparison.
With respect to the ‘as cast’ solder bump (a) a second curing e.g. for the adhesive coarsens
the solder (c). This is a phenomenon [43,64] typically observed at high temperatures. Here,
Tc= 160 oC. It does, however, not induce any damage. Clearly visible on the contrary
is the initial damage caused by the vacuum treatment (b). Although this process does
eliminate large voids as seen in figure 4.31, it leaves behind gaps or cavities around the pad
at the preferred location of the voids before their extraction under vacuum. Although the
temperature is well above liquidus, the void does apparently not vanish with a wettable
surface which would allow the solder to close the gap. These gaps are seen in nearly all
bumps for all groups which underwent the vacuum process.
This can be seen in (d) where the void seems to be trapped in being sucked away by the
vacuum. All groups which have undergone this process do show these gaps. It could well
be that the comparability in terms of an identical initial preparation is hence reduced.
Unfortunately this initial damage was not detected until the whole experiment was carried
through. In this respect it produced exactly the effect it was meant to eliminate.
The bump finally cracks below the pad (f). This is so for all groups and no dependence of
the loads on this behaviour is detectable. Interphase and intraphase cracking is observable
in most cases. Fatigue cracking evolves gradually and due to merging of many microcracks
which leave behind a ‘crumbly’ structure of a certain bandwidth. The gaps which are
left behind by the vacuum process seem to be involved in the cracking process and as
they reduce the effective cross-section it may be that they promote failure rather than
122 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
Vacuum
R = R0
Void
Coarsening
R = R0
Fatigue Crack
R >> R0
E0x000_any_0
No Vacuum,
2.Curing
K0u010a_rr1_1750
`Shoulder´
K0x000_any_0
As Cast
(a) (b) (c)
S1Au019a_1250
K0u091b_any_0
K0u008b_2000
(d) (e) (f)
R = R0R = R0
Gap
50 µm
Figure 5.24. Solder as cast (a). Zero cycles: Initial damage due to extraction of voids.
This process leaves behind gaps (b). A second curing process (no vacuum) only coarsens
the solder (c). 2000 cycles: Remaining voids. Note the channel and the extreme coarsening
(d). Side view of bump. A ‘shoulder’ forms at the passivation (e). 1250 Cycles: Fatigue
cracking (f).
reduce it. Their cross-section area passes as already cracked path length. This has already
been mentioned [105]. Big round voids which are far off the crack zone near the pad (as
depicted in figure 5.19 (b)) seem not to have any influence on bump cracking. This may
be the reason for the group L0x having higher lifetime despite the presence of voids.
It may therefore be concluded that the vacuum process did cause some damage to the
bumps which caused them to fail earlier, although they did still fail by low cycle fatigue
cracking as can be inferred from the failure-rate common to all groups. As the problem
occurred in all groups – and as far as could be told from sectioning in nearly every bump
– it may be assumed that on average the bumps act as if they had an even smaller pad
than they actually have. This is consistent with the strong dependence on pad size found
in literature (see e.g. [98,99]).
Further, a huge amount of phase coarsening is seen at large numbers of cycles (d,e). This
is attributed to the very small gap width of the solder b≈47 µm and the prolonged high
temperature creep phase due to the large heat capacity of the aluminium plate as depicted
in figure 5.4. This tendency is confirmed by the high values of creep strain throughout all
groups ¯εcr >0.03.
5.3. RESULTS OF EXPERIMENTAL ANALYSIS 123
5.3.5 Check for Delamination
It is well known that the interfaces of multi-layered assemblies are liable to delamination.
Thereby cracks start near common points of bi- or tri-material interfaces due to high
stresses which are characteristic at these point under thermal loading [112,113]. For elastic
theory this feature exhibits stress singularities which represent numerical artifacts since real
materials will yield at a certain stress [76]. Still high (peel-) stresses will act in these zones
and are likely to cause crack initiation. Several critical points have been detected [28] as far
as flip-chip assemblies are concerned and they will have to be checked for delamination since
this will considerably accelerate bump fracture or may even become the dominant failure
mechanism over solder fatigue [18,33]. This means that we would deal with a second failure
mechanism that cannot be treated conclusively along with the Coffin-Manson relationship
for solder but requires additional fracture mechanical means. Critical points are the chip-
passivation-underfill and solder-underfill interfaces. The damage likely to be caused by
delamination depends on its location and its extension.
In order to check for delamination ultrasound microscopy was employed. The result is to
be seen in figure 5.25.
SEM
SnPb
PI
UF
Local Delamination
US
Chip after
2000 Cycles
K0u
(a) (b)
Figure 5.25. Ultrasound (US) pictures and verification by scanning electron microscopy
(SEM). The white patches in the ultrasounds reveal local delamination, which occurs at
the solder-passivation ( SnPb-PI) interface. Due to its particular shape, the bump forms a
‘shoulder’ at this point. For the US-pictures an 230 MHz transducer was used.
Delaminated layers form a material discontinuity which causes a sudden change in the
elastic modulus at this point of the assembly which reflects the ultrasound waves and is
depicted as bright region on the sonographs. Bright spots can only be seen close to the
pads at a few odd bumps and after about N= 500 cycles (group-dependent). A new chip
does not show any spots.
Metallographic examination revealed local delamination at the ‘shoulder’ which the solder
bump forms at its top surface with the passivation (polyimide) layer. Obviously this
combination displays no strong adhesion. The underfill-polyimide interface however seems
impeccable. There was no delamination found in any group. It was known beforehand
that this material combination had outstanding adhesive properties. On the other hand
no indicative correlation between an early failure of a bump and the appearance of the
white spot could be established.
124 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
(a) (b)
250 µm
= Pitch
Delaminated
Area
UBMBump-
“Shoulder”
Figure 5.26. The delaminated area on the FE-model for small delamination at the ‘shoul-
der’ caused at the interface solder-chip (a) and for larger delamination of the size of one
square pitch (b). The bump itself is surrounded by underfill and soldermask (grey) and
located just below the UBM.
After this finding it has still to be made sure that this kind of very localized delamination
does not interfere with the simulation. First, a delamination which only affects the solder
interface to the polyimide (chip) as intended to mimic the above detected failure. The
delaminated area is depicted in figure 5.26 (a).
K0u Large Delam
K0u Small Delam
K0u Reference
0.000.010.020.030.040.05
25..-10 ˚C
-10..-38 ˚C
-38 ˚C
-38..90 ˚C
90..120 ˚C
120..125 ˚C
125..25 ˚C
Eqv. Creep Strain
Figure 5.27. Influence of delamination on creep strain as predicted by simulation. Sim-
ulated is the first cycle for the unconstrained chip K0u. For details about the simulation
refer to the appendix, section C.2.
For this case no negative influence on the solder was detected, on the contrary, a slight
reduction of creep strain was noticed (see figure 5.27, K0u, small delamination). So this
result agrees with the experimental observation. The corresponding FE-model is depicted
in figure C.10 in the appendix.
In order to see if this tendency pertains, i. e. if a certain delamination could even be
beneficial, a second, larger delamination between the underfill- and polyimide layer was
simulated (see again appendix figure C.12). Hereby the ablated area was of square shape
centred about the pad and measured one pitch (250 µm) as shown in figure 5.26 (b). Here a
small rise in creep strain could be detected in the centre of the bump, whereas on the outer
rim of the bump there was a pronounced increase in creep strain. So larger delamination
may indeed be harmful.
The delamination was simulated using a contact-target pair with sliding contact mode.
5.4. COMPARISON OF EXPERIMENTAL AND COMPUTATIONAL RESULTS 125
A model which considered delamination on other interesting surfaces between solder and
underfill or underfill and chip was not attempted yet.
In any case we may be sure that we mainly deal with pure solder fatigue failure and are
allowed to use the Coffin-Manson relationship which is based on this assumption.
5.4 Comparison of Experimental and Computational
Results
Now the interpretation of the results in comparison between simulative prediction and
experimental verification follows. This is done via the Coffin-Manson approach.
It is shown that the experiments agree well with the simulatively predicted results within
25 % accuracy. The Coffin-Manson coefficients are determined, some peculiarities com-
mented on and extrapolations to some other interesting configurations are made.
As die crack did occur in some flexible foil groups a stress-based fracture criterion is
evaluated and correlated to experiment and simulation.
Finally we draw some conclusions and venture an outlook to future activities.
5.4.1 Coffin-Manson Plot
The experimentally obtained results of figure 5.23 are now plotted as mean cycles to failure
versus the simulated accumulated equivalent creep strain given in figures 5.7 (first cycle)
and 5.8 (second cycle) respectively. (The values are explicitly given in the appendix in table
D.1.) For each configuration the corresponding simulated strain was averaged over both
bumps (#2 and #6 in figure 5.6). As there was no detectable difference in the experimental
value of cycles to failure between the two bumps no separate analysis was made.
So the Coffin-Manson plot for the first simulated cycle can be seen below in figure 5.28.
For the indicated groups (see symbols in legend of figures) a best fit to the Coffin-Manson
relationship ¯
Nf=c1(¯εcr)c2(5.8)
in order to determine the coefficient c1,c
2was undertaken to calibrate the bump as a
‘reliability sensor’. Thereby the void containing group L0x has never been incorporated in
the fit since it displays a different failure behaviour (different failure rate) due to a different
treatment and existing voids. Also its value for the creep strain seems vague because voids
were not considered by the simulation. For reasons of completeness its value for the creep
strain ¯εcr
L0x=¯εcr
K0xwas set equal to the corresponding group with extracted voids K0x.But
it is for this reason not considered any further in this contemplation and the mark in the
graph has been put in brackets.
The tendency, larger creep strain – lower reliability, is met. Two curves have been cal-
culated to fit the data. The green, dotted curve features a specified exponent of c2=2
which is the value most often reported (cf. section 3.1.5) in theory. It is here stated for
126 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
Nf= 1.20 ε-2.0
Nf= 42.7 ε-0.9
0.030 0.035 0.040 0.045 0.050 0.055
400
600
800
1000
1200
1400
F1Au*
F1Bu*
F2Mx**
First Simulated Cycle
Fit, c2 = -2
Fit
( )
S2Ax
E2Ax
S1Ax
S2Au E1Ax
S1Au
C1Bu
E1Au
E2Au
C2Au
E2Mu
S0x
E0x
K0u
L0x
K0x
Experiment:
Mean Cycles to Failure
Simulation: Equivalent Creep Strain
Figure 5.28. Coffin-Manson plot for first simulated cycle. The system features too low a
Coffin-Manson exponent. The colour scheme resumes the one from figure 5.23. The shape
of the symbols indicate identical process steps. The graphs of the CM-fit do not include
L0x.
0.034 0.036 0.038 0.040 0.042 0.044
400
500
600
700
800
900
1000
1100
1200
1300
1400
F2Mx**
F1Au*
F1Bu*
Second Simulated Cycle
Fit, c2 = -2
Fit
S2Ax
E2Ax
S1Ax
S2Au E1Ax
S1Au
C1Bu
E1Au
E2Au
C2Au
E2Mu
S0x
E0x
K0u
K0x
Experiment:
Mean Cycles to Failure
Simulation: Equivalent Creep Strain
Nf= 1.06 ε-2.0
Nf= 0.35 ε-2.33
0.00 0.02 0.04 0.06
0
500
1000
1500
2000 Fit
Nf
εcr
Figure 5.29. Coffin-Manson plot for second simulated cycle. The zoomed graph (inset)
includes the origin. The dashed curve represents the fit with expected exponent c2=2.
5.4. COMPARISON OF EXPERIMENTAL AND COMPUTATIONAL RESULTS 127
comparison. As can be seen the red curve, which includes all save L0x, is still far from
this value. It exhibits a very low value for the Coffin-Manson exponent. But this is just
an other manifestation of the transient response of the simulation during the first cycle as
has been mentioned already and for the second cycle the curves do very nearly obey the
theoretical prediction of c2=2.
Several things are remarkable though: The groups E0x and S0x were expected to display
better reliability since they did not see any further mechanical loading apart from being
attached by an adhesive. Also the simulation does predict a high reliability. E2Mu was
expected to show a low lifetime but the simulation of a first cycle does not reflect this yet.
Also the ‘gap’ on the x-axis between the mechanically loaded and the unloaded groups to
the left and the right of E2Mu need an explanation which could indicate a dependance
on the make-up of the test-specimen, namely the thermal misfit between board and plate
communicated by the fixation whenever a non-zero displacement is specified.
25050075010002500
250
500
750
1000
2500Second Simulated Cycle
1
Groups
± 25 %
N
f
by Experimental Verification
N
f
by Simulative Prediction
Figure 5.30. Correlation of lifetime prediction model with test data.
Many of these queries are resolved when analyzing the Coffin-Manson plot for the second
cycle in figure 5.29 as it shows a much more consistent picture. The accommodation process
of the chips to the loads already described earlier in section 5.2 shifts the equivalent creep
strain (x-axis) of the loaded groups towards smaller values and the unconstrained chip
K0u,x experiences a slight shift to the right. The resulting fit reproduces a value of
c2=2.33, which is still close to c2= 2 (see section 3.1.4).
The discrepancy to the red curve is accredited to the seemingly low resolution of the
experiment. An other explanation is that the simulated creep strain should actually be
higher due to the pre-cracked bumps. As this would affect the loaded groups more strongly,
the curve would be flatter, i.e. the exponent smaller. But as can be inferred from figure
5.30, the actual inaccuracy between simulative prediction and test still is around 25 %,
128 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
which is of the order of values found in literature (see e.g. [39], also 25 %). In this respect
the encountered deviations are within the normally expected range.
Due to the high values of creep stain, which are mainly caused by the underfill-solder
mismatch (normal creep strain component), all configurations are located within a region
of the Coffin-Manson curve where its slope is rather gradual as can be seen from the inset
in figure 5.29: For smaller values of creep strain one expects a much larger split up between
the individual configurations and a much greater effect of the individual load variations
in the experiment. The influence of the external loads in the simulation, a pronounced
increase in the shear components of the bump creep strain, is additionally attenuated by
the extraordinarily large normal component.
As a result one can state that the experiments do confirm the simulative predictions. The
ranking given in section 5.2.1 can therefore be taken to correctly serve as calibration scale
for the solder bump creep strain.
Still there remain some points to discuss. For instance the ‘gap’ of values which was
originally between the loaded and unconstrained groups has been greatly reduced in the
second cycle. This ‘gap’ can indeed be shown to be due to the fixation of the board to the
plate and therefore a characteristic particularity of this very test-specimen. This can be
seen when again we have a look at the curvature over the period of one cycle in the next
section.
5.4.2 Effect of Fixation and Influence of Displacement
The first graphs of figure 5.31 (a) show a chip on a thin board with medium load attached
by an epoxy-silicone adhesive (E1Au). At high temperatures the chip goes slightly convex.
If the CTE of the aluminium plate (normally αal =23.5ppm/K) is set equal to the CTE
of the board (αbd(T<Tg)=11.5ppm/K) for a test, then the result looks as in (b), the chip
would not bend convexly, i.e. it is not stretched out by thermally induced stress in (a). The
same result as in (b) is obtained if the fixation is loose (c), i.e. there is a displacement which
holds the board parallel to the plate but allows sliding – a configuration which is easy to
simulate but very difficult to adjust experimentally for reasons given in the last chapter.
The two groups display also similar creep strains (f) which are both much lower than for
the tested group (a). For a thicker board and corresponding loads (d) the force induced by
the thermal mismatch is not as strong to flatten out the chip as in (a) and the for this case
stiffer board maintains a concave state of bending. One has to consider that near Tgof the
underfill the internal stiffness of the chip is greatly reduced. So the less compliant thick
board causes the bump to creep more. As the large creep strains for this configuration
show, a fixation has to be considered harmful although the chip accommodates to it in the
following cycles.
The effect of the presence of the fixation is so large that it overshadows the influence of the
actual value of the displacement, a tendency which is only apparent in the convergence limit
of the second cycle. This is predicted by simulation in figure 5.32, where this is exemplified
for the silicone adhesive groups which feature two different displacements (d1= 100 µm and
d2= 200 µm) once with fixation and once without (loose). Although there is a tendency
that larger displacements (this results in a larger curvature) reduce lifetime, this cannot
5.4. COMPARISON OF EXPERIMENTAL AND COMPUTATIONAL RESULTS 129
-1012345678
-0.02
-0.01
0.00
-1012345678
-0.02
-0.01
0.00
-1012345678
-0.02
-0.01
0.00
-1012345678
-0.02
-0.01
0.00
-1012345678
-0.02
-0.01
0.00
E1Au (1): Epo-Sil Adhesive
d = 100 µm, F = 17.7 N, b = thin
25 ˚C
-10 ˚C
-38 ˚C
-38 ˚C
90 ˚C
120 ˚C
125 ˚C
25 ˚C
u
z
[mm]
E1Au (1):
CTE
Plate
= CTEBoard
Key to Arrows:
-> High-T creep
-> Open cycle
-> Converged cycle
E0x (1): Epo-Sil Adhesive
d = 0 µm, F = 0 N, b = thick
(f)
(e)
(d)
E1Au (1):
Loose Fixation of Board
u
z
[mm]
E1Ax (1): Epo-Sil Adhesive
d = 100 µm, F = 30.3 N, b = thick
(c)
(b)
(a)
c [mm]
c [mm]Eqv. Creep Strain
u
z
[mm]
E0x
E1Ax
E1Au, loose
E1Au, CTE pl
E1Au
0.000.010.020.030.040.05
25..-10 ˚C
-10..-38 ˚C
-38 ˚C
-38..90 ˚C
90..120 ˚C
120..125 ˚C
125..25 ˚C
Figure 5.31. Effect of CTE mismatch board-plate: The chip is stretched at high T(a).
This does not occur if board and plate are CTE-matched (b). A loosely fixed board (c)
has the same effect. A stiffer thick board (d) displays stronger curvature even at high T.
Groups with d=0show convergence already for first cycle (e). Shown is the first cycle.
Groups (b) and (c) represent a simulative extrapolation.
130 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
S1Au loose fixation (2)
S2Au loose fixation (2)
S1Au (2)
S2Au (2)
S1Au loose fixation (1)
S2Au loose fixation (1)
S1Au (1)
S2Au (1)
0.000.010.020.030.04
S1Au:
Silicone Adhesive
d = 100 µm,
F = 17.7 N,
b = thin
25..-10 ˚C
-10..-38 ˚C
-38 ˚C
-38..90 ˚C
90..120 ˚C
120..125 ˚C
125..25 ˚C
(a)
(b)
Eqv. Creep Strain
Figure 5.32. Influence of fixation of the board with respect to the value of the displacement
exemplified for the silicone adhesive group. A ‘loose’ attachment has not been realized
experimentally and so this diagram represents a simulative extrapolation. Depicted are
first (1) and second (2) cycle.
be resolved by the experiment. In any case this means that a fixation is not recommended
unless the heat-spreader is thermally matched to the board as in figure 5.31 (b).
Apparently the flip-chip assembly likes best a movement which is dominated by the thermo-
mechanical coupling of underfill and soldermask only. The more constrained the chip is and
the larger the elongation from equilibrium are, the larger the relaxation will be, resulting in
a transient phase of higher creep strain. As seen in figure 5.31 (e) for the adhesive without
mechanical loads the chip behaves as if it were unconstrained for high temperatures. This
is also obvious from the fact that it has already converged after the first cycle.
5.4.3 Effect of Board-Viscoelasticity and Orthotropism
In section 4.3.3 it was found that both sets of data, the viscoelastic-isotropic and elastic-
orthotropic could adequately describe the measured macroscopic behaviour under thermal
and mechanical loads when a calibration factor was introduced. (The problem of the
correct choice arose due to the fact that Ansys does currently not support orthotropic
viscoelasticity.) So the global effect of orthotropism seemed to be included and so the
viscoelastic set of data was used for all simulations to additionally consider rate-dependent
behaviour which could have an effect if the whole test-assembly is simulated.
At the end a simulation was run using the elastic-orthotropic data and the results are
seen in figure 5.33. For the curvature there is, as expected, hardly any difference for low
temperatures (compare (a) and (c)). At high Tthe elastic board shows greater stiffness and
more creep strain which is also in accordance with the expectations. But both elastic and
viscoelastic board show a convergence behaviour concerning curvature (nearly identical)
and creep strain which corroborates the thesis of underfill and soldermask being responsible
5.4. COMPARISON OF EXPERIMENTAL AND COMPUTATIONAL RESULTS 131
-1012345678
-0.04
-0.03
-0.02
-0.01
0.00
-1012345678
-0.04
-0.03
-0.02
-0.01
0.00
-1012345678
-0.04
-0.03
-0.02
-0.01
0.00
-1012345678
-0.04
-0.03
-0.02
-0.01
0.00
S1Au El-Ort (2)
S1Au El-Ort (1)
S1Au (2)
S1Au (1)
0.000.010.020.030.040.05
S1Au (1):
Viscoelastic-Isotropic Board
25 ˚C
-10 ˚C
-38 ˚C
-38 ˚C
90 ˚C
120 ˚C
125 ˚C
25 ˚C
u
z
[mm]
Key to Arrows:
-> High-T creep
-> Open cycle
-> Converged cycle
S1Au (2):
Viscoelastic-Isotropic Board
S1Au:
Silicone Adhesive,
d = 100 µm,
F = 17.7 N,
b = thin
S1Au (1):
Elastic-Orthotropic Board
(e)
(d)
u
z
[mm]
S1Au (2):
Elastic-Orthotropic Board
(c)
(b)
(a)
c [mm]
25..-10 ˚C
-10..-38 ˚C
-38 ˚C
-38..90 ˚C
90..120 ˚C
120..125 ˚C
125..25 ˚C
Figure 5.33. Effect of fixed viscoelastic-isotropic board (a,b) compared to fixed elastic-
orthotropic (c,d) exemplified for a silicone-attached chip S1Au. Note that the board prop-
erties do not influence the macroscopic behaviour of the chip but the creep strain.
132 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
for the stabilization of the cycle. But the converged second cycle produces much lower creep
for the elastic board (d) compared to (b). This must be a local effect. But it is to the
largest part not due to the rate dependence:
01000200030004000
-50
0
50
100
150
T
Time [s]
0.00
0.01
0.02
0.03
Outer
bump
Group: K0u
Viscoelastic Isotropic Board
Eqv.
zz-Comp
xz-Comp
Elastic-Ortotropic Board
Eqv, etc
Elastic-Isotropic Board
Eqv, etc
Temperature [˚C]
Equivalent Creep Strain
Figure 5.34. The reduced ¯εcr (arrows) for the elastic board is a local effect of symmetry
(orthotropism with respect to isotropy), not of rate-dependence.
01000200030004000
-50
0
50
100
150
T
Time [s]
-120
-100
-80
-60
-40
-20
0
20
40
60
80
Group: K0u
Viscoelastic
Isotropic Board
Eqv.
zz-Comp
xz-Comp
Elastic-Ortotropic Board
Eqv, etc
Temperature [˚C]
Stress [MPa]
Figure 5.35. The orthotropic board produces less stress in the bump at low Tdue to a
smaller Ezmodulus which would induce creep strain εzz at high T.
As shown in figure 5.34 for the unconstrained chip K0u it is seen that the elastic board
influences only the normal strain component. This is a local effect of symmetry, not of
rate-dependence. The orthotropic elastic modulus Ezis only one third compared to the
isotropic case. Therefore it induces less stress at low Tin the bumps as seen in figure 5.35
which in return leads to lower drive for creep strain εcr
zz as the temperature is ramped up.
Board orthotropism, i.e. a low Ez, is therefore beneficial for the lifetime of a bump. A
similar effect has been quoted in [62], where a local variation of the board-modulus was
5.4. COMPARISON OF EXPERIMENTAL AND COMPUTATIONAL RESULTS 133
assumed to be due to the underlying glass-fibres.
So viscoelasticity is the smaller effect as can be seen when a third variant is introduced: An
isotropic-elastic board. It produces only slightly larger values as the isotropic viscoelastic
one, a deviation that can only be attributed to rate-dependence.
So orthotropism has greater influence on creep strain than board- viscoelasticity. This
may be due to the fact that it maintains still half of its stiffness above Tgbecause of the
fibre reinforcement. But since the variation in Ezis the only difference board-orthotropism
should only influence εcr
zz for all groups in an identical way and our ranking still valid.
Still there is a need for a orthotropic viscoelasticity subroutine in FE-tools to represent an
organic board adequately.
5.4.4 Check for Thermal Contact in Gap-Filler Groups
A remarkable result was obtained for the foil groups. As the curvature of the chip reaches
the largest values for these groups at low temperatures, it is interesting to ask if the contact
to the thermal adhesive is still established.
T = -40 °C
Smallest Contact Surface
T = 125 °C
Largest Contact Surface
Group: C2Au
Def: 3x
10x10 mm
Chip uz
[mm]
-0.2
0.0
No
Contact Plate
Board
Chip
Figure 5.36. Carbon-foil groups (here C2Au): Effective chip-foil contact at extreme tem-
peratures. The inset shows contact areas shaded red. (Magnification: 3×).
As can be seen in figure 5.36 to the left, the effective surface is indeed reduced at low T
due to extreme bending. As the temperature rises, the chip touches the thermal interface
medium with its entire surface (to the right). This effect depends on the chip size and
has to be considered for large chips in that cooling is assured. But as the chip dissipates
heat, the assembly will relax and become flat again. For this reason it will still be able to
accomplish its task of heat transfer. For a softer gap filler the effect is less severe though.
An experimental proof of the thermal performance of these materials and the applicability
for flip-chip reverse side cooling has been carried out in parallel and been published in [8].
134 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
5.4.5 Die Crack in Flexible Foil Groups
In disassembling the samples as part of the routine test during thermal cycling die crack in
the flexible foil groups was found. This could be correlated to the resistance’s increase of
the daisy chain which went to infinity whenever a die was cracked. Unfortunately infinite
resistance is not sufficient but only a necessary criterion for die crack in that all flexible foil
samples had to be disassembled to check for a good die and hence for statistical viability.
A dependence of the percentage of dies cracked per group on the applied external loads
could be found as depicted in figure 5.37.
F2MxF1AuF1BuF2AuF1AxF2BuF2AxF1Bx
Concave Bending
Convex
0
50
100
-300
-150
0
150
30050
25
Displacement [µm]
Force [N]
Group
Original Displacement
Original Force
Percentage
Die Crack [%]
Figure 5.37. Percentage of dies cracked per group. This value is a function of the origi-
nally applied mechanical loads dand F. A negative displacement result in a small convex
curvature and shows consequently no die crack.
For groups with a positive displacement (enlarged concave curvature of the die), the proba-
bility for die crack increases with the applied force. The group with a negative displacement
(slightly convex curvature) was not affected. So die crack could have been caused by an
unforseen exceeding of the critical deflection of the die as specified in section 4.3.4. Typical
cracks are depicted in figure 5.38.
This kind of failure could only be observed with the flexible foil groups since this gap filler
did exhibit a non-recoverable deformation which nearly halved its initial thickness under a
constant compressive load induced by the external force. This was not known beforehand
or noticed during the material’s characterisation in section 3.3, as it obviously takes a
higher temperature and some time for this effect to occur.
So during thermal cycling the foil shrunk from its initial thickness h≈250 ±10 µm to
about half its value i.e. in this case to a final thickness of h≈100 ···150 µm depending on
the group. This reduction in thickness could be measured by the device in figure 4.9 but
it was also confirmed by a pronounced decrease in thermal resistance as observed by [8].
This decrease could be unambiguously correlated to this reduction, the effect of which is
5.4. COMPARISON OF EXPERIMENTAL AND COMPUTATIONAL RESULTS 135
Fd, k Fd’, k’
US
(a) (b)
hh’
Figure 5.38. Die crack in flexible foil (‘F’) groups during thermal cycling due to a thin-
ning of the foil down to half its initial thickness. The broken dies (US-pictures) show typical
cracks.
depicted in figure 5.38. As the foil shrinks, the displacement of the die and with it its
curvature is increased since the force remains constant.
Revised Configurations and Applied Loads for Flexible Foil Groups
Group and Material Code d d’ F b Type
Units [µm] [µm] [N] [mm]cf. Fig. 5.3
FC, Flexible Foil F1Au∗100 200 17.7 0.8 (c)
F1Bu∗100 225 25.4 0.8 (c)
FC, Flexible Foil, neg. Displ F2Mx∗∗ -200 -100 -20.3 1.2 (d)
Table 5.4. Table in analogy to table 5.2: Due to a reduction in foil-thickness the adjusted
displacements dof table 5.2 are no longer valid. The results obtained by simulation and
experiment have to be accredited to these new values d.
As can be told from the daisy-chain resistance the die crack occurred already within the first
250 cycles. This means that for most of the thermal cycles the surviving chipshaveseen
amuchgreater(F1Au, F1Bu)5or a much smaller load (F2Mx) than originally6specified.
This is given in table 5.4. The chips did operate off their adjusted work-points (figures 5.1)
and cannot be directly compared to the other groups for cross-checks. However, simulations
were rerun for the new load cases given by the shrunk foil and plotted in the Coffin-Manson
diagram among the others and are marked with an asterisk.
5As can be seen from figure 5.37 these groups still contain enough chips for a statistical analysis.
6See table 5.2.
136 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
5.4.6 Failure Criterion for Die Crack
It is interesting to see why the die cracked in the sense of a fracture criterion. Based on the
considerations of section 4.3.4 the range of the variables has been extended by simulation
in figure 5.39.
-30-20-10
0
10
20
0
10
20
30
40
50
60
0
100
200
300
400
Thin Board
Thick Board
k [µm]
d [µm]
T [˚C]
Figure 5.39. The curvature kas a function of Tand dfor both board thicknesses.
It was concluded that a critical situation could arise for d>d
c≈300 µm or equivalent,
k>k
c≈47 µm at low temperatures where the critical curvature or deflection7of the thin
board is slightly higher. If we add an (average) displacement h−hcaused by foil thinning
to the specified displacement dthen we get values d=d+(h−h)≥dcvery close and
beyond the critical displacement dc.
If the corresponding values of maximum top surface stress are calculated for the silicon die
and incorporated into the above scheme then we can set up a stress criticality criterion.
This is depicted in figure 5.40. Obviously the critical stress should be the same for each
configuration and not depend on any geometric feature but only on the silicon and the way
it was processed (polished, diced).
One obtains, that although the temperature contributes largely to the deflection, it hardly
influences the stress. The stress is in return a strong function of the displacement and
therefore the mechanically induced curvature. For equal states of overall curvature the thick
board induces more surface stress which means that the deflection is not an independent
7We recall that for this set-up and within the specified loading regime the curvature κis proportional
to the deflection kto a very good approximation: κ=1/r ∼k, see also figure B.6.
5.4. COMPARISON OF EXPERIMENTAL AND COMPUTATIONAL RESULTS 137
-0.06-0.05-0.04-0.03-0.02-0.01
10
30
50
70
90
110
130
150
d
c
=300 µm at T = -35 ˚C
k
c
d=200 µm
d=0 µm
d=400 µm
T=-35 ˚CT=25 ˚C Thin Board
Thick Board
Stress (max. Principal) [MPa]
Deflection k [mm]
Figure 5.40. Maximum principal top-surface stress in silicon die as a function of cur-
vature k. Highlighted (dots) are the corresponding displacements which lie on the equally
spaced isothermal curves. FLTR: T={−35; −25; −15; −5; 5; 15; 25}oC. Dotted lines
signify the dcand kcfrom section 4.3.4. The discrepancy concerning σcfor thin and thick
board could be due to the measurement inaccuracy of kcin the first place.
parameter for die-crack but dependent on bbd, the board thickness. For a given value of
stress the thin board can tolerate higher displacement and deflection. This is confirmed
very well in figure 5.40. Unfortunately the values for dhave not been measured for each
group but only at random over all groups8. Hence the mean value of h= 125 ±25 µm.
Drawing upon the critical deflection kcand displacement dcdetermined both experimen-
tally and computationally in section 4.3.4 we can set an upper threshold limit for the stress
to be σc≈100 MPa. This value seems low, but as already stated the simulation slightly
underestimates the deflection. This could explain this low value. But it should be kept in
mind that the considerations given in this section do serve more as a qualitative illustra-
tion. For a quantitative analysis more experimental data is needed and the problem of die
crack needs a fracture mechanical approach for rigorous treatment. A resulting fracture
parameter is still expected to be proportional to σdue to the fact that silicon can be
treated linear elastically9. Die crack was not expected after all and not the focus of this
work.
8The idea for this correlation was born later.
9K-concept in fracture mechanics, see e.g. [114]
138 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
5.4.7 Extrapolation by Simulation:
Variation of some Interesting Parameters
Some simulations were run to investigate the influence of some geometric and material
parameters. Results were only obtained for the first cycle but from the experience gained we
can assume that the ranking is preserved. In this respect the following outcome represents
a tendency only. In figure 5.41 (a) the thickness of the adhesive layer is varied. Its original
thickness was had = 260 µm. The simulations were carried out for the epoxy-silicone
adhesive and hence for a viscoelastic material:
Overload (E1Bu)
No External Force
--
1/2 CTE & 10 E-Modulus
10 E-Modulus of Adhesive
1/2 CTE of Adhesive
1/4 Thickness of Adhesive
1/2 Thickness of Adhesive
E1Au Reference Group
0.000.010.020.030.040.05
25..-10 ˚C
-10..-38 ˚C
-38 ˚C
-38..90 ˚C
90..120 ˚C
120..125 ˚C
125..25 ˚C
(a)
(b)
(c)
Eqv. Creep Strain
Figure 5.41. Simulative extrapolation concerning the adhesive layer. Varied is its CTE
and E-Modulus with respect to the first configuration (reference group).
•Variation of Adhesive Thickness
For a smaller gap with which is more advantageous for cooling purposes there is a
rise in creep strain an so one expects a lower reliability (a).
•Variation of Adhesive CTE and E-Modulus
The CTE of the adhesive seems not to be very influential, whereas its elastic modulus
does. A softer material should produces more reliable results (b).
•Variation of External Force
The magnitude of an external force itself has no influence on the creep strain at
all (c). This is true only for adhesive groups or as long as the chip touches the
thermal interface medium. The force only bends the board, but it is much too
small to influence the stress in chip and bumps directly and to cause additional
strain. A maximum force of F=50Nonly results in a negligibly small stress
of σzz =−0.5MPa for a die with an area of 10 ×10 mm2as is used here. A
5.4. COMPARISON OF EXPERIMENTAL AND COMPUTATIONAL RESULTS 139
quick estimation by Hooke’s law yields, based on the high-TYoung’s modulus of the
underfill, a total strain delta of ∆εtot ≈0.0002 which is negligible.
Unfortunately the groups meant to prove this relationship experimentally were lost
due to die crack. Configurations with force Aand Bfor equal displacement were
only set for the flexible foil groups (see table 5.2). But this result still holds when
comparing F1Bu and F1Au in figure 5.23: Due to the foil thinning described in the
last section both have been subjected to loads different from those originally specified.
But still the displacements are nearly comparable as to be seen in table 5.4 and the
force of F1Bu larger than the one applied to F1Au. The experimentally obtained
reliability is similar.
1/2 CTE of Plate (= CTE Board)
Pure Adhesive Reference (E0x)
Smaller Chip (7 x 7 mm)
FC&RSC - Reference (E1Au)
Smaller Chip (7 x 7 mm)
FC - Reference (K0u)
0.000.010.020.030.040.05
(a)
(b)
(c)
25..-10 ˚C
-10..-38 ˚C
-38 ˚C
-38..90 ˚C
90..120 ˚C
120..125 ˚C
125..25 ˚C
Eqv. Creep Strain
Figure 5.42. Variation of other parameters of interest. Notable is the effect of chip size.
The respective reference group is underlined for each comparison.
•Variation of Chip Size
Figure 5.42 shows the effect of some geometric alterations. For the unconstrained chip
K0u the creep strain does not depend on die size10 (a), whereas for a mechanically
constrained chip E1Au this relationship is lost. A smaller chip will show longer life
than a big one under mechanical load (b) as the shear-strains, which depend on bump
position, will be smaller (see e.g. figure 5.8).
•Variation of Further Parameters
Further results show (figure 5.42): There is no dependence on the CTE of the plate
(c) on reliability as long as there is no fixation (as for E0x). The simulation (c) was
motivated by a paper [10] in which the contrary was stated.
10A related observation has been mentioned by [27].
140 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
5.5 Conclusions, Design Guidelines and Outlook
In this thesis we have numerically evaluated and experimentally verified the thermo-
mechanical reliability of flip-chip assemblies on organic boards under mechanical and ther-
mal loads11 induced by the attachment of a heat-spreader and thermal cycling. Boundary
conditions for this study were set by the automotive industry and the application for a
real (e.g. controller-) housing. Reliability was examined as function of thermal interface
material, displacement (with fixation) of the board, external force and board thickness.
These are characteristic variables which describe the load situation for flip-chip reverse
side cooling. Experiment and simulation could be consistently and to a good accuracy
correlated by the Coffin-Manson relationship, where bump creep strain was evaluated as
failure criterion. So for the first time it is possible to correlate reliability and flip-chip
cooling.
•It was found that reverse side cooling in flip-chip technology is a reliable option
for high-power thermal management. Each tested configuration reached more than
¯
Nf= 600 cycles under the given boundary conditions but for a thermally mismatched
assembly. This can still be largely improved by an optimized, thermally matched
set-up as already stated and summarized by the guidelines given below. The Coffin-
Manson coefficients could be determined to be c1=0.36 and c2=−2.33 which is
close to values found in literature.
•Low cycle solder fatigue was found to be the only failure mechanism, therefore the
Coffin-Manson approach is justified a posteriori. Delamination did not occur on a
large scale. Locally confined ablation did only concern the solder-passivation interface
and was shown to be uncritical for solder bump fatigue and therefore negligible.
•It was found that the reverse side attachment of a flip-chip assembly generally reduces
lifetime. A prolongation by means of a special fixation or state of bending is not
possible, therefore the mechanically unconstrained chip yields the best results.
•From a computational point of view mechanical loading leads mainly to an increase in
shear strain, whereas normal strain is mainly influenced by the thermal mismatch of
the solder-underfill/soldermask system. Shear strain depends on the kind and amount
of constraint on the free movability of the chip as a function of temperature. These
constraints, however, depends on board thickness (largest effect), fixation (large ef-
fect), displacement and interface material (pronounced effect) as can be concluded
from the ranking of configurations with respect to lifetime. The sign of curvature has
hardly got any influence on lifetime. A convexly bent chip yields a slightly higher
reliability than its concave counterpart. A force has no effect on reliability.
•The flip-chip assembly can be conceived as a system which undergoes periodic, ther-
mally driven deformation. Under the test conditions of thermal cycling the assembly
accommodates to the applied load after a convergence period of transient response.
11The thermal performance and viability of this concept has recently been studied and proved in [8]
using the same set-up, loads and thermal interface materials.
5.5. CONCLUSIONS, DESIGN GUIDELINES AND OUTLOOK 141
The movement of the chip diagonal (centre to corner) under periodic thermal load
stabilizes around a new equilibrium position determined by the applied mechanical
loads. The bump creep strain shows corresponding convergence behaviour.
•A modular parametric FE-model was developed, optimized and experimentally veri-
fied for this study. A novel concept consisting in the combination of standard modules
allows a very flexible, accurate and accelerated model generation and subsequent eval-
uation of creep strain within the bump. Corresponding guidelines are given. This
approach may also be extended to related packages wherever repetitive parts can be
modelled as standard module as e.g. any solder joint.
Design Guidelines
A distinct ranking can be drawn up according to the tested variables based on the com-
putational value for better resolution. The results and consequent design guidelines (DG:)
are once more compiled in table 5.5.
•The most reliable configurations are the unconstrained chips K0u,x together with
the adhesive groups without displacement E0x and S0x (a chip-sized heat-spreader
glued to the chip), followed by groups featuring displacement and fixation. DG: It is
not possible to increase reliability by reverse side attachment.
•A flip-chip assembly which is attached by an epoxy-silicone adhesive only shows
slightly higher reliability than the unconstrained one. It was shown that this is an
exception and only the case for a thermally mismatched solder-underfill system. For
this reason this result cannot be generalized, as normally the technically relevant
matched system is preferred which guarantees smaller bump creep strain and hence
a longer lifetime. The silicone adhesive group S0x, however, comes last for the con-
sidered configurations. DG: If a small (chip-sized) heat-spreader is sufficient, a very
reliable configuration can be realized by gluing it to the chip.
•Thick boards largely reduce lifetime. DG: As this is the strongest effect boards should
be as thin as possible. Tested values were b∈[0.8; 1.2] mm.
•A fixation of the board considerably increases bump creep strain and hence reduces
reliability. DG: The board should not be fixed unless global mismatch board-plate
can be eliminated. A sliding fixation solves the problem.
•Larger displacements produce lower reliability. DG: Displacement should be mini-
mized, but compared to fixation and board thickness its value has only a small effect.
So if no fixation is used, a comparatively large displacement can be realized.
•A convex curvature of the chip seems to produce slightly better results than a concave
one (which is the normal state of bending for an unconstrained chip). DG: Achip
may also be bent convexly, allowing negative values of displacement if needed.
142 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
•Groups using a gap-filler prove slightly more reliable than those with an adhesive.
The epoxy-silicone adhesive yields slightly better results than the silicone-based one.
A distinction between the gap-fillers is hardly possible. DG: Gap-fillers are to be
given preference. If an adhesive is employed, it should have a low E-modulus (E<
500 MPa) and low CTE (α<100 ppm/K) for all Tto maintain a low stress bond
and prevent a stretching out of the die at low Tas encountered for the silicon adhesive
which features a CTE of α≈200 ppm/K and increasing Eat low T.
•A force has no detectable influence on reliability. DG: A design need not consider
the magnitude of a force.
•In the temperature and time domain used for testing this assembly board-viscoelasticity
is not as important an effect as board-orthotropism for the simulation. There is,
however, a reduction of normal bump strain which is due to a lower out-of-plane
E-modulus for an orthotropic formulation. DG: Therefore a board should be highly
orthotropic for high reliability, Ez<6GPa. Still, the board should be implemented
as orthotropic and viscoelastic material to capture both characteristic properties.
This, however, requires a new element capability for the respective FE-tool in use.
•For a mechanically loaded flip-chip assembly its reliability is not independent from
chip size any more. The chip should be kept small, as under identical loads a chip
with A=7×7mm2did show lower creep strains than the A=10×10 mm2chip.
•A fracture criterion for die crack based on the maximally allowed surface stress could
be evaluated to σc= 100 MPa. This corresponds to a (board thickness-dependent)
critical deflection kc=52µm and kc=44µm for thin and thick board respectively.
In the experiment this condition was met if a maximum displacement of dc≈300 µm
was not exceeded.
The early overall failure is in accordance with the large simulated creep strains, which are
mainly due the high normal strains induced by the solder/underfill mismatch. As can be
seen from the inset in figure 5.30, reliability and the difference between the groups would
be much larger for lower values of strain. The effect of the mechanical loads (shear strain)
would also be better resolved in that case. Then values above ¯
Nf>1500 can be reached
for most loaded groups12 in contrast to the experimentally obtained value of ¯
Nf>600.
This can be realized by following the guidelines given below.
•The solder gap is very small (h=47µm). So the bump creep more. DG: Creep
strain depends strongly on h, so the gap should be maximized.
•There is a prolonged creep phase due to the heat capacity of the attached heat
spreader during thermal cycling. This may be responsible for the large amount of
solder coarsening.
12Based on the values of a matched underfill-solder system taken from figure 5.10 and extrapolated with
the inset of figure 5.30
5.5. CONCLUSIONS, DESIGN GUIDELINES AND OUTLOOK 143
•The very large underfill-solder mismatch (αUF ≈2αSnPb) induces additional normal
strain in the bump which reduces reliability. DG: The underfill (and if possible also
the soldermask) must be thermally matched to the solder. Use αUF >24 ppm/K
and αSM <70 ppm/K.
•The extraction of voids (non-standard process) under vacuum caused initial damage
(gaps, pre-cracks) and blurs the statistical outcome. DG: Flip-chip processes should
be optimized not to produce any voids.
•The pad diameter is small φ=75µm – there is less solder to crack. The lateral
extension of the bump is of no influence. DG: Bumps with larger pads respond
favourably in terms of reliability.
Compilation of Results and Design Guidelines
Variable Effect on Reliability Design Guidelines
positive (+), neutral (0), negative (−) (Values as tested)
Displacement −Proportional to value d∈[−200; 200] µm
Fixation −If αBoard(T)=αP late(T) Sliding, matched or none
Force 0Within checked range F∈[17; 50] N
Adhesive +Low Efor all TE<500 MPa
+Low α(T) for all Tα<100 ppm/K
0Large gap b∈[65; 260] µm
Gap Filler + Slightly better than adhesives by <10 %
Curvature −If constrained at high TUse low stress bond
(Response) 0 At low T
+If convex d<0 is possible
Processes 0 Curing of adhesives Tcure = 160 oC
−Extraction of voids by vacuum To be avoided
Delamination 0 Localized around pad Width a<20 µm2
−If of size of pitch around bump A= 250 ×250 µm2
Board +Thin b∈[0.8; 1.2] mm
Board +Low EzEz<6GPa
Underfill −If αUF(T)=αSnPb(T)αUF >24 ppm/K
Soldermask −If αSM(T)αUF(T)αSM <70 ppm/K
Heat Spreader 0 α(T) (if no fixation)
Chip +If small size A∈[7 ×7; 10 ×10] mm2
0 Size if die is unconstrained
Bumps +If small pad; If large gap width φ>75 µm;b>47 µm
0Lateral extension a∈[160; 230] µm
−Voids φ<10 µm†
Surface stress 0 If below value for die fracture σ<σ
c= 100 MPa
Table 5.5. The individual factors and their impact on Flip-Chip reliability according to
this study. Recommendations are given based on the checked range of values. For remaining
details refer to the text. †Below this value no voids could be detected, φis a diameter.
144 CHAPTER 5. RESULTS AND DISCUSSION – SIMULATION VS EXPERIMENT
Optimum Configuration
Working on the given design guidelines the configuration optimized for reliability looks as
follows. Based on the a multi-chip module as depicted in figure 2.3 one obtains:
•A flexible foil is used as thermal interface material as this produces the most reliable
results and allows for lateral movement of the die (i.e. a thermo-mechanical decou-
pling) if more than one chip is on the board. Otherwise other chips may have the
negative effect of a fixation.
•As there a manufacturing tolerances G, a force per chip of
F≥FG+FN=1
pb
dG+FN, (5.9)
which displaces the board by dGto bridge the hence existing gap should be applied
(cf. equation 5.1). The force may exceed the calculated value as this does not affect
reliability. A displacement reduces lifetime only slightly in this configuration. Should
convex bending of the die occur, this is of no further concern.
•The board is thermo-mechanically decoupled from the housing (i.e. the heat-spreader,
e.g. aluminium) to eliminate the thermal mismatch. For this purpose a sliding fixation
is used to hold the board in place.
•The flip-chip assembly is mounted on a thin board (b=0.8mm) and its under-
fill is thermally matched to the void-free eutectic solder bumps. The CTE of the
soldermask is lower than αSM <70 ppm/K.
For the situation where only a chip-sized heat-spreader is needed (in a casing where there is
enforced convection) the following reliable solution is possible as a ’spin-off’ of this study:
•A low stress bond is established between the chip’s reverse side and the heat-spreader
by a thermal adhesive with low CTE α(T)<100 ppm/K and low stiffness E<
500 MPa for all temperatures.
•The thickness of the adhesive is set by thermal boundary conditions, but if a highly
conductive material is used a larger gap can be realized which increases reliability.
•A curing process t= 900 s,T= 160 oCdoes not reduce the reliability of the assembly.
Outlook
•Extreme solder coarsening was observed during cycling. It was speculated if this was
due to a prolonged ramping time which theoretically allows more creep. A cross-
check should be made with chips subjected to a different thermal cycle to see if this
phenomenon persists.
5.5. CONCLUSIONS, DESIGN GUIDELINES AND OUTLOOK 145
•For future experimental analysis of bump failure use a chip which is devised for four-
point measurements for a maximum number of bumps (not just eight bumps) for more
data. Desirable is further a daisy-chain which allows multiple access to measure its
resistance for a smaller group of bumps (for example around the corner) for failure
localization. This measurement should be conducted in four-point arrangement, too.
Appendix A
Annotations on Theory
Here we give an overview over the definitions, mathematical conventions and most impor-
tant abbreviations which are used in this work.
An other section will provide a brief summary about the Weibull distribution and how it
is applied to fatigue phenomena.
A.1 Conventions and Notation
A.1.1 Units
If not specified otherwise, this consistent system of units is used [57].
Units
Quantity Unit
Length mm (Millimetres)
Force N(Newtons)
E-Modulus, Stress, Pressure MPa (Megapascals)
Time s(Seconds)
Mass t(Tons)
Temperature Kor oC
Table A.1.
Helpful is: 1 psi = 6890 Pa.
A.1.2 Mathematical Representation
Throughout the thesis stress is normally symbolised by the tensor σij and strain by εij
(mathematical notation). Engineering notation {σi,τ
ij}is hereby translated into {σii,σ
ij}
and {εi,1/2γij}into {εii,ε
ij}.
146
A.1. CONVENTIONS AND NOTATION 147
Mathematical Notation
Quantity Symbol
Scalar a
Vector a,ai
Tensor ˆa,aij
Equivalent Entity ¯a
Derivative with respect to td
t,∂t
Table A.2.
Einstein’s sum convention is used. Hereby the sum extends over doubly appearing indices.
bi=
j
αijaj=αijaj.(A.1)
Ansys commands are printed in typewriter style.
A.1.3 Abbreviations
Table of Abbreviations
Abbreviation Meaning
CSP Chip Size Package
CTE Coefficient of Thermal Expansion
DC Daisy Chain
DMA Dynamic Mechanical Analyis
DNP Distance to Neutral Point
FC Flip-Chip
FC&RSC Flip-Chip and Reverse Side Cooling
FE Finite Element(s)
PCB Printed Circuit Board
QFP Quad Flat Package
SB Single Bump
SEM Scanning Electron Microscopy
TMA Thermo Mechanical Analysis
UBM Under Bump Metalisation
US Ultrasound
Table A.3. A compilation for quick reference.
For material abbreviations see table 4.1.
For group encoding see table 5.1.
148 APPENDIX A. ANNOTATIONS ON THEORY
A.2 Heat Transfer
The heat energy flow per unit time PTtransferred though any area Ato a conductive
medium can be evaluated as (see e.g. [115]):
PT=dQT
dt =A
jdA,(A.2)
where jis the heat current density
j(r)=−ˆ
λT(r)∇
rT(r). (A.3)
In its most general form the thermal conductivity λis a tensor. If the current density is
homogeneous and passes through the area orthogonally, the equations reduce to
|PT|=jA =λ∆T
∆bA.(A.4)
As the temperature rises heat can be transferred also by radiation. The fraction of energy
per unit time and area dissipated by the whole frequency spectrum νof electromagnetic
waves is according to the Stefan-Boltzmann law for black body radiation [59] proportional
to T4:PT
A=ν
dν p(ν)=c(T4−T4
0), (A.5)
where c=5.6×10−8W
m2K4,p(ν) the spectral power density and T0the ambient temperature.
A.3 Time Dependence of Viscoelastic Moduli
We will briefly outline the derivation of equation 3.52. Point of departure is the hereditary
integral form of the stress-strain relationship for isotropic viscoelastic materials:
σij(t)=t
0
dt2G(t−t)˙eij(t)+3K(t−t)˙em(t)δij,(A.6)
We consider a relaxation test. An oblong bar is strained in x-direction: εxx(t)=εxxθ(t−t0).
This entails εyy(t)=εzz(t) and no shear strains. For the stresses only σxx =0. Wecan
write:
σxx(t)=t
0
dt4
3G(t−t)(˙εxx(t)−˙εyy(t)) + K(t−t)(˙εxx(t)+2˙εyy(t)) . (A.7)
Then we exploit
σyy(t)=t
0
dt2G(t−t)(˙εyy(t)−˙εxx(t)) + 3K(t−t)(˙εxx(t)+2˙εyy(t)) = 0. (A.8)
A.4. WEIBULL-DISTRIBUTION 149
If we insert this into the previous equation we may eliminate e.g. K(t)andobtain:
σxx(t)=t
0
dt2G(t−t)( ˙εxx(t)−˙εyy(t)) and (A.9)
σxx(t)=t
0
dt3K(t−t)( ˙εxx(t)+2˙εyy(t)). (A.10)
Rewriting the first equation using ˙εyy(t)=−˙ν(t)εxx(t)−ν(t)˙εxx(t) like
σxx(t)=t
0
dt2G(t−t)(1 −ν(t)) ˙εxx(t)+t
0
dt2G(t−t)˙ν(t)εxx(t) (A.11)
yields after insertion of the initial conditions εxx(t)=εxxθ(t)and ˙εxx(t)=εxxδ(t), i.e. as-
suming the strain to be applied at zero time
σxx(t)
εxx
=E(t)=2G(t)(1 −ν0)+t
0
dt2G(t−t)˙ν(t). (A.12)
We take the Laplace transform of the above equation taking into account L(f(t)) = ˜
f(s)
and L(dtf(t))=s˜
f(s)−f(0+) and the convolution theorem
˜
E(s)=2˜
G(s)(1 + ν0)+2˜
G(s)s˜ν(s)−2˜
G(s)ν0. (A.13)
Applying the same procedure to the second equation in A.10 and simplifying yields
˜
G(s)= ˜
E(s)
2(1 + s˜ν(s)) (A.14)
˜
K(s)= ˜
E(s)
3(1 −2s˜ν(s)). (A.15)
which is equivalent to equation 3.52 as was to be proved.
A.4 Weibull-Distribution
The Weibull distribution is often encountered in the description of lifetime phenomena as
for example solder fatigue [68,110,111]. It can reflect decreasing, constant and increasing
failure rate λ(t), i.e. the percentage occurrence of failure as a function of increasing ran-
dom variable t. This behaviour manifests itself in the well-known ‘bathtub’-shaped curve
depicted in figure A.1.
The Weibull distribution is a two-parameter function (λ, β) and can be defined by its
probability density function:
f(t)=λβ(λt)β−1e−(λt)β. (A.16)
Then the Weibull cumulative distribution function describes the probability ¯pthat an event
that item iwill have failed under given service conditions after a time τihas elapsed:
¯p(τi<t)=F(t)=t
0
dtf(t)=1−e−(λt)β. (A.17)
150 APPENDIX A. ANNOTATIONS ON THEORY
10
010
110
210
310
4
10
0
10
1
10
2
10
3
Wearout
Failure
Constant
Failure
Early
Failure
Failure Rate [a.u.]
Random Variable [a.u.]
Figure A.1. Typical ‘bath-tub’-shaped failure rate of Weibull distribution.
Then the reliability function R(t) describes the probability pfor the inverse event, that
the item performs flawlessly until t=τi:
p(τi<t)=R(t)=1−F(t)=et
0dtλ(t)as ∞
0
dtf(t) = 1. (A.18)
This means for the failure rate λ(t) according to the definition:
λ(t)=−dtR(t)
R(t)=λβ(λt)β−1, (A.19)
where always λ=1/tcand tcis the characteristic lifetime where 63 % of the items have
failed (dtis the derivative with respect to t).
The mean time to failure of the distribution is calculated to
¯
t=∞
0
dttf(t)=tcΓ(1 + 1/β), (A.20)
i.e. the time after which 50 % of the items have failed. Here, Γ is the Gamma-function [116].
Working on the principle that no defects are detectable at t= 0, the distribution can
describe, depending on the Weibull exponent β, different cases (cf. figure A.1).
•β<1: Early failures (or infant mortality1) due to randomly distributed weaknesses
in the material due to process or quality related problems, not deterministic. Failure
occurs during burn-in or initial tests. λ(t) tends to infinity as the random variable
approaches zero.
Samples belonging to this group are be sorted out for lifetime evaluation.
1This curve also reflects a human death table.
A.4. WEIBULL-DISTRIBUTION 151
•β= 1: Constant failure rate: In this region no aging or wearout occurs. The
distribution essentially resembles a exponential distribution.
•β>1: Increasing failure rate: Degradation processes (aging and wearout) occur,
damage accumulates. These region is typical for solder fatigue. For β= 2 this failure
rate is linearly increasing (cf. A.19), for values even larger the distribution becomes
a normal distribution.
In a logarithmic representation2as e.g. in figure 5.22 F(t) appears as a straight line and β
represents the function gradient of this Weibull plot according to:
ln ln 1
1−F(t)=βln(t)+βln(λ). (A.21)
For the numerical evaluation the experimental F(t) is linearly fitted (by a least squares
algorithm) to this line to yield tcand β.
For the analysis of the failure mode solder fatigue we contemplate the failure mechanism of
creep crack growth which causes electrical failure or breakdown of the component (flip-chip
assembly).
Important for the evaluation of the lifetime of a flip-chip assembly is the failure of the
first bump. This is a system without redundancy, i.e. all items (bumps) must work to
assure function of the system. The used daisy-chain is a series-structure and theoretically
signalises the event of failure of the one first bump. We have to consider: If
p(t<τ
i)=R(t)=e−(λit)βi(A.22)
is the reliability of one bump, then – given that all bumps are identical (λi=λ, βi=β)–
the reliability of nbumps is:
Rtot(t)=
n
i=1
pi(t<τ
i)=
n
i=1
Ri(t)=
n
i=1
e−(λit)β
i(A.23)
=e−n(λt)β=e−(λn1/βt)β=e−(λtott)β, (A.24)
where now a higher failure rate for the system λtot =λn1/β could be derived. Obviously
this results in a lower overall reliability. In this vein the characteristic lifetime ttot
ccan be
evaluated to:
ttot
c=tcn−1
β. (A.25)
For calculation of the mean equation A.20 is used.
2X-axis logarithmic, y-axis double logarithmic.
Appendix B
Annotations on Materials
Here we give the results of the characterisation of the remaining materials including the
data files for Ansys-input.
B.1 Dimensions of Dog’s-bone Specimen
The dog’s bone specimens as they are depicted in figure 3.8 were shaped according to the
below depicted dimensions. Thickness is 2 mm.
&
"
#
#
Figure B.1. Dimensions of test-specimen # 53504 in [mm].
B.2 Organic Board
B.2.1 Measured Viscoelastic Material Data
The measured data for the organic board was recorded on a Zwick 1446 universal testing
machine. The last measured curve (T= 150 oC) shows a different relaxation behaviour.
This might be due to measurement inaccuracies as this value does not fit into the WLF
regime (figure B.4). It could be attributed to more than one relaxation processes (deviation
from pure exponential decay) occurring at this temperature.
A typical feature of organic boards, i.e. glass fibre reinforced epoxy compounds, is a severe
reduction of the CTE above Tg. This is caused by the dominance of the (relaxed) glass
fibres which exhibit CTEs close to α≈2ppm/K or even lower.
152
B.2. ORGANIC BOARD 153
1101001000
10000
12000
14000
16000
18000
20000
22000
24000
Sim 70 ˚C
150 ˚C
Sim 125 ˚C
125 ˚C
100 ˚C
70 ˚C
50 ˚C
T = 30 ˚C
E(t) [MPa]
t [s]
Figure B.2. Measured relaxation data of organic board. Simulated data is printed in
dashed lines.
01234567
9000
12000
15000
18000
21000
24000
21000 MPa
from Pull - Test
T < 150 ˚C
Tref = 30 ˚C
T=30˚C -> lg t
T=50˚C -> lg t +0.6
T=70˚C -> lg t +1.2
T=100˚C -> lg t +1.55
T=125˚C -> lg t +1.8
T=150˚C -> lg t +2.7
E(t) [MPa]
lg t'
Figure B.3. Temperature-time shifted data for construction of mastercurve (dashed line).
154 APPENDIX B. ANNOTATIONS ON MATERIALS
280300320340360380400420440
-1
0
1
2
3
not taken
into account
T [˚C]
C
1
= 3.3
C
2
= 77.5
T
ref
= 303 K
Shift Factor from Data
WLF - Fit, T
ref
= 30 ˚C
lg a(T)
T [K]
727476787107127147167
Figure B.4. WLF shift function for organic board.
B.2. ORGANIC BOARD 155
B.2.2 Ansys Data File for Viscoelastic-Isotropic Board
!============================================================================
! Organic Board
!--viscoelastic constants input for usrve5x.f
!----------------------------------------------------------------------------
tb,evisc,mat_fr ! initialize
tbda, 1, 3.28 ! wlf c1
tbda, 2, 77.44 ! wlf c2
tbda, 4, 303 ! wlf tref
tbda, 5, 20 ! function key, must be 20
!--temperature and cte input-------------------------------------------------
!- follows 5 temp in ascending order covering t-range of simulation
tbda, 26, 210, 273, 388, 408, 440
!- follows 5 corresponding cte values
tbda, 36, 11.5e-6, 11.5e-6, 11.5e-6, 1.2e-6, 1.2e-6
!--prony setup---------------------------------------------------------------
!-- these next four coeff are modified by x 0.7 to account for orthotropy
tbda, 46, 6729.12 ! 9613.04 ! G0
tbda, 47, 2495.40 ! 3564.87 ! Ginf
tbda, 48, 7370.02 ! 10528.6 ! K0
tbda, 49, 7370.02 ! 10528.6 ! Kinf
tbda, 50, 7 ! # g
! -- prony coeff shear-------------------------------------------------------
tbda, 51, 0.0187527001065796
tbda, 52, 0.009571006487340366
tbda, 53, 0.15913976237286734
tbda, 54, 0.4571182689898273
tbda, 55, 0.2610001403657228
tbda, 56, 0.05423469041781277
tbda, 57, 0.04018343125984965
! -- prony times shear-------------------------------------------------------
tbda, 61, 99.72507728233133
tbda, 62, 998.6102310320236
tbda, 63, 4366.5765878401835
tbda, 64, 11722.110300122671
tbda, 65, 47951.251043004006
tbda, 66, 197666.3873758236
tbda, 67, 497700.88540016394
!-- end of viscoelastic data input-------------------------------------------
!-- Comment: Viscoelastic Input has assumed an effective nu = 0.15, since
!-- the material, although orthotropic, can only be simulated isotropically.
!----------------------------------------------------------------------------
!============================================================================
156 APPENDIX B. ANNOTATIONS ON MATERIALS
B.2.3 Ansys Data File for Elastic-Orthotropic Board
!============================================================================
! Organic Board, orthotropic, elastic, temp-dep.
mptemp,1, 220, 268, 308, 348, 368 ! T-Table in Kelvins
mptemp,6, 388, 398, 408, 443
!----------------------------------------------------------------------------
mpdata,ex,mat_fr,1, 17850, 17850, 17850, 17850, 17850
mpdata,ex,mat_fr,6, 17000, 16000, 15725, 15725
mpdata,ey,mat_fr,1, 17850, 17850, 17850, 17850, 17850
mpdata,ey,mat_fr,6, 17000, 16000, 15725, 15725
mpdata,ez,mat_fr,1, 7055, 7055, 7055, 7055, 7055
mpdata,ez,mat_fr,6, 5695, 5000, 4420, 4420
!----------------------------------------------------------------------------
mpdata,gxy,mat_fr,1, 6630, 6630, 6630, 6630, 6630
mpdata,gxy,mat_fr,6, 6290, 6000, 5822, 5822
mpdata,gxz,mat_fr,1, 2250, 2250, 2250, 2250, 2250
mpdata,gxz,mat_fr,6, 2122, 2100, 2040, 2040
mpdata,gyz,mat_fr,1, 2250, 2250, 2250, 2250, 2250
mpdata,gyz,mat_fr,6, 2122, 2100, 2040, 2040
!----------------------------------------------------------------------------
mpdata,prxy,mat_fr,1, 0.15, 0.15, 0.15, 0.15, 0.15
mpdata,prxy,mat_fr,6, 0.15, 0.15, 0.15, 0.15
mpdata,prxz,mat_fr,1, 0.35, 0.35, 0.35, 0.35, 0.35
mpdata,prxz,mat_fr,6, 0.35, 0.35, 0.35, 0.35
mpdata,pryz,mat_fr,1, 0.35, 0.35, 0.35, 0.35, 0.35
mpdata,pryz,mat_fr,6, 0.35, 0.35, 0.35, 0.35
!----------------------------------------------------------------------------
mpdata,alpx,mat_fr,1, 9.80e-6, 9.30e-6, 8.60e-6, 7.20e-6, 5.95e-6
mpdata,alpx,mat_fr,6, 3.48e-6, 2.27e-6, 1.20e-6, 1.20e-6
mpdata,alpy,mat_fr,1, 9.80e-6, 9.30e-6, 8.60e-6, 7.20e-6, 5.95e-6
mpdata,alpy,mat_fr,6, 3.48e-6, 2.27e-6, 1.20e-6, 1.20e-6
mpdata,alpz,mat_fr,1, 61.0e-6, 68.3e-6, 78.6e-6, 90.2e-6, 106.0e-6
mpdata,alpz,mat_fr,6, 135.0e-6, 140.0e-6, 142.0e-6, 142.0e-6
!--- use secant gradient for CTE Definition T= 433 K
!============================================================================
The data is temperature-dependent. It is important to note that Ansys wants the CTE to
be inserted as secant value ¯α(T), not as tangent value α(T). Therefore the given tangent
values (which are needed for the viscoelastic routine) are transformed into secant values.
This can be effectuated by:
¯α(T)= 1
T−Tref Tref
T
dT α(T). (B.1)
There is a trick which applies to polymers to circumvent this tedious procedure: For
increasing α(T) the corresponding values of ¯α(T) may be automatically calculated by
inserting the α(T) values together with the command mpamod,mat,Tg,whereTgis the
glass transition temperature. Unfortunately this does not work here for alpx due to a
decreasing α(T). Tref = 160 oCas stress-free point.
B.2. ORGANIC BOARD 157
B.2.4 Calibration of Viscoelastic Board Data (Full Account)
The main steps and results of the calibration process of the organic board data has been
explained in section 4.3.3. Here we give the steps of this process in full and in chronological
order.
It will be shown that the simulation can reproduce the experimental values for either
viscoelastic-isotropic and elastic-orthotropic material behaviour if an effective modulus is
introduced. This can be ascribed to the material’s inhomogeneity and layered structure.
Viscoelastic behaviour does seem not to govern the bending of the assembly in the examined
temperature and time domain. In the discussion we refer to table B.1; The columns from
left to right are:
Variables: Thickness of the board; Temperature drop after cooling down from curing tem-
perature; Material law (elastic-orthotropic/viscoelastic-isotropic); Cooling time; Poisson’s
ratio (in plane, out of plane); Glass transition temperature; Coefficient of thermal expan-
sion (in plane, out of plane) below Tg; CTE above Tg; Factor for effective stiffness; Applied
external force aimed for d= 100 µm;
Observables: Thermal deflection of chip; Mechanical deflection of chip; z-displacement of
board.
For reasons of clarity the variations of the individual variables are grouped together. Now
it is the task to vary the variables in that the observables for thin and thick board show
maximum accordance under the given boundary conditions. Hereby every computationally
obtained result is to be compared to rows (1a,b) from the experiment.
•Row (2a):
First of all the elastic-orthotropic set was used. This had been the time-honoured
way to simulate an organic board and accounts for the fact that the board is clearly
not isotropic. It is obvious that kTis largely overestimated. Apart from that, the
board is too stiff. The values of kFshould only be compared at the experimental
value d= 100 µm.
•Row (2b):
It was checked if the poisson’s ratio could have any influence since these values were
only determined by the method of the ‘educated guess’: As we have to deal with
pure fibre-epoxy (hardly any copper) the in-plane value is dominated by the glass
fibres (0.15) whereas the out-of-plane value should be epoxy-like (0.35). An exchange
of the values produces the expected result, a board which is less stiff (less in-plane
contraction).
•Row (3a):
It was checked if this discrepancy could be remedied by the assumption of a vis-
coelastic board, i.e. if this overestimation of kTis due to any not considered stress
relaxation effects which were clearly measured and were described in the last sec-
tion. Still, the value of the deflection is hardly influenced by this alteration. Here,
(too large) values from literature for the CTE have been assumed. As Ansys only
supports isotropic viscoelasticity the in-plane value of νwas chosen.
158 APPENDIX B. ANNOTATIONS ON MATERIALS
•Row (3b,c):
A scaling factor βis introduced which results in an effective E-modulus according to
equation 4.11 which affects only dbut not kT. The thick board is evaluated, too.
•Row (4a,b,c,d)
shows the strong dependence of kTon Tgand the CTE for both thicknesses. Better
values are reached when smaller values for either quantity are used. This tendency
is indeed experimentally confirmed (TMA). At the same time the thickness of the
board is remeasured and found to differ from the manufacturer’s value.
•Row (5a,b,c,d,e)
shows the influence of board thickness. To the measured value for pure fibre-epoxy
(rows (1a,b)) a thickness for the solder mask averaged over the area of the board is
added (20 µm for either side of the board). This levels out the difference between
the thick and the thin board. Now the newly measured values for Tgand CTE are
used, too. (5b,e) represent the closest sets.
•Row (6a,b,c)
show the small influence of the cooling time. This states that the decrease in the E-
modulus of the board in this time domain is not a very crucial factor for bending. But
also a smaller, time independent E-modulus (Eeff ) has no influence on the deflection
kT.
•Row (7a,b)
checks if a further reduction of Poisson’s ratio has any influence.
•Row (8a,b)
proves the linear relationship between kF,dand F.
•Row (9a,b,c,d,e,f):
These simulations check for the influence of βon the optimized sets. The factor only
influences dlinearly and kTnot at all. The dependence of kFon βis not linear in
Fthough as can be seen from row (9f). Row (9e) uses a different factor also for
comparison to the elastic material data set in the next lines.
•Row (10a,b,c,d):
Back to the elastic-orthotropic data. Optimized values for CTE and Tgand bare
used to recheck to accordance with the experiment. A factor βel =0.85 can be
calculated for best agreement with the experimental data and comes very close also
to the viscoelastic simulations. This fact is depicted in figure 4.16 where the best
sets of either material behaviour are compared.
•Row (11a):
Influence of degree of orthotropism. In (11a) elastic-isotropic material data was
used. The orthotropic case is (10a). The anisotropy accounts for a reduction of
approximately 10% of the stiffness of the board.
•Row (12a,b,c):
Introduction of an effective board thickness according to equation 4.12 instead of an
B.2. ORGANIC BOARD 159
effective modulus. This is possible for a pure board and has been checked against the
experiment for three board thicknesses (see figure B.5). But for a flip-chip on board
the effecive E-modulus produces better results as to kTso this version was preferred
in the end.
0.80.91.01.11.21.31.41.51.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
Original Viscoelastic
Material Data
Equation:
b
eff
= 0.878 * b
0
+ 0.01 [mm]
Calibrated for
100 µm z-displacement
Linear Fit
Simulated Board Thickness beff
[mm]
Measured Board Thickness b0
[mm]
Figure B.5. Measured versus simulated data using an effecive board thickness instead of
an effective E-modulus.
-0.06-0.05-0.04-0.03-0.02-0.01
0.3
0.5
0.7
0.9
1.1
1.3
1.5Thin Board
r(k) = -0.0208*1/k + 0.055 [m]
Temperatures:
25 ˚C
15 ˚C
5 ˚C
-5 ˚C
-15 ˚C
-25 ˚C
-35 ˚C
Fit
d=200 µm
d=0 µm
d=400 µm
T=-35 ˚C
T=25 ˚C
r [m]
k [mm]
Thick Board
Figure B.6. The radius of curvature as a function of the deflection k. The values com-
prise different temperature and board thickness and displacement. To a very good approx-
imation the inverse proportionality is confirmed and independent from the applied loads
within the given range.
160 APPENDIX B. ANNOTATIONS ON MATERIALS
Board Data: Elastic vs Visco-elastic (Full Version)
#b T Law tcool νxy,xz Tgαxy,xz,T<T
gα,T>T
gβ F kTkFdComment
Units [mm] [ oC] [s] [ oC] [ppm/K] [ppm/K] [N] [mm] [µm] [µm](chronological)
Exp 1a 0.78 160-25 ?? 300 ?? 115-135 11.5; 42.0 1.2; 140 -7.7 20.3 4.6 100 measured data:
1b 1.15 160-25 ?? 300 ?? 115-135 11.5; 42.0 1.2; 140 -20.3 15.8 6.9 100 kand dlinear in F
Sim 2a 0.8 160-20 el-ortho 300 0.35, 0.15 125 13.0; 42.0 4.5; 140 17.7 27.2 4.5 81.5 d, kF-good, kT-bad
2b 0.8 0.15, 0.35 17.7 27.2 591.8 Effect of Poisson’s ratio
3a 0.8 160-20 ve-iso 1000 0.15 125 13 4.5 17.7 27.8 4.7 73.4 try ve: kTstill too large
3b 0.8 0.8 7.7 28.3 5.5 90 try factor β
3c 1.2 0.8 20.3 20.1 6.3 83.5 same for thick board
4a 0.8 160-25 ve-iso 300 0.15 134 12.2 1.5 0.7 7.7 25.3 6.3 106 all values still too large
4b 0.8 125 0.7 7.7 23.5 5.7 106 vary Tg,α
4c 1.2 1000 134 0.7 20.3 18.1 6.9 94 vary tcool
4d 1.2 125 0.7 20.3 16.6 6.7 94
5a 0.8 160-25 ve-iso 300 0.15 125 11.5 1.2 0.7 7.7 21.5 5.8 105.8 newly measured α
5b 0.82 0.7 7.7 21.1 5.2 99.9 newly measured thickness b
5c 1.2 0.7 20.3 15.51 6.8 94 vary b
5d 1.22 0.7 20.3 15.3 6.5 90 vary b
5e 1.18 0.7 20.3 15.7 7.05 98.5 vary b
6a 1.2 160-25 ve-iso 300 0.15 125 12 1.2 0.7 20.3 16.45 6.7 94 vary tcool
6b 1.2 600 0.7 20.3 16.17 6.7 94 has only small effect
6c 1.2 1000 0.7 20.3 16.02 6.7 94
7a 1.2 160-25 ve-iso 300 0.05 125 0.7 20.3 16.28 6.95 96 vary ν
7b 1.2 0.15 12 10.7 20.3 16.4 6.7 94
8a 1.2 160-25 ve-iso 1000 0.15 125 12.2 1.5 0.7 20.3 16.6 6.9 94 show linearity for d, kF
8b 1.2 0.7 40.6 16.6 13.7 187
9a(5e) 1.18 160-25 ve-iso 300 0.15 125 11.5 1.2 0.7 20.3 15.7 7.05 98.5 best set visco
9b 1.18 120.3 14.9 5.4 70 βhas no effect on kT
9c(5b) 0.82 0.7 7.7 21.1 5.2 99.9 best set visco
9d 0.82 17.7 20.5 4.3 70.3 βhas no effect on kT
9e 0.82 0.83 7.7 20.9 4.8 83 compare to elastic
9f 0.82 0.7 5.4 21.1 3.9 70 βhas no effect on kT
10a 0.82 160-25 el-ortho 300 0.15, 0.35 125 11.5; 42.0 1.2; 140 17.7 20.6 4.5 85 adjusted set elastic
10b 1.18 120.3 15.2 5.9 83 adjusted set elastic
10c 0.82 0.85 7.7 20.6 5.1 99 βhas no effect on kT
10d 1.18 0.85 20.3 15.5 797.5 best sets elastic
11a 0.82 160-25 el-iso 300 0.15 125 11.5 1.2 0.85 7.7 20.4 4.9 90.7 isotropic and elastic - stiffer
12a 0.73 160-25 ve-iso 300 0.15 125 11.5 1.2 17.7 22.3 5.3 97 beff for 0.8mm board
12b 1.045 120.3 16.7 797 beff for 1.2mm board
12c 1.38 143.8 12.7 8.4 100 beff for 1.6mm board
Table B.1. Detailed and chronological account of adjustment process of board data.
B.3. SOLDERMASK 161
B.3 Soldermask
1101001000
0
1000
2000
3000
4000
5000
6000
7000
Sim. 100 ˚C
Sim. 25 ˚C
Sim. 60 ˚C
125 ˚C
100 ˚C
85 ˚C
70 ˚C60 ˚C
50 ˚C
T = 25 ˚C
E(t) [MPa]
t [s]
Figure B.7. Measured relaxation data of soldermask adhesive.
03691215
0
1000
2000
3000
4000
5000
6000
7000
25 ˚C -> lg t
50 ˚C -> lg t + 2.6
60 ˚C -> lg t + 3.6
70 ˚C -> lg t + 4.7
85 ˚C -> lg t + 2.6
100 ˚C -> lg t + 7.9
125 ˚C -> lg t + 9.8
Mastercurve
E(t) [MPa]
lg t'
Figure B.8. Temperature-time shifted data to construct mastercurve.
162 APPENDIX B. ANNOTATIONS ON MATERIALS
300320340360380400
0
2
4
6
8
10
12
T [˚C]
C
1
= 181
C
2
= 1535
T
ref
= 298 K
Shift Factor from Data
WLF - Fit, T
ref
= 25 ˚C
log a(T)
T [K]
27476787107127
Figure B.9. WLF shift function.
The soldermask (epoxy resin) data as it was measured on a dynamic testing machine
(MTS). Special clamps were used to fix the b= 100 µm thin foil. The dog’s-bone specimens
were cut from a sheet after etching away the copper foil it was dispensed on.
B.3. SOLDERMASK 163
B.3.1 Ansys Data File for Soldermask
!============================================================================
! Soldermask: isotropic, viscoelastic, userdefined subroutine "UsrViscEl.F"
!--viscoelastic constants input for usrve5x.f
!----------------------------------------------------------------------------
tb,evisc,mat_sm ! initialize
tbda, 1, 181.0 ! wlf c1
tbda, 2, 1532.99 ! wlf c2
tbda, 4, 293 ! wlf tref
tbda, 5, 20 ! function key, must be 20
!--temperature and cte input-------------------------------------------------
!- follows 5 temp in ascending order covering t-range of simulation
tbda, 26, 210, 273, 373, 393, 440
!- follows 5 corresponding cte values
tbda, 36, 72.9e-6, 72.9e-6, 72.9e-6, 156.4e-6, 156.4e-6
!--prony setup---------------------------------------------------------------
tbda, 46, 2441.48 ! G0
tbda, 47, 27.3674 ! Ginf
tbda, 48, 7324.44 ! K0
tbda, 49, 7324.44 ! Kinf
tbda, 50, 10 ! # g
! -- prony coeff shear-------------------------------------------------------
tbda, 51, 0.030597294502196178
tbda, 52, 0.059023078725877635
tbda, 53, 0.10943680056118402
tbda, 54, 0.1409904718964544
tbda, 55, 0.1947144430454931
tbda, 56, 0.17721652033962254
tbda, 57, 0.16325100147644703
tbda, 58, 0.07187638056888405
tbda, 59, 0.032087381624738086
tbda, 60, 0.02080662725910286
! -- prony times shear-------------------------------------------------------
tbda, 61, 1.255117014313305
tbda, 62, 78.96810063161455
tbda, 63, 1567.5991535818268
tbda, 64, 31173.843173684763
tbda, 65, 309922.3379767589
tbda, 66, 7.796365875725074e6
tbda, 67, 1.2370433351844682e8
tbda, 68, 3.137656715427452e9
tbda, 69, 1.5793444828408884e11
tbda, 70, 6.295199578594803e12
!-- end of soldermask viscoelastic data input--------------------------------
! An effective nu = 0.3 has been used for conversion of data
!============================================================================
164 APPENDIX B. ANNOTATIONS ON MATERIALS
B.4 Epoxy-Silicone Adhesive
The data was measured on a Zwick 1446 universal testing machine in combination with a
temperature chamber. The deviation from the expected behaviour at low temperatures is
due to problems with the cooling chamber. Therefore the corresponding value was taken
from the DMA measurements which in this domain does produce very good accordance
with the tension testing and the rate-dependence was assumed to follow the behaviour
predicted by the WLF-function.
A peculiarity was found when doing the TMA and DMA measurements: The relatively
low Tgresults form the two-component chemically cross-linked co-polymeric (epoxy and
silicone) system. Around Tgthe CTE produces a plateau, and the tan δ=E”/Eassumes
one single maximum. This is accredited to this fact, too.
1101001000
0
100
200
300
400
500
600
Sim.30 ˚C
Sim.15 ˚C
Sim.-12 ˚C
50 ˚C
30 ˚C
15 ˚C
0 ˚C
-12 ˚C
T=-25 ˚C
T = 70 ˚C
T = 100 ˚C
T = 125 ˚C
T = 150 ˚C
E(t) [MPa]
t [s]
Figure B.10. Measured relaxation data of epoxy-silicone adhesive.
B.4. EPOXY-SILICONE ADHESIVE 165
-6-30369
0
100
200
300
400
500
600
700
DMA:
E
-40
= 570 MPa
Tref = 30 ˚C
T=-25˚C -> lg t -5.5
T=-12˚C -> lg t -5.1
T=0˚C -> lg t -3.6
T=15˚C -> lg t -2.0
T=30˚C -> lg t
T=50˚C -> lg t +1.0
T=70˚C -> lg t +1.7
T=100˚C -> lg t +2.1
T=125˚C -> lg t+3.5
T=150˚C -> lg t +3.7
E(t) [MPa]
lg t'
Figure B.11. Temperature-time shifted data to construct mastercurve.
240260280300320340360380400420440
-6
-4
-2
0
2
4
Not taken into account
WLF - Constants
T
ref
= 303 K
c
1
= 6.3 ± 0.6
c
2
= 91.5 ± 6.7
T [˚C]
Shift Factor from Data
WLF - Fit, T
ref
= 25 ˚C
log a(T)
T [K]
-33-137274767
Figure B.12. WLF shift function.
166 APPENDIX B. ANNOTATIONS ON MATERIALS
B.4.1 Ansys Data File for Epoxy-Silicone Adhesive
!============================================================================
!--viscoelastic constants input for usrve5x.f
!--for epoxy-silicone adhesive ----------------------------------------------
tb,evisc,mat_ad ! initialize
tbda, 1, 6.3 ! wlf c1
tbda, 2, 91.5 ! wlf c2
tbda, 4, 303 ! wlf tref
tbda, 5, 20 ! function key, must be 20
!--temperature and cte input-------------------------------------------------
!- follows 5 temp in ascending order covering T-range of simulation
tbda, 26, 210, 313, 333, 353, 440
!- follows 5 corresponding cte values
tbda, 36, 90.6e-6, 90.6e-6, 1.0e-6, 102.4e-6, 102.4e-6
!--prony setup---------------------------------------------------------------
tbda, 46, 221.583 ! G0
tbda, 47, 2.00278 ! Ginf
tbda, 48, 480.0 ! K0
tbda, 49, 480.0 ! Kinf
tbda, 50, 10 ! # g
! -- prony coeff shear-------------------------------------------------------
tbda, 51, 0.10106419116302987
tbda, 52, 0.17329189629833477
tbda, 53, 0.19144061293761264
tbda, 54, 0.13406066700026065
tbda, 55, 0.12109937658888058
tbda, 56, 0.09447770345769652
tbda, 57, 0.09043346806500113
tbda, 58, 0.051227981346581866
tbda, 59, 0.024583576834513676
tbda, 60, 0.018320526308088367
! -- prony times shear-------------------------------------------------------
tbda, 61, 0.000012422246332449864
tbda, 62, 0.00006163258024196875
tbda, 63, 0.0004880138871352868
tbda, 64, 0.0049171171648512094
tbda, 65, 0.06199857340784209
tbda, 66, 0.7833585011853264
tbda, 67, 15.636604334249645
tbda, 68, 313.7946421922904
tbda, 69, 19878.423293103053
tbda, 70, 1.98971242703975e6
!-- end of adhesive viscoelastic data input----------------------------------
!-- used effective nu = 0.3 for conversion of data.
!-- note the low Tg and the peculiar CTE which displays a dip at 60C
!============================================================================
B.5. SILICONE ADHESIVE 167
B.5 Silicone Adhesive
The first data for this elastomer was recorded on a Zwick 1446 universal testing machine.
The measured data does not respresent a qualitatively meaningful result. Only the order
of magnitude of the E-modulus could be determined, the influence of temperature cannot
be resolved. This is due to the fact that the very soft silicone was very difficult to clamp
in the first place, thus giving rise to artifacts. Then the sensitivity limit of the load cell
was obviously reached.
To make up for these shortcomings the frequency method was employed and the measure-
ments were repeated (for high temperatures only due to lack of a cooling system) on a
rheometre. The much better results can be seen in figure B.14.
Still the relaxation was not thought significant enough to arouse the need for a viscoelastic
modelling of the material. As DMA measurements below T=−40 oCdoshowapro-
nounced frequency (time) dependence. But this temperature range is not important for
our experiment or simulation. No CTE variation was measured either in this range since
the material already works above its (typically very low) Tgfor silicone.
Still the comparison of these two results clearly indicate that for very soft materials the
rheometre has the edge over the relaxation test.
110100100010000
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
T = -25 ˚C
T = 0 ˚C
T = 25 ˚C
T = 50 ˚C
T = 70 ˚C
T = 100 ˚C
T = 125 ˚C
T = 150 ˚C
E(t) [MPa]
t [s]
Figure B.13. Measured relaxation data of silicone adhesive. There is neihter any signif-
icant relaxation nor a meaningful temperature dependence in the covered T-interval.
168 APPENDIX B. ANNOTATIONS ON MATERIALS
0.1110
2
3
4
5
6
T = 40 ˚C
T = 60 ˚C
T = 80 ˚C
T = 100 ˚C
T = 120 ˚C
T = 140 ˚C
T = 160 ˚C
E [MPa]
f [Hz]
Figure B.14. Data recorded with a rheometre. This method is much better suited for soft
materials.
B.5.1 Ansys Data File for Silicone Adhesive
!============================================================================
! -- Elastic Data Input for Silicone Thermal Adhesive
mptemp, 1, 223, 248, 273, 323, 433
mpdata, ex, mat_ad, 1, 812.0, 8.3, 6.0, 5.5, 2.8
mpdata, prxy, mat_ad, 1, 0.3, 0.3, 0.3, 0.3, 0.3
mpdata, alpx, mat_ad, 1, 175.9e-6, 175.9e-6, 175.9e-6
mpdata, alpx, mat_ad, 4, 175.9e-6, 175.9e-6
!-- behaves as a normal silicone. Tg is very low, < 45C
!============================================================================
B.6. LINEAR-ELASTIC AND ELASTIC-PLASTIC MATERIALS 169
B.6 Linear-Elastic and Elastic-Plastic:
Material Data for Si,CrNi-Steel, Cu, Al, Ni
Here the employed material data for the remaining materials is given. The respective data
was taken from standard literature (see e.g. [55] or [115]).
For the description of elasto-plastic materials one needs the yield stress and the tangent
modulus in the plastic regime.
Silicon
!============================================================================
mp, ex, mat_si, 168000 ! Elastic Isotropic Modulus
mp, nuxy, mat_si, 0.3 ! Poisson’s Ratio
mp, alpx, mat_si, 2.8e-6 ! CTE
!============================================================================
Steel (X5CrNi18 10)
!============================================================================
mp, reft, mat_st, 298 ! Define: Stress-free State at Room-T
mp, ex, mat_st, 220000 ! Elastic Isotropic Modulus
mp, prxy, mat_st, 0.28 ! Poisson’s Ratio
mp, alpx, mat_st, 11.0e-6 ! CTE
!============================================================================
Copper
!============================================================================
mp, ex, mat_cu, 97000 ! Elastic Isotropic Modulus
mp, nuxy, mat_cu, 0.35 ! Poisson’s Ratio
mp, alpx, mat_cu, 16.5e-6 ! CTE
tb, biso, mat_cu, 1 ! Isotropic Plastic Hardening
tbdata, 1, 180, 6685 ! Yield Stress, Tangent Modulus
!============================================================================
Aluminium
!============================================================================
mp, ex, mat_al, 72000 ! Elastic Isotropic Modulus
mp, nuxy, mat_al, 0.32 ! Poisson’s Ratio
mp, alpx, mat_al, 23.5e-6 ! CTE
tb, biso, mat_al, 1 ! Isotropic Plastic Hardening
tbdata, 1, 180, 7000 ! Yield Stress, Tangent Modulus
!============================================================================
Nickel
!============================================================================
mptemp, 1, 233, 293, 373, 463 ! T(Kelvins)
mpdata, ex, mat_ni, 1, 233000, 227500, 221300, 214400 ! E-Moduli
mpdata, nuxy, mat_ni, 1, 0.3, 0.3, 0.32, 0.38 ! PR
mpdata, alpx, mat_ni, 1, 12.5e-6, 12.5e-6, 12.5e-6, 12.5e-6 ! CTE
tb, biso, mat_ni, 1 ! Pl. Hard.
tbdata, 1, 420, 20280 ! Y.S., T.M.
!============================================================================
Appendix C
Annotations on FE-Simulation and
Test-Specimen
C.1 FE-Models
C.1.1 Abaqus-Ansys Comparison
[%]
0.1
0.5
[%]
0.1
0.5
Abaqus
Ansys
Figure C.1. Equivalent creep strain in Ansys and Abaqus. Note the qualitative and
quantitative accordance of the result. (Unfortunately the scale uses different colours.) A
‘slice’-model (see figure C.5) was used for comparison.
170
C.1. FE-MODELS 171
C.1.2 HEX-TET Model
TETs as well as HEX elements may be used to describe creep of solder materials. Here
also a creep limit of clmt = 10 was specified.
Figure C.2. The model created to compare a HEX mesh to a TET mesh. Underfill and
soldermask are not depicted.
[%]
0.0
0.5
1.0
TET-Mesh
HEX-Mesh
Figure C.3. Comparison of the results. Depicted is the equivalent creep strain for a
sufficiently dense mesh.
172 APPENDIX C. ANNOTATIONS ON FE-SIMULATION AND TEST-SPECIMEN
C.1.3 Variation of the Mesh Density Parameter
These are the nine combinations that were tested for solution stability concerning the
creep strain as described in section 4.2. The best compromise between speed and accuracy
was found for the bump and the chip respectively depicted in the middle. The pictures
correspond to the mesh-densities referred to in figure 4.5
(a) (b) (c)
(1) (2) (3)
Figure C.4. Different mesh densities which were tested for numerically stable results.
C.1.4 Slice Model
Figure C.5. FE-‘slice’ model for quick determination of critical parameters.
C.1. FE-MODELS 173
C.1.5 Stator Model
External
Force
Figure C.6. Full model with stator (screw and backplate). The simulation indicates that
the omission of the stator in the model does not affect the results. The elements are not
depicted for the sake of clarity.
C.1.6 Solder Barrel Model
Bump at one
Pitch Distance
Barrel-Shaped
oversized
Solder Bump
Check
Influence on
this Bump
Figure C.7. Model crated to clarify the influence of a neighbouring solder bump and the
omission of all but two of them. A giant solder bump (barrel) was therefore inserted.
174 APPENDIX C. ANNOTATIONS ON FE-SIMULATION AND TEST-SPECIMEN
C.1.7 Polyimide Model
The polyimide was modelled elastically by data determined through DMA measurements.
Passivation Layer „Shoulder“
Figure C.8. FE-model adjusted to assess the influence of the presence of a passivation
layer (polyimide) between chip and underfill. The bump exhibits a non-embedded UBM
now, which still does not alter the result. Three element layers have been used for the
polyimide.
C.1.8 Quarter Model for Verification of Curvature with Adhe-
sive
Plate
Adhesive
Chip
Board
Figure C.9. FE-model to simulate the curvature of the chip measured along the edge after
the chip is cut in half. This requires quarter-symmetry.
C.2. DELAMINATION AND CONTACT-MODE SIMULATION 175
C.2 Delamination and Contact-Mode Simulation
Ansys provides the capability of contact mode simulation. This means that areas which
are not adhesively bonded may come into contact and lose contact again in the course of
a simulation. This situation arises when delamination occurs. No friction was assumed
in the simulations due to lack of the respective parameter. Still this should be a good
approximation since the very slowly varying internal forces which act at the boundary are
strong enough to overcome any kind of fixation.
C.2.1 Small Local Delamination at Solder-Chip Interface
(Feature of this special Bump-Shape)
UBM
SnPb
UF
Contact-
Target Pair
Normal Small Local Delamination
Displacements ux
Figure C.10. Delamination at the solder-chip interface. The effect of delamination is
visualized by the displacements diverging from the ones in the region around.
[%]
1.0
5.0
Normal
Small Local
Delamination
3.21 % 3.18 %
Figure C.11. The equivalent creep strain after one thermal cycle: The small local delam-
ination has no effect on the creep strain.
As depicted in figure 5.25 this is the kind and extent of delamination which occurs at the
‘shoulders’ (cf. figure 5.24 (e)). The simulation shows no influence, rather there seems to
be a small improvement. This means that we do not have to be concerned about a second
failure mechanism apart form solder fatigue in this work.
176 APPENDIX C. ANNOTATIONS ON FE-SIMULATION AND TEST-SPECIMEN
C.2.2 Large Local Delamination at Underfill-Chip Interface
But this tendency is not a trend. Larger delamination (as does not occur in our model)
does cause harm to the bump. Distinctly a local increase in creep strain is discernable.
Displacement Field ux
Elements
Contact-
Target Pair
Figure C.12. Delamination at underfill-chip interface. Highlighted are the contact and
target elements. Again the effect of delamination is visualized through the displacement
fields. The ablation region measures one square pitch.
[%]
1.0
5.0
Normal
Large Local
Delamination
3.21 % 3.36 %
Figure C.13. The equivalent creep strain after one thermal cycle: A delamination around
the pad of this size significantly increases creep strain. The maximum strains follow the
damage path. Peak value is ¯εcr =6.7%.
C.3. ANNOTATIONS ON TEST-SPECIMEN 177
C.3 Annotations on Test-Specimen
C.3.1 Comments on Technological Constraints and Design
Alternatives
For a discussion of alternative methods or materials there has been no space yet. This
section is meant to briefly outline why a specific choice was made and why it was given
preference over at first glance seemingly more obvious alternatives.
Type of Fixation of the Board
Many ways of attaching the board to the plate were considered involving an initial fixa-
tion, fixation with special bolts or no fixation at all. All of them had severe shortcomings
either because of an incompatibility with the production steps (and hence the modelling
of an technologically irrelevant method) or because the type of fixation did not establish
an reproducible state but caused additional warpage of the board. The ‘free’ board, i.e. no
fixation at all (the board merely hinges on the spacers) was ruled out due to two concerns:
First, the test-specimen loses all its intrinsic stability. This may cause damage to chip and
interfaces when it is put into the needle-pin adaptor for resistance measurement. Second,
the spacers assume their nominal thickness only under pressure. Therefore the fixation of
the board sandwiched between precision spacers and given permanence through tightening
of the nuts in the last assembly step represented in every respect – apart form the other
advantages already mentioned in section 4.4.2 or 4.3.1 – also the best technological solution.
Use of Aluminium as Material for the Heat-Spreader
Aluminium serves better here, since adhesives do form a strong joint to prevent delami-
nation. Then a housing/heatsink will very likely be made of aluminium in the end. This
outweighs the advantage of steel which there are: CTE close to the one of the board, higher
stiffness which means a thinner plate and less thermal mass for the cycling chamber.
Use of an Aluminium Tray During Reflow
One of the problems encountered was the warpage of the boards, especially the thin ones.
The initial warpage could easily be corrected by gently bending the board until it was even
again. However, the warpage developing during reflow could not be remedied. But for
automatic underfill dispensing also an even board is needed.
So two measures were successfully employed: First, the circuit layout and soldermask were
printed on either side of the board. This helped reduce distortions due to different thermal
expansion. Second, warpage could nearly be eliminated (down to δd < ±15 µm over an
area of 41 ×41 mm2) when the board was laid on a thin aluminium tray during reflow.
This had no influence on void formation, as the profile was designed for this purpose.
Use of Washer-like Spacers for Gap-Adjustment
Commercially available silicone spacers (tiny spheres) which are mixed into the adhesive
before curing were first considered. But here again it is not clear how to simulate some
randomly distributed spheres of unknown (very difficult to measure) material behaviour
178 APPENDIX C. ANNOTATIONS ON FE-SIMULATION AND TEST-SPECIMEN
neither would the manufacturers provide any material data. It was therefore opted for the
approach explained above.
Use of a Spring for Force Application
The spring has the advantage that its stiffness is no function of temperature in the range
required here. It allows a reliable and easily adjustable way of applying a force. This
renders it particularly suitable for FE-representation as a pure surface load. The spring
itself need not be modelled at all. For the use in a real casing the force might be applied
by another means.
Reason for Value of Gap-Width
There are two reasons: First, due to the intrinsic warpage of the board any displacement
can only be adjusted to an accuracy of δd=±15..20 µm (Refer to section 4.3.1 and 4.3.5).
Therefore the gap was chosen to be made as wide as possible to minimize the percentage
of deviation from the adjusted value. Extrapolations to smaller gap widths are made by
simulation.
Second, the spacers1are only available in a few discrete thicknesses but have to exactly
match the thicknesses bsp of equation 4.15 and btot and 4.16. For reasons of comparability
the gap should be identical for adhesive and foil groups, and most gap-fillers are available
in thicknesses in multiples of bgap ≈10 mil ≈250 µm. Therefore this lowest gap-width
was chosen which could fortunately also be formed with a suitable combination of spacers.
1DIN-988
Appendix D
Annotations on Results
D.1 Failure Analysis According to Single-Bump Mea-
surements
0.5
0.2
99
93
100 200 300 500 1000 2000 5000
Cycles to Failure
Percent Failure [%]
63 %
β
1
5
2
1C2Au
S0x
L0x
40
20
10
70
Figure D.1. Weibull plot according to all single bump failures per group for three repre-
sentative groups (cf. figure 5.22). Note the difficulty in fitting the data by a straight line
and the consequently vague extrapolation to ¯
N50 %, let alone ¯
N63 %. Not enough single bump
failures are detectable for a meaningful analysis. A more adequate method was chosen as
explained in section 5.3.2.
179
180 APPENDIX D. ANNOTATIONS ON RESULTS
D.2 Tabulated Results of Simulation and Experiment
Results: Simulation vs Experiment
Group nch nSB N63% N50% ˜
NcβCI ¯εcr
1[%] ¯εcr
2[%]
K0u 20 13 1266 1144 115 3.78 80 3.21 3.47
K0x 20 18 1110 983 100 2.22 150 3.32 3.56
L0x 16 61465 1376 330 7.55 150 3.32 3.56
E0x 20 16 793 707 360 2.85 150 3.50 3.54
S0x 20 14 863 766 360 2.07 200 3.53 3.60
E2Mu 16 14 757 671 310 2.34 250 3.66 3.75
E1Au 16 9720 638 330 2.14 250 4.32 3.78
E2Au 20 17 806 716 235 2.57 200 4.57 3.81
E1Ax 20 15 795 712 320 3.22 150 4.74 4.02
E2Ax 20 16 712 631 125 2.09 200 5.15 4.06
S1Au 20 17 675 599 260 2.56 200 4.40 3.89
S2Au 20 15 747 666 200 2.86 180 4.69 3.96
S1Ax 20 16 739 658 200 2.74 180 4.86 4.11
S2Ax 20 15 711 634 210 2.90 150 5.35 4.25
C1Bu 20 15 922 835 350 3.98 150 4.22 3.77
C2Au 20 15 751 665 180 2.28 200 4.51 3.79
F2Mx∗∗ 8 3 860 778 410 3.90 250 4.20 4.01
F1Au∗20 12 741 660 270 2.85 180 4.45 3.77
F1Bu∗17 11 780 693 180 2.65 220 4.53 3.76
Table D.1. Groups are sorted by kind of reverse side attachment.
Columns:
nch - Number of chips per group;
nSB - Number of chips with a single bump failure;
N63 % - Characteristic lifetime;
N50 % - Mean cycles to failure;
Nc- Correction number for daisy chain value;
β- Weibull exponent;
CI - Confidence intervall (goodness of fit);
¯εcr
i- Equivalent creep stain for ith cycle.
The creep strain is averaged over both bumps as no significant difference was found in the
experiment. For L0x the same value as for K0x is used since voids could not be simulated
consistently. Groups with an asterisk do have other loads as originally specified (cf. table
5.4).
Bibliography
[1] R.P. Feynman. There is plenty of Room at the Bottom.
http://www.zyvex.com/nanotech/feynman.html. The talk was given in 1959.
[2] J. Braine. Room at the Top. Arrow Books, UK, 1997. Originally published 1957.
[3] G.E. Moore. Cramming more components onto integrated circuits. Electronics, 38(8),
1965. http://www.intel.com/research/silicon/mooreslaw.html (4 pages).
[4] R.R. Tummala and E.J. Rymaszewski. Microelectronics Packaging Handbook.Van
Nostrand Reinhold, New York, 1996.
[5] Semiconductor Industry Association. The international technology roadmap for semi-
conductors. http://public.itrs.net, 2001.
[6] H. Reichl, B. Michel, and A. Schubert. Materials Science and Engineering – A Major
Topic in the Future of Microelectronic Packaging. Proc. 3. Int. Conf. Micromaterials,
pages 72–73, April 17-19 2000.
[7] C.P. Wong, S. Luo, and Z. Zhang. Flip the Chip. Science, 290(5500):2269–2270,
2000.
[8] T. Maeder. Die Thermische Modellierung von Flip-Chip Aufbauten zur Untersuchung
und Simulation von Entw¨armungskonzepten. Technische Universit¨at Dresden - Insti-
tut f¨ur Grundlagen der Elektrotechnik und Elektronik, Germany and Robert Bosch
GmbH Stuttgart, Germany, 2002. Diploma thesis.
[9] N. Saito, O. Yamada, T. Ono, and T. Uda. Design Method for High Reliability Flip-
Chip BGA Package. Proc. 51. Electronic Components and Technology Conference,
pages 270–275, 2001.
[10] Y. Li, J. Xie, T. Verma, and V. Wang. Reliability Study of High-Pin-Count Flip-Chip
BGA. Proc. 51. Electronic Components and Technology Conference, pages 276–280,
2001.
[11] H. Doi, K. Kawano, A. Yasukawa, and T. Sato. Reliability of Underfill-Encapsulated
Flip-Chips with Heat Spreaders. Journal of Electronic Packaging, 120:322–327, 1998.
[12] H. Reichl, A. Schubert, and M. T¨opper. Reliability of Flip-Chip and Chip Size
Package. Microelectronics Reliability, (40):1243–1254, 2000.
181
182 BIBLIOGRAPHY
[13] J.H. Lau and Y. Pao. Solder Joint Reliability of BGA, CSP, Flip Chip, and Fine
Pitch SMT Assemblies. Mc Graw-Hill, 1997.
[14] J.H. Lau. Thermal Stress and Strain in Microelectronic Packaging. Van Nostrand
Reinhold, New York, 1993.
[15] D. Frear, H. Morgan, S. Burchett, and J. Lau. The Mechanics of Solder Alloy
Interconnects. Van Nostrand Reinhold, New York, 1994.
[16] R.R. Tummala. Fundamentals of Microsystems Packaging. McGraw-Hill, 2001.
[17] J.H. Lau, C.P. Wong, J.L. Prince, and W. Nakayama. Electronic Packaging: Design,
Materials, Process, and Reliability, chapter 4. McGraw-Hill, 1998.
[18] T.Y. Wu, Y. Tsukada, and W.T. Chen. Materials and Mechanics Issues in Flip-Chip
Organic Packaging. Proc 46. Electronic Components and Technology Conference,
pages 524–534, 1996.
[19] W. Engelmaier. Guidelines for Accelerated Reliability Testing of Surface Mount Sol-
der Attachments, volume IPC-SM-785. IPC, 1992.
[20] S. Rzepka and E. Meusel. Realistic Finite Element Modelling of Underfill Effects in
Flip-Chip Modules. DVS Berichte, 191:47–51, 1998.
[21] E. Suhir. Calculated Thermally Induced Stresses in Adhesively Bonded and Soldered
Assemblies. International Symposium on Microelectronics, pages 383–392, 1986.
[22] R. Darveaux and K. Banerji. Fatigue Analysis of Flip-Chip Assemblies using Thermal
Stress Analysis and a Coffin Manson Relation. IEEE, pages 797–805, 1991.
[23] W. Engelmaier and A. Attarwala. Surface-Mount Attachment Reliability of Chip-
Leaded Cheramic Chip Carriers on FR-4 Circuit Boards. IEEE Trans. Components,
Hybrids, and Manufacturing Technology, 12(2):284–296, 1989.
[24] A. Schubert, R. Dudek, J. Auersperg, D. Vogel, B. Michel, and H. Reichl. Thermo-
Mechnical Reliability Analysis of Flip-Chip Assemblies by Combined Microdac and
Finite Element Method. Conf. Proc. Interpack ’97, Hawaii, USA, pages 1647–1654,
1997.
[25] A. Schubert, R. Dudek, B. Michel, and H. Reichl. Package Reliability Studies by
Experimental and Numerical Analysis. Proc. 3. Int. Conf. on Micromaterials, pages
110–119, April 17-19, Berlin, Germany 2000.
[26] A. Schubert, R. Dudek, H. Walter, E. Jung, A. Gollhardt, and B. Michel. Lead-free
Flip-Chip Solder Interconnects – Materials Mechanics and Reliability Issues, pages
12–25. Micromaterials and Nanomaterials. Micro Materials Centre Berlin at the
Fraunhofer Institute IZM, Germany, 1 edition, 2002.
BIBLIOGRAPHY 183
[27] A. Schubert, R. Dudek, R. Leutenbauer, P. Coskina, K.-F. Becker, J. Kloeser,
B. Michel, H. Reichl, D. Baldwin, J. Qu, S. Sitaraman, C.P. Wong, and R. Tummala.
Numerical and Experimental Investigations of Large IC Flip-Chip Attach. Proc. of
50. Electronic Components and Technology Conference, pages 1338–1346, 2000.
[28] S. Rzepka, M.A. Korhonen, E. Meusel, and C.Y. Li. The Effect of Underfill and
Underfill Delamination on the Thermal Stress in Flip-Chip Solder Joints. Journal of
Electronic Packaging, 1998.
[29] C.A. Le Gall et. al. Influence of Die Size on the Magnitude of Thermomechanical
Stresses in Flip-Chips Directly Attached to Printed Wiring Board. ASME EEP-Vol.
19-2, Advances in Electronic Packaging - Proc. Interpack 1997, pages 1663–1670,
1997.
[30] R. Dudek, A. Schubert, and B. Michel. Thermo-Mechanical Reliability of Microcom-
ponents. Proc. 3. Int. Conf. on Micromaterials, pages 206–213, April 17-19, Berlin,
Germany 2000.
[31] C.E. Hanna, S. Michaelides, P. Palaniappan, D.F. Baldwin, and S.K. Sitaraman.
Numerical and Experimental Study of the Evolution of Stresses in Flip-Chip Assem-
blies During Thermal Cycling. IEEE Proc. Electronic Components and Technology
Conference, 1999.
[32] J.H.L. Pang and D.Y.R. Chong. Flip-Chip on Board Solder Joint Reliability Anal-
ysis Using 2-D and 3-D FEA Models. IEEE Transactions on Advanced Packaging,
24(4):499–506, 2001.
[33] Q.Yao and J.Qu. Three-Dimensional versus Two-Dimensional Finite Element Mod-
elling of Flip-Chip Packages. Journal of Electronic Packaging, 121:196–201, 1999.
[34] G.Q. Zhang, L.J. Ernst, and O. de Saint Leger. Benefiting from Thermal and Me-
chanical Simulation in Micro-Electronics.Proc.1
st. EuroSimE Conference. Kluwer
Academic Publishers, Eindhoven, The Netherlands, March, 23-24 2000.
[35] B. Michel, T. Winkler, M. Werner, and H. Fecht. Micro Materials. Verlag DDP
Goldenbogen, Dresden, Germany, 2000. Proceedings of the 3rd MicroMat.
[36] H.D. Solomon, V. Brzozowski, and D.G. Thompson. Prediction of Solder Fatigue
Life. Proc. 40. ECTC, pages 351–360, 1990.
[37] K. Doi, N. Hirano, T. Okada, Y. Hiruta, and T. Sudo. Prediction of Thermal Fatigue
Life for Encapsulated Flip-Chip Interconnection. Int. Journal of Microcircuits and
Electronic Packaging, 19(9):231–237, 1996.
[38] R. Dudek, M. Nylen, A.Schubert, B.Michel, and H. Reichl. An Efficient Approach to
Predict Solder Fatigue Life and its Application to SM- and Area-Array Components.
Proc. 47. Electronic Components and Technology Conference, pages 462–471, 1997.
184 BIBLIOGRAPHY
[39] A. Syed. Predicting Solder Joint Reliability for Thermal, Power & Bend Cycle within
25 % Accuracy. Proc. 51. Electronic Components and Technology Conference, pages
255–265, 2001.
[40] L.F. Coffin. A Study of the Effects of Cyclic Thermal Stresses on a Ductile Material.
Trans. ASME, 76:931–950, 1954.
[41] S.S. Manson. Behaviour of Materials under Condition of Thermal Stresses. NACA
TN-2933, Report 1170, pages 317–350, 1954.
[42] S. Wiese, A. Schubert, H. Walter, R. Dudek, F. Feustel, E.Meusel, and B. Michel.
Constitutive Behaviour of Lead-Free vs. Lead-Containing Solders – Experiments on
Bulk Specimens and Flip-Chip Joints. IEEE Proc. Electronic Components and Tech-
nology Conference, pages 890–902, 2001.
[43] P.L. Hacke, A.F. Sprecher, and H. Conrad. Thermomechanical Fatigue of 63Sn-37Pb
Solder Joints, chapter 15, pages 466–499. van Nostrand Reinold, NY, USA. In:
Thermal Stress and Strain in Microelectronic Packaging,editedbyJ.H.Lau.
[44] Z. Guo and H. Conrad. Effect of Microstructure Size on Deformation Kinetics and
Thermo-Mechanical Fatigue of 63Sn37Pb Solder Joints. Journal of Electronic Pack-
aging, 118:49–54, 1996.
[45] A. Syed. Creep Crack Growth Prediction of Solder Joints During Temperature Cy-
cling – An Engineering Approach. Journal of Electronic Packaging, 117:116–122,
1995.
[46] S.H. Ju and B.I. Sandor and M.E. Plesha. Life Prediction of Solder Joints by Damage
and Fracture Mechanics. Journal of Electronic Packaging, 118:193–200, December
1996.
[47] S.N. Atluri, T. Nishioka, and M. Nishioka. Incremental path-independent inte-
grals in inelastic and dynamic fracture mechanics. Engineering Fracture Mechanics,
20(2):209–244, 1983.
[48] H.G. de Lorenzi. On the energy release rate and the j-integral for 3d crack configu-
rations. Int. Journal of Fracture, 19:183–193, 1982.
[49] B. Wunderle, W. N¨uchter, A. Schubert, B. Michel, and H. Reichl. Parametric FE-
Approach to Flip-Chip Reliability under various Loading Conditions. Proc. 3rd Eu-
roSime Conf., Paris, France, pages 52–60, April 15-17 2002.
[50] W. N¨uchter. Konzepte f¨ur die Entw¨armung von Flip-Chip Aufbauten. Internal
report, Robert Bosch GmbH, P.O.Box 300240, D-70442 Stuttgart, Germany, 1998.
[51] J.H. Lau. Flip-Chip Technologies. McGraw-Hill, 1996.
[52] K. Verma, S.Park, B. Han, and W. Ackerman. On the Design Parameters of Flip-
Chip PBGA Package Assembly for Optimum Solder Ball Reliability. IEEE Trans.
Components and Packaging Technologies, 24(2):300–307, 2001.
BIBLIOGRAPHY 185
[53] J.B. Nysther, P. Lundstr¨om, and J. Liu. Measurement of solder joint lifetime as a
function of underfill material properties. IEEE Transactions on Components, Pack-
aging and Manufacturing Technology, 21(2):281–287, 1998.
[54] G.W. Ehrenstein, G. Riedel, and P. Trawiel. Praxis der Thermischen Analyse von
Kunststoffen. Carl Hanser Verlag M¨unchen, Germany, 1998.
[55] M. Merkel and K-H. Thomas. Taschenbuch der Werkstoffe. Fachbuchverlag Leipzig-
K¨oln, Germany, 1994.
[56] ABAQUS. ABAQUS Theory Manual V. 5.8. Hibbit, Karlsson and Sorensen, Inc.,
Pawtucket, RI, USA, 1998.
[57] P. Kohnke. ANSYS Theory Reference V. 5.7. ANSYS, Inc., 2000.
[58] J.J. Skrzypek and R.B. Hetnarski. Plasticity and Creep. CRC Press, Boca Raton,
Florida, USA, 2000.
[59] R. Lenk and W. Gellert. Fachlexikon ABC Physik, volume 2. VEB F.A. Brockhaus
Verlag Leipzig, GDR, 1989.
[60] P.L. Hacke, A.P. Sprecher, and H. Conrad. Microstructure Coarsening During
Thermo-Mechanical Fatigue of Pb-Sn Joints. Journal of Electronic Materials,
26(7):774–782, 1997.
[61] D. Grivas, K.L. Murty, and J.W. Morris. Deformation of Pb-Sn Eutectic Alloys at
Relatively High Strain Rates. Acta Metallurgica, 27:731–737, 1979.
[62] D. Vogel, C. Jian, and I. de Wolf. Experimental Validation of Finite Element mod-
eling. Proc. 1st EuroSime Conf., Eindhoven, Netherlands, pages 113–133, 2000.
[63] D. Vogel, A. Gollhardt, A. Schubert, R. K¨uhnert, and B. Michel. MicroDAC strain
Measurement for FEA-Support. Proc. 3rd MicroMat Conf., Berlin, Germany, pages
311–314, 2000.
[64] J.W. Morris and H.L.Reynolds. The Influence of Microstructure on the Mechanics
of Eutectic Solders. Advances in Electronic Packaging, 19(2):1529–1534, 1997.
[65] R.J Klein-Wassink. Soldering in Electronics. Electrochemical Publications LTD,
Scotland, 1984.
[66] H.E. Cline and T.H. Alden. Rate Sensitive Deformation in Tin-Lead Alloy. Trans.
ASME, 239(710-714), 1967.
[67] P. Hacke, A.F. Sprecher, and H. Conrad. Computer Simulation of Thermo-
Mechanical Fatigue of Solder Joints Including Microstructure Coarsening. Journal
of Electronic Packaging, 115:153–158, 1993.
[68] R. Darveaux and K. Banerji. Ball Grid Array Technologies, chapter 13. Mc Graw-
Hill, New York, USA, 1995. Edited by J.H. Lau.
186 BIBLIOGRAPHY
[69] R. Darveaux and K. Banerji. Constitutive Relations for Tin-Based Solder-Joints.
IEEE Trans. Components, Hybrids, and Manufacturing Technology, 15(6):1013–1024,
1992.
[70] W.J. Plumbridge. Materials behaviour and the Reliability in Performance of Solder
Joints. Soldering and Surface Mount Technology, 11(3):8–11, 1999.
[71] E. Hinton. NAFEMS Introduction to Nonlinear Finite Element Analysis. NAFEMS,
Glasgow, Scotland, 1992.
[72] Ansys INC. Ansys Guide to User Programmable Features. Ansys, Inc., 2000.
[73] F. Ellyin. Fatigue Damage, Crack Growth and Life Prediction. Chapman & Hall,
1997.
[74] J. Lemaitre. A Course on Damage Mechanics. Springer Verlag, Berlin, Germany,
1996.
[75] R. Dudek, M. Scherzer, A. Schubert, and B. Michel. FE-Simulations for Polymeric
Packaging Materials. IEEE Transactions on Components, Packaging and Manufac-
turing Technology, 21(2):301–308, 1998.
[76] T.L. Anderson. Fracture Mechanics. CRC Press Inc., Boca Raton, Florida, USA, 2
edition, 1995.
[77] J. Auersperg, A. Schubert, D. Vogel, B. Michel, and H. Reichl. Fracture and Damage
Evaluation in Chip Scale Packages and Flip-Chip Assemblies by FEA and MicroDAC.
Application of Fracture Mechanics in Electronic Packaging, 20:133–138, 1997.
[78] S.S. Manson. Thermal Stress and Low Cycle Fatigue. McGraw-Hill, NY, USA, 1966.
[79] H.D. Solomon and E.D. Tolksdorf. Energy Approach to the Fatigue of 60/40 Sol-
der: Part I – Influence of Temperature and Cycle Frequency. Journal of Electronic
Packaging, 117:130–135, 1995.
[80] C. Kanchanomai, Y. Miyashita, and Y. Mutoh. Low Cycle Fatigue Behaviour and
Mechanisms of a Eutectic Sn-Pb solder 63Sn37Pb. International Journal of Fatigue,
24:671–683, 2002.
[81] S.Wei, R. Lee, and X. Zhang. Sensitivity Study on Material Properties for the
Fatigue Life Prediction of Solder Joints under Cyclic Thermal Loading. Advances in
Electronic Packaging, 19(2):1559–1566, 1997.
[82] A. Schubert, R. Dudek, H. Walter, E.Jung, A. Gollhardt, and B. Michel. Lead-Free
Flip-Chip Solder Interconnects – Materials Mechanics and Reliabilita Issues.
[83] A. Schubert, R. Dudek, E. Auerswald, A. Gollhardt, B. Michel, and H. Reichl. Fa-
tigue Life Models for SnAgCu and SnPb Solder Joints Evaluated by Experiments and
Simulation. Proc. of 53. Electronic Components and Technology Conference, 2003.
to be published.
BIBLIOGRAPHY 187
[84] R. Dudek. Mechanical Failure in COB-Technology using Glob-Top Encapsulation.
IEEE Trans. Components, Packaging and Manufacturing Technology, 19(4):232–239,
1996.
[85] A. Schubert, H.Jiang, R.Dudek, B. Michel, and H. Reichl. Materials Mechanics and
Mechanical Reliability of Flip-Chip Assemblies on Organic Substrates. Proceedings
of 3rd Int. Symposium and Exhibition on Advanced Packaging Materials, Braselton,
USA, pages 106–109, March 1997.
[86] H. Walter, W. Schneider, R. Dudek, E. Auerswald, and A. Schubert. Evaluation of
Glob Top Materials for Chip-on-Board COB Applications. Proc.3.Int.Conf.on
Micro Materials, pages 1269–1271, April 17-19 2000. Berlin, Germany.
[87] H. Schmiedel. Kunststoffpr¨ufung. Hansa Verlag, M¨unchen, 1992.
[88] Y.M. Haddad. Viscoelasticity of Engineering Materials. Chapman & Hall, London,
1995.
[89] J.D. Ferry. Viscoelastic Properties of Polymers. John Wiley & Sons, New York, 3
edition, 1980.
[90] N.W. Tschoegl. The Theory of Linear Viscoelastic Behaviour. Academic Press, 1981.
[91] O. Wittler, P. Sprafke, H. Walter, A. Gollhardt, D. Vogel, and B. Michel.
Time and Temperature Dependent Mechanical Characterization of Polymers
for Microsystems Applications. In Proceedings: Materials Week 2000, pages
URL: http://www.materialsweek.org/proceedings/index.htm (6.2.2002), 8 pages,
M¨unchen, Germany, 25-28 Semptember 2000. Werkstoffwoche-Partnerschaft
GbRmbH.
[92] L.J. Ernst. Polymer Material Characterisation and Modeling. Proc. 1st EuroSimE
Conf., Eindhoven, NL, pages 37–58, 2000.
[93] P.B. Koeneman. Viscoelastic Stess Analysis and Fatigue Life Prediction of a FCOB
Electronic Package. PhD thesis, University of Texas at Austin, Austin, TX 78712,
Texas, USA, 1999.
[94] J. Vogel, E. Kaulfersch, J. Auersperg, and K. Kreyssig. FE-Analyse zum thermis-
chen Strukturverhalten von gestackten MATCH-X-Systemen. 47. Internationales
Wissenschaftliches Kolloquium, Technische Universit¨at Ilmenau, Germany, pages
677–678, September 23-26 2002.
[95] A. Desgupta et.al. Miscellaneous Modeling Issues in Thermomechanical Stress Anal-
ysis of Surface-Mount Interconnects. ASME EEP-Vol. 19-1, Advances in Electronic
Packaging - Proc. Interpack 1997, pages 1095–1100, 1997.
[96] Y. Tsukada. Solder Bumped Flip-Chip Attach on SLC Board and Multichip Module,
pages 410–443. Van Nostrand Reinold, New York, USA, 1994. in Chip on Board
Technologies for Multichip Modules.
188 BIBLIOGRAPHY
[97] A. Schubert, H. Walter, A. Gollhardt, and B. Michel. Materials mechanics and
reliability issues of lead-free solder interconnects. Proc. 2nd EuroSimE Conference,
pages 171–178, 9-11 April, Paris, France 2001.
[98] L. Mercado, V. Sarihan, Y. Guo, and A. Mawer. Impact of Solder Pad Size on Solder
Joint Reliability in Flip-Chip PBGA Packages. Proc. 49. Electronic Components and
Technology Conference, 1999.
[99] A.M. Deshpande, G. Subbarayan, and R.L. Mahajan. Maximizing Solder Joint Relia-
bility Through Optimal Shape Design. Journal of Electronic Packaging, 119:149–155,
1997.
[100] M. Anwander, B.G. Zagar, B. Weiss, and H. Weiss. Noncontacting Strain Measure-
ment at High Temperatures by the Digital Laser Speckle Technique. Experimental
Mechanics, 40(1):98–105, 2000.
[101] B. Lewen. The Nonlinear Viscoelastic Behaviour of Plastic Materials – The Time-
Temperature-Shift and the Poisson’s Ratio. Ph.d. thesis, Fakult¨at f¨ur Maschinenwesen
der Rheinisch-Westf¨alischen Technischen Hochschule Aachen, Germany, 1991.
[102] R. Dudek and A. Schubert. Unpublished data by Fraunhofer IZM, Berlin, Germany.
[103] B. Wunderle, W. N¨uchter, A. Schubert, B. Michel, and H. Reichl. Lifetime Prediction
of Extended Flip-Chip Packages under Thermal and Mechanical Loading. Proc. 2nd
EuroSime Conf., Paris, France, pages 123–128, 2001.
[104] R. Kreuzkamp and T. Reiber. Improving the Solder Joint Reliability of BGAs.
Electronic Packaging and Production, pages 45–52, Oct. 1998.
[105] M. Yunus, A. Primavera, K. Srihari, and J.M. Pitarresi. Effect of Voids on the
Reliability of BGA/CSP Solder Joints. IEEE/CPMT Int. Electronics Manufacturing
Technology Symposium, pages 207–213, 2000.
[106] J. Lau and S. Erasmus. Effects of Voids on Bump Chip Carrier (BCC++) Solder
Joint Reliability. Proc. 52. Electronic Components and Technology Conference, pages
992–1000, 2002.
[107] B. Wunderle. Untersuchung zur Entstehung von Lunkern in Flip-Chip Bumps. In-
ternal report, Robert Bosch GmbH, P.O.Box 300240, D-70442 Stuttgart, Germany,
2000.
[108] B. Roesner, X. Baraton, K. Guttmann, and C. Samin. Thermal Fatigue of Solder
Flip-Chip Assemblies. Proc. 48. Electronic Components and Technology Conference,
pages 872–877, 1998.
[109] M. Sumikawa, T. Sato, C.Yoshioka, and T. Nukii. Reliability of Soldered Joints in
CSPs of Various Designs and Mounting Conditions. IEEE Trans. Components and
Packaging Technologies, 24:293–299, 2001.
BIBLIOGRAPHY 189
[110] C.-U. Ronniger. Zuverl¨assigkeitanalyse mit Weibull. URL: http://www.weibull.de,
2001. CRGraph, Munich, Germany.
[111] A. Birolini. Quality and Reliability of Technical Systems. Springer, Berlin, Germany,
second edition, 1997.
[112] E. Madenci, S. Shkarayev, and R. Mahajan. Potential Failure Sites in a Flip-Chip
with and without Underfill. Journal of Electronic Packaging, 120:336–341, 1998.
[113] Y. Gu, T. Nakamura, W.T. Chen, and B. Cotterell. Interfacial Delamination Near
Solder Bumps and UBM in Flip-Chip Packages. Journal of Electronic Packaging,
123:295–301, 2001.
[114] G. Gross. Bruchmechanik. Springer Verlag, Berlin, Germany, 2 edition, 1996.
[115] C. Gerthsen and H. Vogel. Physik. Springer Verlag Berlin, 17 edition, 1993.
[116] H. Fischer and H.Kaul. Mathematik f¨ur Physiker, volume 1. Teubner Studienb¨ucher,
Stuttgart, Germany, 2 edition, 1990.
Curriculum Vitae
Name: Bernhard Wunderle
Geburtstag: 14.06.1970
Geburtsort: Sindelfingen
1976-1980 Grundschule in Sindelfingen
1980-1990 Gymnasium Unterrieden in Sindelfingen
Mai 1990 Allgemeine Hochschulreife
1990-1991 Zivildienst bei der Arbeiterwohlfahrt in B¨oblingen
1991-1993 Studium der Physik an der Universit¨at T¨ubingen
1993-1994 Studium der Physik an der University of York, England
1994-1998 Studium der Physik an der Universit¨at T¨ubingen
Sep. 1998 Abschluss des Studiums als Diplom-Physiker am Institut f¨ur theo-
retische Festk¨orperphysik der Universit¨at T¨ubingen
1998-2002 T¨atigkeit als Doktorand bei der Robert Bosch GmbH in Stuttgart
in Zusammenarbeit mit dem Fraunhofer Institut ”Zuverl¨assigkeit
und Mikrointegration” in Berlin
Feb. 2002 T¨atigkeit als wissenschaftlicher Mitarbeiter am Fraunhofer Institut
”Zuverl¨assigkeit und Mikrointegration” in Berlin
191
