P e r i o d i c L a t e r a l P o l a r S t r u c t u r e - b a s e d
W a v e g u i d e s i n III - N i t r i d e s f o r Q u a s i - P h a s e
M a t c h e d S e c o n d H a r m o n i c G e n e r a t i o n
vorgelegt von
Diplom-Ph y sik er
Dorian Ed uardo Alde n Angeles
ge b. in M exiko Stadt, Mexiko
Von der Fakultät II – M athematik und Naturwisse nschaften der Technischen
Universität Berlin zur Erlang ung des akademischen Grades
Doktor der Naturwissenschaften
Dr. rer. nat.
ge n ehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr. Michael Lehmann
Gutachter: Prof . Dr. Axel Hoffmann
Gutachter: Prof . Dr. Zlatko Sitar
Gutachter: Prof . Dr. André Strittmatter
Tag der w issens chaftlichen Aussprache: 24. April 2017
Berlin 2017
ABSTRA CT
La s ers emitting in the ultraviolet spectrum below 300 nm are desired for a variety of
applications. Currentl y available deep U V laser s ystems are expensive, in efficient,
stationary , require frequent maintenance and have a hi gh operation cost.
Alternatively, UV laser l ight can be obtained thro ugh frequenc y doubling as second
harmonic generation using nonline ar cr y st als. The III- Nitrides a re attractive for
nonlinear optical applications due to their large nonli near optical coefficients, wide
transparency window and high thermal conductivit y. The birefringence in III-
Nitrides is week, thus an alterna tive ph ase matching approach is necessar y .
In this work, quasi-phas e matched second harmonic generation in the UV u sing AlN
lateral polar structu re b ased wav eguides is demonstrated fo r the first time. A process
scheme for controllin g t he polarit y of epitaxial AlN and GaN la yers deposited on
sapphire substrates vi a metalor ganic chemical vapor deposition (MOCVD) is
presented. The p rocess is ex tended to achieve p eriodic lateral polar structures with
domain sizes in the nanometer scale b y introducing laser interference l ithography.
Subsequently, the surface rou ghness RMS value of the lateral polar str uctures is
reduced to 10 nm and below, over a 90 µm 2 area through p romoting step flow
growth at the nitrogen p olar surface throu gh con trol of the v apor supersaturation.
Next, thickness differe n ces between the alternating pola r domains at reduced vapor
supersatura tion values i s demonstrated to arise from mass transport betwee n the
adjace nt opposite-polar domains, and the growth conditions leading to equal
deposition rate for both polarities are established. W aveg uides are then etched into
the AlN l ateral polar stru ctures and tested fo r quasi -phase mat ched s econd harmonic
ge n eration. Employing 5 50 nm and 250 nm thi ck AlN lateral polar stru ctures -based
waveguides, 5 th and 7 th order q uasi phas e mat ched se cond harmonic gen eration is
demonstrated at 344 nm and 386 nm respectivel y, in agreement with t heoretical
calculations. In parallel, single polar AlN waveguides are fabricated f or modal
dispersion phase match ed second harmonic gener ation, where wavelengths as low as
305 nm are achieve d.
La stl y , the transparenc y in AlN bulk sin gle cr ystals are investigated w here point
defects leading to below bandgap en ergy absorption centers in the UV -C spectral
range are identified and attributed t o carbon impurities. For this, a nov el approach
for det ermining the imp urities t ype and concentrations in the cr y stal is presented,
where photoluminescence spe ctroscopy, photol uminescence excitation
spectroscopy, transmission spectroscop y and sec ondary ion mass spectroscopy data
is used in combination with a densit y fun ctional theory based theoreti cal model
which accounts for char ge bal ance cons ervation in the cr y stal and the formation
energy of defects.
ZUSA MMENFASSUN G
La s er mit Emission im UV-C Spektralbereich hab en viele potentielle Anwendungen.
Die zurz eit verfügbaren La ser mi t Emi ssionswellenlängen zwischen 1 50 nm und
300 nm sind Excimer Laser, welche ineffizient, teuer, und groß sind. Alternativ,
kann UV-C Lase r Licht durch Fre qu enzverdopplung erzeugt werden. Die Gruppe
III -Nitride sind durch ihre besonderen Materialeigenschaften (hoh e elektrische
Suszeptibilität, Transparenz und thermische Leitfähigkeit) besonders attra ktiv für
nichtlineare opti sche Anwendungen. D a Doppelbrechung in V -III Krista llen n icht
ausreicht um W inkel-Phasenanpassung zu erreichen w erden alternative
Phasenanpassungsmethoden für die Erzeug un g von UV L i cht benötigt.
In dieser Arbe it wird gezeig t, dass UV L aser L icht du rch Fre quenz verdopplung
mittels quasi-Phasenanpassung in W ellenleitern basierend auf periodisch gepolten
AlN erzeugt w erden k ann. Dazu wurde ein Verfahren zur makrosk opischen
Polaritätskontrolle von MOCVD gewachsenen AlN und GaN Schichten entwickelt,
welches hie r vorgestellt wird. Des Weiteren wurden Strukturen im
Nanometerbere i ch mittels La s er Interferenz Lithographie erzeu gt, und die mi ttlere
Oberflächenrauigke it d er periodische Strukturen a uf 10 nm übe r ein e 90 µm 2 Fläche
verringert. Dieses wurde durch Kontrolle der Üb ersättig un g der Gasphase erreicht
welche S tufenwachstum in der N-polaren AlN Domäne kontrolliert.
Höhenuntersc hi ede zwischen nebeneinanderliege nd en Domänen gegensätzlicher
Polarität werden dur ch Massentransport in der Gasphase erklärt. Durch eine
Anpassung d er W achstumsbedingung konnten gleich dick e Al- und N-polare
Domänen erreicht werden, was notwendig ist um Wellenleiter basierend auf
periodisch gepolten AlN S trukturen herzustellen. Frequenzverdopplungsversuche
wurden durchgeführt an 550 nm und 250 nm dicken W ellenleiter mit 10 µ m
Periodizität. Dabei konnte UV L aser Licht mit 344 nm und 386 nm W ellenlänge
erzeugt werden. Die ex perimentellen Ergebnisse zeigten eine exzellente
Übereinstimmung mit theoretischen Berechnungen für die 5te beziehungsweise 7te
Ordnung der quasi-Phasenanpassung. D es Weiteren wu rden Al-p olare AlN
Wellenleiter her gestellt und untersucht, wobei Freque nzverdopplun g mitt els Moden
Dispersion (MDPM) wurde erreicht. Die niedr igste Wellenlänge für die
Frequenzverdopplung die e rreicht wurde war 305 nm.
Abschließend wurden die opti schen Eigenschaften von AlN Einkristalle mitt els
Photolumineszenz-Anregungsspektroskopie, Transmissionspektroskopie und SI MS
untersucht, und die Ergebnisse mit Berechnungen basierend auf
Dichtefunktionaltheorie verglichen. Dabei wurde festgestellt, dass Kohlensto ff auf
einem Stickstoff Gitterplatz verantwortlich für da s Absorptionsband mit Maxim um
um 4.7 eV ist. Dieses Ergebnis b asiert auf einer Korrelation der
Photolumineszenzbänder um 3.9 eV und 2.7 eV und dem Absorptionsband
bei 4.7 eV.
Contents
List of Figures ............................................................................................................. i
List of Tables ............................................................................................................. ix
1 Introduction ........................................................................................................ 1
1.1 Group III-Nitrides: History and Their Role in Current Tec hnolo gies .......... 1
1.2 Material Propertie s and Potential Future Applications ................................. 2
1.3 Objectives of this work ................................ ................................................. 6
2 Theoretical background ..................................................................................... 9
2.1 Second Order Nonlinear Optical Processes .................................................. 9
2.1.1 Second Harmonic Generation (SHG) ................................ .................... 9
2.1.2 Waveguide Modes ............................................................................... 14
2.1.3 Modal Dispersion Phase Matching ...................................................... 17
2.1.4 Quasi-Phase Matching in III-Nitride Waveguide Structures ............... 18
2.2 Surface Kinetics in III-Nitride Growth ....................................................... 22
2.3 Point Defects ............................................................................................... 27
2.3.1 Energy of Forma tion for P oint Defects ................................ ............... 27
2.3.2 Franck-Condon Approximation ........................................................... 31
3 Experimental Setup .......................................................................................... 34
3.1 Optical Spectroscopy .................................................................................. 34
3.1.1 Photoluminescence a nd Photoluminescence Excitation Spectroscopy 34
3.1.2 Second Harmonic Generation Spectroscopy ....................................... 36
3.1.3 Transmission Spectroscopy ................................................................. 36
3.1.4 Micro-photoluminescence Spec troscop y Se tup .................................. 38
3.2 Growth Setup .............................................................................................. 39
3.3 La s er Interference Lithography .................................................................. 40
4 Polarit y Control ................................................................ ................................ 43
4.1 Historical Perspec tive ................................................................................. 43
4.2 III -Polar AlN and GaN ................................................................ ................ 45
4.3 N-Polar AlN and GaN ................................................................................. 48
4.4 Polarity De p endent Wet Etching in KOH ................................................... 50
5 Lateral Polar Str uc tures .................................................................................. 53
5.1 AlN Lateral Polar Structures ....................................................................... 53
5.1.1 Nanometer Scale AlN L a teral Polar Structures ................................... 61
5.1.2 Promoting Step Flow Growth through Co ntrol of Al Vap or
Supersaturation ................................................................................................... 73
5.1.3 Mass Transport between Polar Domains ............................................. 77
5.1.4 Influence of Crystallographic Orie ntation on the IDB ........................ 88
5.2 GaN La t eral Polar Structures ................................................................ ...... 90
5.2.1 Nanometer Scale GaN Latera l Polar Structures ................................... 92
5.2.2 Promoting Step Flow Growth for Smooth GaN LPS........................... 94
6 Point De fe cts in AlN ......................................................................................... 99
6.1 PVT Grown AlN Bulk Single Crystals ....................................................... 99
6.1.1 Historical Perspec tive ................................................................ .......... 99
6.1.2 Absorption, PL and PLE Charac teriz ation................................ ......... 101
6.1.3 High Tempera tu re Absorption Spectra .............................................. 109
7 UV Laser Light as Second Harmonic Gener atio n ....................................... 116
7.1 Modal Phase Matche d S HG ...................................................................... 116
7.2 Quasi Phase Matched SHG in AlN L PS Wave guides............................... 118
7.2.1 10 µm Periodicity ............................................................................... 120
7.2.2 1.2 µm Periodicity .............................................................................. 124
8 Conclusions and Future Work ...................................................................... 127
8.1 Summary a nd Conclusio ns ........................................................................ 127
8.2 Future Work .............................................................................................. 129
9 Publications and Conference Cont ributions ................................................ 130
9.1 Publications ............................................................................................... 130
9.2 Conference Ta lks ...................................................................................... 131
10 References ....................................................................................................... 132
11 Acknowledgements ......................................................................................... 148
i
List of Figures
Fig u re 1 -1: Schematic o f the III-Nitride wurtzite structure, where the basal plane ( c -
plane) and the p rimar y ( m-plane) and secondar y (a-plan e) p rismatic planes
are highlighted. ................................................................................................ 3
Fig u re 1-2: C alculated bandgap ener gy as a funct ion of III-Metal composi tion x for
the III- Nitrides ternary allo y s using Vegard’s law . Bowing parameters b a re
taken from Pelá et al. 22 .................................................................................... 5
Fig u re 2-1: Intensity of the sec ond harmonic generated wave as a function of
propagation length. Highlighted in red is the coherence leng th dist ance lc,
which is the length in which the wave v ectors of the driving and indu ced
wave accumula te a phase - shift of π. .............................................................. 12
Fig u re 2-2: Schematic of planar waveguide structure used to descr ibe the
propagation of TM electromagnetic modes. Three la yers with different
refractive index
i
n
are displayed. ................................................................... 15
Fig u re 2-3: El ectric field amplitude of the second harmonic wav e as a function of
propagation length for th ree different phase matching scenarios. ................. 21
Fig u re 2-4: Intensity of the second harmonic wave as a function of propaga tion
length for three different phase matching scenarios. ..................................... 21
Fig u re 2-5: I llustration of a formation energy diagra m of a point defe ct
X
for
various cha rged states q (+2, +1, 0, -1) as a function of F ermi energ y
referenced to the valence band max imum (the bandgap en ergy of AlN was
chosen as a n example). ................................................................ .................. 29
Fig u re 2-6: Illustration of a formation energ y d iagram of a point defect, with its
thermody n amic transition energies highlighted. ........................................... 30
Fig u re 2-7: Configuration coordinate dia gra m illu strating the shift in energy between
the peak absorption and emission bands, due to elect ron-phonon coupli ng.
An optoelectronic transi tion invol ving a point defect
X
in the -1 charg ed
state leading to a free el ectron in the conduction band and a neutral char ged
state is shown and the re s pective recombination process. ............................. 31
Fig u re 3-1: Ex perimental setup for photoluminescence spectroscop y measurements.
....................................................................................................................... 34
Fig u re 3-2: Schematic of the photoluminescence ex citation spectroscopy setup. .... 35
ii List of Fig u res
Fig u re 3-3: Schematic of ex perimental setup used for testing the AlN and GaN
based waveguides for second harmonic ge n eration. ..................................... 36
Fig u re 3-4: Experimental setup for temperature dependent transmission spectra up to
900 °C. .......................................................................................................... 37
Fig u re 3-5: Micrometer spatiall y resolved photolumi nescence exc itation
spectroscopy se tup. ....................................................................................... 38
Fig u re 3 -6: Picture of the metal organic chemical vapor deposition reactor during
vacuum annealing at 1100 °C (left). Clockwise sta rting at the top le ft, picture
of the coolin g s y st ems containing the metalor ganic sources (TMA and TE G),
liquid nit roge n tank which provides the N 2 gas source, ammonia gas source
and hy d rogen gas source. .............................................................................. 39
Fig u re 3-7: Llo y d's mirror configuration setup. ........................................................ 40
Fig u re 3-8: Laser interference intensit y profile at the sample surface. ..................... 41
Fig u re 4-1: Schematic displa y in g the cr ystal structure for different polar growth
directions and mixed polar growth ............................................................... 43
Fig u re 4-2: Growth run temperature profile of an AlN nucleation layer. ................. 46
Fig u re 4-3: AFM image of the surface of a typica l AlN nucleation layer. ............... 47
Fig u re 4-4: AFM measurements of the surface mo rpholog y of a Ga -polar GaN (left)
and Al-polar AlN (right) epitaxial laye r. ...................................................... 48
Fig u re 4 -5: AFM measurements of the surface morphology of N -polar GaN (left)
and AlN (right) respectivel y with high (top) and l ow (bottom) ma gni fication.
....................................................................................................................... 49
Fig u re 4-6: Tilted cross section SEM image displaying the etched surface of a III -
polar (top) and N-polar (bottom), GaN (left) and AlN (right) epitaxial layer.
....................................................................................................................... 51
Fig u re 5-1: Schematic of mask design us ed for photolithography. The mask
contains 8 different r egions of 1 cm 2 areas with different stripe structu res.
The stripe structures are composed of equally sp aced covered and uncovered
stripes. The periodicit y of the stripe structures a re 10, 20, 40 and 100 µ m.
Every p eriodic structure is available in two o rientations at a 90° an gle from
each oth er in order to st ud y the influence of the substrate orientation on the
grown structur es. Th e center region is half covered and h alf uncov ered to
achieve 0.5 x 1 cm 2 single polar domains and compare with the
corre spondin g polar domains in the lateral polar structure s. ........................ 54
iii
Fig u re 5-2: AFM ima ge of a 20 µm periodic st ripe pattern o f an AlN nucleation
layer deposited on a sap phire substrate with color coated height scal e (left).
Line scan across the periodic structure showing the height profile. .............. 55
Fig u re 5-3: AFM image of a 20 µm periodic AlN lateral pola r structure ................. 55
Fig u re 5 -4: D IC optical microscope images of a 100 µm periodic AlN LPS as grown
(left) and after wet etching for 30 seconds in 1M KOH at 70 °C. ................. 56
Fig u re 5-5: SEM im age s of a 10 µm periodic AlN L PS as grow n (le ft). On the right
a 100 µ m periodic AlN LPS after wet etchin g in a 1M KOH solution in DI
water at 70 °C for 30 s. .................................................................................. 57
Fig u re 5-6: SEM measurements of a wet etched 100 µm periodic AlN LPS. (Left)
The wet etched N-pola r domain where the remaining low densit y of large
conical features are highlighted. (Center) high ma gnification of the inversion
domain boundary with hig hli ghted high densit y of conical features. ........... 57
Fig u re 5-7: SEM ima ge of a wet etched N-polar AlN film in a 0.5 M KOH solution
in D I water for 20 s at 7 0 °C. The app arent Al -polar inversion domains are
encircled. ....................................................................................................... 58
Fig u re 5 -8: A FM ampli tude image s of the patt erned AlN nucleatio n layer on a
sapphire substrate prior to the growth of an Al N LPS (Top images). SEM
image s of w et etched AlN L PS showing a series of ali gned Al -polar
inversion domains in a simil ar pattern to the p olishing scratches (Bott om
image s ). ......................................................................................................... 59
Fig u re 5-9: SEM image display in g a magnified view of the re sidual hexag onal
pyramids after wet etching. Vertical AlN wires located at the top of t he
hexagonal pyramids are highlig ht ed. ............................................................. 60
Fig u re 5 -10: Calculated coherence length in bulk AlN sin gle crystal as a function of
fundamental (driving) wavelength. ............................................................... 62
Fig u re 5-11: Both sides of equati on (5.1.2) are plotted. I n red, th e effective
refractive index for the 0 th order mode of the fundamental wave. In purp le,
the effective r efractive i ndex for t he 0 th order m ode of the second harmonic
wave reduced a term given b y th e periodicity of the AlN L PS with Λ =1.2
µm. ................................................................................................................. 63
Fig u re 5-12: N anoscale polarity control process scheme. Step 1: MOCVD
deposition of AlN nucleation la y er on c -plane sapphire. Step 2: Photor esist
and ARC are spin coated onto the substrate. Step 3: Photoresist layer is
iv List of Fig u res
exposed to the laser interference periodic patter n a nd deve loped. Step 4:
Pattern is transferred to the AlN nu cleation la yer b y reactive ion etchi ng.
Step 5: The residual phot oresist and ARC are removed b y O 2 plasma . S tep 6:
The patterned substrate is reinserted in the MOCVD chamber, where the AlN
film is deposited leading to the AlN periodic latera l polar structure. 95 ........ 64
Fig u re 5-13: Differential interference contrast optical microscope ima ge of 1.2 µm
periodic pattern of the photoresist lay er. ....................................................... 65
Fig u re 5-14: Reflected intensit y at the ARC -photoresist interfac e as a fu nction of
ARC thickness. ................................................................ ............................. 66
Fig u re 5 -15: Atomi c force microscop y image a nd heig ht profile line s can of the
patterned substrate, displaying domains of 25 nm thick AlN lay ers and
domains with the sapphire substrate e xpos ed. .............................................. 67
Fig u re 5-16: Hei ght profile AFM images of the patterned subst rate b efore (left) and
after the AlN thin film growth (ri ght). In th e right ima ge, domains with a
rough h exagonal columnar surf ace, characteristic of the N-pola r domain, is
observed as well domai ns with a smoo th (sub -nanometer RMS rou ghness)
Al -polar surf ace with similar domain siz es as the patterned substrate,
pointing at the vertical inversion domain boundaries. .................................. 68
Fig u re 5 -17: Tilted view S EM image of the AlN LPS as grown (a) and after being
submerged in a 1 molar KOH solution in deionized wat er for 1 minute at 70
°C (b). ............................................................................................................ 68
Fig u re 5-18: Cross-s ectional SEM im ag es of AlN L PS samples with varying
thicknesses. The inversi on domain boundaries are highli ghted with yellow
dashed lines. Complete coalesce n ce at the IDBs is observe d. ...................... 70
Fig u re 5 -19: AFM ima ge of a 1.2 µm periodic AlN L PS before (top left) and after
(bottom left) mechanical polishing with compa rable sclaes. Th e r espective
height profile li nescans across the periodic struc ture are shown on the top
right and bottom right. .................................................................................. 72
Fig u re 5-20:SEM images showing the AlN LPS- basded wave guides at a low (left)
and high (right) magnification re spectivel y.. ................................................ 73
Figure 5-21: Surface m orpholog y of N -pol ar AlN thin films grown at different
temperatures. The growth temperatures for the di spla y ed samples is 1250 °C,
1400 °C, 1500 °C and 1550 °C for a)-d) respectively. ................................ 74
Fig u re 5-22: Al vapor supersaturation as a function of growth temperature ............ 75
v
Fig u re 5-23: Temperatur e and pressure dependen ce of measured growth rates for Al-
and N-polar AlN epitaxial films. ................................................................... 76
Fig u re 5-24: Al vapor supe rsaturation as a function of total pressure inside the
growth chamber. ............................................................................................ 76
Fig u re 5 -25: AlN LPS for a series of growth runs, where the grow th temperature
was varie d to reduce the Al vapor supersaturation. ....................................... 78
Fig u re 5 -26: Amplitude AFM ima ges o f a g rown AlN LPS sample before (top left)
and after (top right) KOH etching in a 1M solution at 70 °C for 30 s.
(bottom) Height profile line sc ans for the co rresponding amplitude AFM
image . ............................................................................................................ 79
Fig u re 5 -27: Amplitude AFM images of AlN LPS before (top left) and after (top
right) KOH etching in a 1M concentrated solution at 70 °C for 30 s. ........... 80
Fig u re 5 -28: Polar domain thickness difference and Al vapor supe rsaturation as a
function of temperature . ................................................................................ 81
Fig u re 5-29: (left) AFM images of 550 nm thick (top) and 250 nm thi ck AlN LPS -
based wave guides with 10 µm periodicity. (right) Height profile line scans
across and along the waveguide corresponding to their respective AFM
image s. ........................................................................................................... 82
Fig u re 5-30: (left) A FM image of 1.2 µm periodic AlN LPS grow n at 1500 °C.
(rig ht ) Opti cal D IC im age of the same sample after b eing submerged in
KOH, displa ying inho mogeneous etching, indicating th at the AlN LPS
contained mixed polar domains. .................................................................... 83
Fig u re 5 -31: Amplitude AFM image o f 1.2 µm AlN LPS s amples grown at 1500 °C.
Regions where one pol arity is over growing the neighborin g polarity are
encircled. A few inversion domain boundaries (I DB’s), as determined b y the
surface morpholo gies characteristic of the respective polarities, a re marked
with yellow da sh ed lines. .............................................................................. 83
Fig u re 5-32: AFM hei ght images for 1.2 µ m AlN LPS grown at
3
5 1 0 x 10
(left)
and
5
1 x 1 0
(right) Al vapor supersaturation values. ................................. 84
Fig u re 5-33: A FM h eight images of 1.2 µ m AlN LPS grown b y a two -step
temperature process. The first step growth temperature for all samples was
1250 °C. In the secon d step the tem perature was increased to 1400 °C (top),
1500 °C (center) and 15 50 °C (bottom ) in o rder t o achieve a smooth sur face
morphology of the 1.2 µ m AlN L PS. ............................................................ 85
vi List of Figures
Fig u re 5-34: Tilted SEM image s of a KO H w et-etched 1.2 µm AlN LPS sample
grown in a two-step temperature process...................................................... 86
Fig u re 5-35: AFM height (top) and amplitude (bottom) image of two different 1.2
µm periodic AlN L PS, where thi cker Al -polar d omains compared to the N-
polar domains are measured.......................................................................... 86
Fig u re 5-36: AFM hei ght (top) and amplit ude (bottom) image of the 1.2 µ m periodic
AlN LPS display ed in Figure 5-35 after regrowth at x temperature for x
minutes, where hi gher deposition rates for the N -polar domains compared to
the Al-polar domains were determined. ........................................................ 87
Fig u re 5-37: AFM amplitude image s of the IDB in AlN LPS sam ples with
periodicities along the a- direction (top) and alon g the m -direction (bottom).
The left images, are taken from a sample where the stripe pattern is well
aligne d with the crystallographic orient ations an d the samples on the right
are taken from a sample where the stripe pattern is slig htl y misali gned with
respec t to the cr y stallo graphic orienta tions. .................................................. 89
Fig u re 5-38: AFM im age with corresponding height profile line -scans of a GaN LPS
grown at a V / III ratio of 250. ........................................................................ 91
Fig u re 5-39: D IC optical microscope images for a GaN L PS before (top left) and
after different polishing times. ...................................................................... 91
Fig u re 5-40: 75 min long mechanically poli shed GaN LPS with 0.3 µm alumina
particles in DI water solu tion. ................................................................ ....... 92
Fig u re 5-41: Calculated coherence length for bulk GaN as a f unction of fundamental
wavelength. ................................ ................................................................... 93
Fig u re 5-42: (left) AFM amplitude image of a 1.2 µm periodic GaN L PS showing
N-polar GaN bein g overgrown b y Ga -polar G aN. (rig ht ) AFM h eight image
where the N-polar GaN areas that ha v e been etched awa y are highli ghted. . 94
Fig u re 5 -43: Tilted cross -section S EM ima ge of a 1.2 µm GaN L PS b efore (left) and
after (right) we t etching in a KOH solution. ................................................. 94
Fig u re 5-44: C alculated Ga vapor supers aturation as a function of temperature. Fo r
comparison the values are calculated fo r H 2 and N 2 diluent gas (left) and for
different total reactor pressures (right). ........................................................ 95
Fig u re 5-45: Calculated Ga vapor supersaturation as a function of V/III ratio for
different temperatures under N 2 diluent gas (left) and under H 2 diluent gas
(rig ht ). ................................................................................................ ........... 95
vii
Fig u re 5-46: AFM hei ght im age o f the surface of an N -pol ar GaN thi nfilm grown
under the conditions described in the text. A scan area of 5 x 5 µ m 2 (left) and
90 x 90 µm 2 (right) is presented. ................................................................... 96
Fig u re 5-47: AFM height (left) and amplitude (rig ht) ima ge of a GaN LPS grown at
relatively low Ga v apor supersaturation values (
100
). ......................... 96
Fig u re 5-48: Cross section SEM image s displa y in g a GaN LPS grown at a Ga vapor
supersatura tion valu e of 100. ......................................................................... 97
Fig u re 5-49: AFM amplitude im ages (top) and h eight pr o file linescans (bottom) of a
1.2 µm periodic GaN L PS grown at a Ga vapor superseaturation of 100
before (left) and after (KOH) etching. ........................................................... 98
Fig u re 6-1: Point de fect formation energy as a functi on of fermi level energy for
various likely point de fects present in PVT grown AlN. ............................ 103
Fig u re 6 -2: Schematic displa y in g the thermodynamic transition ene rg y sat es for th e
respec tive point defects, as horiz ontal lines, referenced to the valence ba nd
maximum. .................................................................................................... 103
Fig u re 6-3: Photoluminescence spectra (blac k) overlapped with the absorption
spectra (red) of a PVT grown AlN single cry stal . ....................................... 104
Fig u re 6-4: Color coded logarithmic int ensity 2 D map photol uminescence excitation
spectroscopy measurements of an AlN single cry s tal recorded at 5 K. The
vertical lines correspond to PLE spectra for a fix ed detection energy and a re
displaye d as red curves in Fig ure 6-5. Horizontal li nes correspond to P L
spectra at a fix ed excitation energy and are displayed in Figure 6 -5 as bla ck
curves. .......................................................................................................... 106
Fig u re 6-5: Photoluminescence spectra (black) for various excitation ene rgies,
overlapped with photoluminescence excitation spectra (red) for various
detection energies. ....................................................................................... 107
Fig u re 6-6: Power dependent photol uminescence measurements for above band gap
excitation. .................................................................................................... 108
Fig u re 6-7: Temperature dependent transmission spectra for an epitaxial GaN la yer
deposited on a sapphir e substrate. The absorption spectra are not corrected
for reflection. ............................................................................................... 110
Fig u re 6 -8: Tempe rature dependence o f absorpti on coefficient spectra. T he spectra
are not corrected f o r reflection. ................................................................... 110
viii List of Fig u res
Fig u re 6-9: T auc relation for temperature dependent transmission spectra measured
for a GaN epita x ial thinfilm. ................................................................ ....... 111
Fig u re 6-10: Bandgap ener gy of a GaN epitaxial film as a function of temperature,
compared with the Varshni model fitted with literature values. ................. 112
Fig u re 6-11: Absorption spectra for an AlN single cr y st al with higher ox y gen
concentration than carbon for different tempe ratures in the ran ge from 295 K
to 1063 K. For comparison a “UV non - transp arent” sample containing higher
carbon impurities than ox y gen and silicon is displayed. ............................ 113
Fig u re 6-12: Abso rption spectra for a n AlN single cr y stal with a higher carbon
concentration than ox y gen and sil icon for a tempe rature range from 296 K to
1070 K. ................................ ........................................................................ 114
Fig u re 7 -1: D IC microsc ope ima ge of Al -polar AlN waveguides for M DPM SHG.
..................................................................................................................... 117
Fig u re 7 -2: Dispersion relation of the fundamental and se cond harmonic waveguide
modes for a 10 µm wide and 550 nm thick Al-polar AlN waveguide, taken
from a publication by Troha et al.. 47 ........................................................... 117
Fig u re 7-3: MDPM SHG measurements using a 10 µm wide and 550 nm thi ck Al -
polar AlN waveguide. 47 .............................................................................. 118
Fig u re 7 -4: 3D AFM ima ge with color -coated h eight scale of 500 nm - 550 nm thick
and 4 µm wide AlN L PS -based waveguides. ............................................. 120
Fig u re 7-5: Dispersion relation for the fundamental (red) and sec ond harmonic
(purple) TM00 wave mode for a 220 nm thick w aveguide. ...................... 121
Fig u re 7 -6:2D top view gra y scale scattering int ensit y profile of th e fu ndamental
laser light propaga ting through the 10 µm periodic AlN L PS -ba sed
waveguide (Top). 1D scattering int ensity profile for a li ne -scan section alo ng
the waveguide surface . ................................................................................ 122
Fig u re 7 -7: QPM SHG spectra at two different fundamental w avelengths for a 500
nm – 550 nm thick and 10 µm periodic AlN L PS -based waveguide. ........ 123
Fig u re 7 -8: QPM SHG spectra at two different fundamen tal w avelengths for a 200
nm – 250 nm thick and 10 µm periodic AlN L PS -based waveguide. ........ 123
Fig u re 7 -9: 1.2 µm periodic AlN LPS-b ased w aveguides fabricated via SiO2 hard
mask deposition and subsequent RIE. 95 ...................................................... 124
ix
Fig u re 7-10: 1.2 µm pe riodic AlN L PS -based waveguides fabricated by standard
masked photolithog raphy using nega tive photoresist and subsequent R IE
etching . ........................................................................................................ 124
Fig u re 7-11: Top view 2D grayscale scattering intensity profile at the coupli ng facet
of 1.2 µm periodic AlN LPS-based waveguides. ................................ ........ 125
List of Tables
Table 1-1: La ttic e parameter and sponta n eous polarization field for III-Nitr ides. 6,21 . 4
Table 1-2: Material properties re l evant for optoelectronic devices. 15,16,21,23 – 28 ........... 5
Table 2-1: Nonlinear properties of prominent nonlinear c r y st als used for S HG in the
UV -C spectral range and AlN for comparison. 36 – 41 ................................ ...... 14
Table 2- 2: Experimentally determined v apor pressure equation constants for the
metalorganic precursors trimethy laluminum (TMA) and trieth ylga lliu m
(TEG). ............................................................................................................ 23
Table 2-3: III-Nitrides c oefficients fo r the equilibrium constant equation in (2.2.7) .
....................................................................................................................... 24
Table 4-1: Etch rates of N- and III -polar G aN and AlN crystals in 1wt% KOH
solution in deionized water a t 70 °C. 85 .......................................................... 50
Table 6-1: Calculated p oint defect concentration accounting for charge balance
conserva tion and for a given measured concentration of C, O and Si. ....... 102
Group III - Nitrides: History and Their Role in Current Tec hnolo gies 1
1 Introduction
1.1 Group III- Nitrides: History an d Their Ro le in Cu rrent
Technolog ies
The group III-Nitrides comm only refers to the compound semiconductors including
indium-, gallium - and al uminum nitride (InN, GaN and AlN) and their ternar y and
quaternary allo y s. Initial reports cl aiming to h ave obtained AlN c r y stals from direct
reaction of aluminum vapor and nitrogen gas at high temperatures, were publi shed
in the late 1800’s and early 1900’s. 1 – 4 These conclusion s were based on the fact that
the investigated cr ystals decomposed into ammonia and other aluminum compounds
containing ox ides when submerged in alkali solu tions. I n a mor e detailed stud y in
1924, Heinrich Ott 5 , b y means of X-ra y di ffracti on determined that AlN cr y stallizes
in a wurtzite structure and measured the lattice constants a and c to b e 3.11 Å and
4.98 Å respectivel y, in a greement with current measured values on state of the art
AlN crystals. 6 GaN was first reported b y J ohnson et al. 7 in 1932, where gallium
metal was heated up to 1200 °C in ammonia atmosphe re and InN was reported in
1938 b y Juza and H ahn 8 , where (NH 4 ) 3 I nF 6 was heated up to 600 °C also in
ammonia atmosphere. T he latter authors, using X-ray diffraction, deter mined the
crystal structure of G aN and I nN to be wurtzit e and calculated the lattice c onstants a
and c to be 3.18 Å and 5.16 Å respec tivel y for Ga N and 3.53 Å and 5.69 Å
respec tivel y for I nN in agreement with curr ent measur ed va lue s 6,9 . The
afore m entioned methods for obtainin g III-Nitride cr ystals, le ads to hi gh impurit ies
concentrations which inh ibited an accurate measurement of their respectiv e electro -
optical properties. The deve lopment of vapor phase epitaxy for III-Nitrides
compound semiconductors using III - chlorides and ammonia as pr ecursors, led to the
realization of thin films with low impurities concentrations and superior optica l
quality. 10 – 12 I n th e earl y 1970’s III -Nitride epitax ial la y ers d eposited on sapphire
substrates were opticall y character ized and a dir ect band gap energy o f 3. 5 eV and
6.2 eV was determined for GaN and AlN resp ectively. 12 – 14 These results and the
possibilit y to control th eir electrical properties through dop ants, intensified research
on the material s y st em due to their potential applications in li ghting and
photodetectors in the blu e, violet and UV spectral range. Since the earl y 1 970’s, InN
2 Introduction
was thought to have a direct band g ap energ y close to 2 eV, how ever D avydov et
al. 15 published a work in 2002, where the ban gap energ y of InN was meas ured to be
closer to 0.9 eV. These results expanded the potential wavelengths for III- Nitrides
emitters into the visible and near infra -red which further motivated research of the
material s ystem. Furthermore, the Baliga’s fi gure of merit 16 for GaN and AlN is
superior when compare d to prominent semiconductors like silicon and sil icon
carbide (SiC ), making th em very attractive for efficient, high po wer, high freque n c y
and high temperatur e stable ele ctronic devices. Afte r the demonstration of
AlGaN/InGaN based L E Ds and laser diodes ( LDs) by Nakamura et al. 17,18 man y
commercial applications were d eveloped in a vari ety of markets includin g efficie nt
lighting , displays, hi gh densit y storage media a nd UV detectors. In th e fie ld of
electronics, GaN based power converters and RF devices have been recently m ade
commercially available, ex hibiting superior performance characteristics to S i and
SiC based devices. Noteworthy , is the recent demonstration of GaN based vertical p -
n junction diodes with breakdown voltages a bove 4 kV. 19 I II-Nitride based
optoelectronic devices are a ke y component in most lighting applications and their
market share in electronic applica tions is rapidly ex panding. W hile rec ord breaking
performance has b een de monstrated for man y d evices using the III -Nitride material
system, point defects and dislocations still limit their theoretical potential. Large
efforts towards th e d evelopment of hi gher puri t y III-Nitride thi n films and substrates
is being conducted, which are expected to significantly improve device performance
and enable nov el devices such as UV-C LDs. Other challenges include p-t ype
doping (particularl y in high Al -content AlGaN), surface p assivation an d c ontact
design. I n summar y, th e III-Nitrides technology has revolutionized the lighting
industry and is already replacing current te chnologies in high power, hi gh
temperature and high fr equenc y electronics. W ith much room for improvement, th e y
will undoubtedly becom e a major player in the se miconductor based electronic
industry.
1.2 Material P roperties and Poten tial Future App lications
Two primar y cr y st allization phases are observed in the I II-Nitrides mat erial s y stem.
At ambient conditions, th e thermod ynamically stable phas e is their hex agona l
wurtzite structure (sp ace group P6 3 mc) which is t he structure of all sampl es studi ed
Material Propertie s and Potential Future Applications 3
in thi s work. 20 Alternatively , their metastable zi ncblende phase c an be obtained b y
heteroepita x y on a cubic substrate. In Figure 1-1 a schematic dia gram displ ay in g the
III -Nitride wurtzite structure is presented.
Fig u re 1 -1: Schematic o f the III-Nitride wurtzite structure, where the basal plane ( c -
plane) and the primar y (m-plane) and seconda ry (a -plane) prismatic p lanes a re
highlig ht ed.
The III -Nitrides can b e c lassified as non -centros ymmetric polar cr y st als, giving ris e
to their piezoelectric it y and py roelectricit y. The ir lattice pa rameters are slightl y
distorted from the ideal tetrahedral arrangement in that the c/ a ratio deviates from
the value of 1.633 for t he ideal wurtzite structure. The observed distortion in the
lattice structure has been found to correlate with the u parameter in such ma nner that
the tetrahedral bond lengths are kept nearl y consta nt . The u parameter being the ratio
between the bond length b and the c lattice co nstant, where b is the b ond length
between th e two n earest neighbors along the c -axis (see Figure 1 -1 ) 20, 21 . The u
parameter in term correlates with the electronegativity o f the respective atoms as
well as the sponta neous polarization field P 0 . The lattice pa rameters of the I II-
Nitrides and their respective spontaneous polariz ation field are displa yed in Table
1-1 for comparison.
4 Introduction
Table 1-1: La ttic e parameter and spontaneous polarization field for III-Nitrides. 6 ,21
AlN
GaN
InN
Ideal
Tetrahe d ral
La ttic e constant a (Å)
3.112
3.189
3.585
La ttic e constant c (Å)
4.982
5.186
5.80
c/a
1.601
1.626
1.618
1.633
u (Å)
0.382
0.377
0.379
0.375
Spontaneous polarization P 0 (C/m 2 )
-0.081
-0.029
-
0.032
The III -Nitrides have a direct band gap spannin g from 0.7 eV for InN t o 6.2 for
AlN. 12,15 Additionall y , the band gap can b e tun ed throughout the entire energ y range
by var ying the composition of the III -m etals in t heir tern ar y and quaternar y allo ys
making them ve r y attract ive for li ght emitting diodes (LEDs) and laser dio des ( LDs)
( Figure 1-2 ). For LEDs and LDs, the tunable bandgap energ y covers the entir e
visible spectra, the n ear IR up to 1.7 µm and the ultraviolet down to 20 0 nm. Other
material properties relevant for high power and high frequenc y opt oelectronic
devices are listed in Table 1-2 and compared to prominent materials.
Material Propertie s and Potential Future Applications 5
Fig u re 1 -2 : Calculated bandgap en ergy as a funct ion of III -Metal composition x for
the III- Nitrid es ternary allo y s using Ve gard’s la w. Bowin g parameters b are taken
from Pelá et al. 22
Table 1-2: Material properties relevant for optoelectronic device s . 15,16,21,23 – 28
Si
4H-SiC
GaAs
AlN
GaN
InN
Bandgap (eV)
1.1
3.3
1.4
6.0
3.5
0.7
Thermal conductivity
(W/cm K)
1.5
3.7
0.5
3.4
2.3
Electric breakdown
E c field (MV/cm)
0.3
3.0
0.4
15
3.75
Electron mobility µ
( cm 2 /V s)
1350
1000
8500
300
1400
4400
Relative dielectric
constant
11
9.7
12.9
9.14
8.9
18.4
Baligas high
freque n c y fi gure of
merit (µ E c 2 )
1
74
11
555
162
Baligas high voltage
figure of merit ( ε r µ
E c 3 )
1
653
17
23080
1638
6 Introduction
1.3 Objectiv es of this work
La s ers emitting in the ultraviolet spectrum below 300 nm are desired for a variety o f
applications, including radiation sterilization, photochemical labeling, bio -sensing,
nanolithography, medical s urgery , micromachining and satellite communication.
Currently ava ilabl e deep UV laser systems are expensive , inefficient, stationar y ,
large, and require freque nt maintenance, limiting their applications. Semiconductor
based LEDs and L Ds are compact (micrometer sc ale), robust, reliable and efficient,
allowing for their low production cost, and wide range of applications. AlGa In N
based LEDs and LDs in the spectral range betw een 370 nm and 520 nm are now
widely available and hav e revolutioniz ed the lighting in dustr y. Advances have been
made toward the fabrication of electricall y inj ected AlGaN based U V-C L Ds,
however doping, carrier injection, and d efect control are still challenging. 29 – 31
Alternatively, UV -C lasers can be obtained throu gh frequency doubling v i a second
harmonic generation (SHG). In fact, diode-pumped solid state las ers with 266 nm
emission wavelength are commerciall y available. These s ystems, t y picall y invol ve
two stages of frequenc y doubling (f requenc y qu adrupling) after pumping a solid
state cr y stal with a laser diode, which makes t hem very in efficient. Furthermore,
they require c omplex opti cs, are large and degradation of the utilized nonlinea r
crystals leads to short lifetimes. The III -Nitr ides are attractive for frequenc y
conversion and nonlinear optical applications due to their rel atively large nonlinear
optical coefficients, wide transparency window and high power dama ge threshold .
Their w eek birefringence does not allow for bir efringence phase matching making a
quasi-phase m atchin g approach necessary fo r second harmonic generation.
Challenges in polarity control and the fabrication of p eriodically poled III-Nitrides
crystals, have limited th eir implementation in nonlinear optical applic ations. I t is
reasona bl e to envision, AlGaInN-based integrated optics where periodically poled
nitride-based wave guides serve as quasi-phas e matching structures for frequenc y
conversion of the laser light emitted from an AlGaInN LD.
In this work a process is developed for the fabrication of high qualit y A lN
and GaN lateral polar structures-b ased waveguides, suitable for quasi-phase matched
nonlinear optical process es. Furthermore, point defects in AlN, leadin g to absorption
centers at energies lowe r than the b andgap energy are id entified. Fin ally , quasi -
Objectives of this work 7
phase mat ched second harmonic g eneration o f UV laser li ght in pe riodic AlN lateral
polar structure s -based waveguides is demonstrated for the first time.
In sec tion 2, the theore tical background relevant for thi s work is su mmarized ,
including second o rder nonli near optical proces s es , where some phase matching
techniques are described , a thermod ynamic su persaturation model describing the
surface kinetics in low -pressure metalorganic chemi cal vapor deposition a nd a brie f
description on how to relate photoluminescence excitation spectra to calculated
thermody n amic transitio n energies of point defects under the Franck-Condon
approximation. Details on the growth, proc essing and characterization setups are
described in se ction 3. In section 4, a polarit y control process scheme for epitaxial
AlN and G aN la ye rs dep osited on sapphire substrates via MOCV D is pres ented . In
section 5 GaN and AlN periodic lateral polar structures with periodicities ran ging
from 1.2 µ m to 100 µm a re demonstrated a n d charac terized , where the shorter
periodicities of 1.2 µm are achieved, b y introdu cing a laser interference lithographic
process. S ubsequentl y , t wo approaches for reduc ing the surfa ce roughness of th e
lateral polar structures ar e described, n amel y post -growth mechanical polishing and
surface roughness reduction during growth b y promoting step flow growth at the
nitroge n polar surface through control of the vapor phase supe rsaturation. Next,
mass transport between the adjacent opposit e-polar domains at reduce d
supersatura tion v alues is demonstrated and growth conditions for equal deposition
rate for both polar domains are established. S ection 6 focuses on identifying point
defects which lead to below bandgap energy absorption centers in single crystal AlN
substrates. A novel approach to determine the impurities t y pe and concentrations in
the cry st al is presented, where P L, P L E, absorption spectra and S I MS data is used in
combination with a DFT based theoretical model which accounts for ch arge balance
conserva tion in the cr y stal and the formation energ y of defects. Absorption and P L
measurements on AlN and GaN thin films are also presented and discussed. I n
section 7, modal dispersion phase matched second harmonic generation of laser light
in single polar AlN and Ga N waveguides a re presented. Followin g, quasi-phase
matched second harmonic generation of UV laser light is demonstrated for the first
time in III-Nitride periodic later al polar structur es -based waveguides. Section 8 will
summarize and discuss the bulk of the results, followed b y an outlook for III-Nitride
quasi-phase matching str uctures.
8 Introduction
Second Order Nonlinear Optical Processes 9
2 Theoretical background
2.1 Secon d Order Non linear Optica l Proc esses
Second order nonli near optical phenomena are well understood and a large pool of
literature containing a thorough theor etical anal ysis and a broad r eview on nonlinear
materials and applications is available. 32 – 34 This section will briefl y describe the
theoretica l framework relevant fo r this work, inclu ding second harmonic generation,
propagation of waveguide-modes in planar waveg uid es, modal dispersion phase
matching and quasi-phase matching.
2.1.1 Seco nd Harm onic Generatio n (SHG)
Nonlinear optical pheno mena in non -centrosymmetric polar cr y stals a re described in
the fr amework of the macrosc opic Maxwell equations (also known a s Maxwell
equations in matter). Assuming no external charges and current, the Maxwell
equations for the electric field 𝐸
(r , t) , and the magnetic flux density field, 𝐵
(r , t) ,
can be reduced to the following form (international s y stem (S I) units):
∇ x E
= − 𝑑 𝐵
𝑑𝑡 , (2.1.1)
∇ x B
= 𝑑 𝐷
𝑑𝑡 , (2.1.2)
∇ ∙ D
= 0, (2.1.3)
∇ ∙ B
= 0. (2.1.4)
With
D
= 𝜀 0 𝐸
+ 𝑃
(2.1.5)
in the electric dipole approximation. Here, 𝜀 0 is the vacuum permittivit y , 𝐷
( r , t ) is
the electric displacement field, and 𝑃 (r , t) is the electric dipole polarization densit y .
In the regime of weak fi elds, namel y fo r electric field amplitudes lower th an that of
the charac teristic atomic electric fi eld E a = 5.14 x 10 11 V/m, corresponding to laser
intensities below ~ 3.5 10 16 W /cm 2 , 32 the standard linear relation d escribing 𝑃 (r , t)
in terms of 𝐸
(r , t) can be ex panded by a Ta ylo r series in 𝐸
(r , t) which in addition
to the linear relation, also describ es nonlinear relations between 𝐸
(r , t) and 𝑃 (r , t)
with: 33
10 Theoretical bac k ground
𝑃 ( r , t ) = ∫ 𝜒 (1) ( 𝑡 − 𝑡 1 )𝐸
(r , 𝑡 1 ) 𝑑 𝑡 1 + ∬ 𝜒 (2) ( 𝑡 − 𝑡 1 , 𝑡 − 𝑡 2 ) 𝐸
( 𝑟 , 𝑡 1 ) 𝐸
( 𝑟 , 𝑡 2 ) 𝑑 𝑡 1 𝑡 2 +
∭ 𝜒 (3) ( 𝑡 − 𝑡 1 , 𝑡 − 𝑡 2 , 𝑡 − 𝑡 3 ) 𝐸
( 𝑟 , 𝑡 1 ) 𝐸
( 𝑟 , 𝑡 2 ) 𝐸
( 𝑟 , 𝑡 3 ) 𝑑 𝑡 1 𝑡 2 𝑡 3 + ⋯ (2.1.6)
When representing the electric field 𝐸
and the pola rization density 𝑃
in the form of
elementary mono chromatic plane waves,
𝐸
= 𝐸
( 𝜔 ) 𝑒 (𝑖 𝑘
𝑟
− 𝜔𝑡 ) + 𝑐 . 𝑐 . and 𝑃
= 𝑃
( 𝜔 ) 𝑒 (𝑖𝑘
𝑟
− 𝜔𝑡 ) + 𝑐 . 𝑐 . , (2.1.7)
an ex pression for 𝑃 (𝜔 ) can be derived from the Fourier tr ansform of the relation
between 𝑃 ( r , t ) and 𝐸
(r , t) in equation (2.1.6) with: 33
𝑃
( 𝜔 ) = 𝜀 0 𝜒 ( 1) ( 𝜔 ) 𝐸
( 𝜔 ) + 𝜀 0 𝜒 (2) (𝜔 ; 𝜔 𝑖 , 𝜔 𝑗 )𝐸
( 𝜔 𝑖 ) 𝐸
(𝜔 𝑗 ) +
𝜀 0 𝜒 (3) (𝜔 ; 𝜔 𝑖 , 𝜔 𝑗 , 𝜔 𝑘 )𝐸
( 𝜔 𝑖 ) 𝐸
(𝜔 𝑗 )𝐸
( 𝜔 𝑘 ) + . . . , (2.1.8)
𝑃
( 𝜔 ) = 𝑃 1
( 𝜔 ) + 𝑃 2
+ 𝑃 3
+ ⋯ . (2.1.9)
Here 𝜒 𝑖 ( 𝜔 ) represent the i- th order susceptibilit y t ensor with
𝜒 (1) ( 𝜔 𝑖 ) = ∫ 𝜒 1 ( 𝑡 1 ) 𝑒 (𝑖 𝜔 𝑖 𝑡 1 ) , 𝜒 (2) (𝜔 𝑖 , 𝜔 𝑗 ) = ∬ 𝜒 (2) (𝑡 1, 𝑡 2, ) 𝑒 𝑖 (𝜔 𝑖 𝑡 1 +𝜔 𝑗 𝑡 2 ) (2.1.10)
The first term in equ ation (2.1.8), describes the linear relation between the
polarization field and the electric field . The following terms describe th e second
order nonlinear relation, the third o rder nonli near r elation and so on. T he second
term, 𝑃
2 ( 𝜔 ) , describes three wave mixing processes , where s etting
i
=
j
=
0
corre sponds to th e se cond harmonic generation proc ess le ading to
0
2
. The
focus of thi s work is on second harmonic generation hence all other terms of the
polarization densit y are neglected. Th e se cond order susceptibilit y t ensor
𝜒 (2) (𝜔 ; 𝜔 𝑖 , 𝜔 𝑗 ) contains the constants of proportionalit y relatin g the amplitude of
the second order pol arization densit y field 𝑃
2 ( 𝜔 ) with the amplitude product o f the
electric fields 𝐸
( 𝜔 𝑖 ) 𝐸
(𝜔 𝑗 ) of the driving wa v es according to 32
𝑃 𝑙 (2) (𝜔 𝑖 , 𝜔 𝑗 ) = 𝜀 0 ∑ ∑ 𝜒 𝑙𝑚𝑘 (2) ( 𝜔 ; 𝜔 𝑖 , 𝜔 𝑗 )
𝑙𝑚𝑘 𝐸 𝑚 ( 𝜔 𝑖 ) 𝐸 𝑘 (𝜔 𝑗 )
𝑖 ,𝑗 , (2.1.11)
where l , m and k can take any x , y and z value. In general, for
=
i
+
j
there exists
12 tensors of the form 𝜒 𝑙𝑚 𝑘 (2) which describe all interactions between the w aves,
where e ach tensor contains 27 Cartesian components. 32 In a specific case, namel y
for second harmonic generation (
00
= a nd 2
ij
) in wurtzite crystal
structures, uni axial propagation and polarization of the d riving waves (polarization
along optical ax is), due to s y mmet r y constraints 𝜒 𝑙𝑚𝑘 (2) ( 𝜔 ; 𝜔 0 , 𝜔 0 ) is reduce d to
one dimension with 32
Second Order Nonlinear Optical Processes 11
𝜒 (2) = 2𝜀 0 𝑑 33 (2.1.12)
For more details on the theoretical fra m ework des cribing the s econd order nonlinear
susceptibility t ensor refer to the literature. 32 ,35
From Maxwell equations (2.1.1)-(2.1.4) and using the identit y
∇ x (∇ x E
) = ∇( ∇ ∙ E
) - ∇ 2 E
the f ollowing wave equation can be derived:
- 𝛻 2 𝐸
+ 𝜀 (1)
𝑐 2 𝜕 2 𝐸
𝜕 𝑡 2 = − 1
𝜀 0 𝑐 2 𝜕 2 𝑃 ( 2 )
𝜕 𝑡 2 , (2.1.13)
where
(1 )
is the relative permittivi ty and c the speed of light in vacuum. Assuming
the electromagnetic waves prop agate along one di rection (z -dire ction), the
monochromatic plane w aves describing the electric field s can take the following
form: 33
𝐸
( r , t ) = Re [ 𝑒 𝐴 ( 𝑧 , 𝑡 ) exp (𝑖𝑘𝑧 − 𝜔𝑡 ) ] , (2.1.14)
where k and
( , ) A z t
are the w ave vector and the envelope f unction of the electric field.
For slowly var y in g envelope functions it follows 𝜕 2 𝐴
𝜕 𝑧 2 ≪ |𝑘 𝜕𝐴
𝜕𝑧 | and
𝜕 2 𝑃 ( 2 )
𝜕 𝑡 2 ≅ − 𝜔 2 𝑃 ( 2 ) , thus inserting equation (2.1.14) into (2.1.13), b y neglecting
higher order derivativ es, with
( 1) 2
2
2
k c
and with
( 2)
0
( ; , ) 2
i j e ff
d
equation
(2.1.13) ca n b e reduced to:
2 2
33 0
2
2
2 ex p( )
A
ik d A i kz
zc
(2.1.15)
where
k
=
0
2 kk
is the wave v ector mismatch between the induced and driving
waves and
0
A
is the field amplitude of the driving waves. Note that
is the
freque n c y of the second harmonic generated wav e with
0
2
. I n the un-deplet ed
pump approximation (
0
A
constant), integrating equation (2.1.15) then leads to an
expression for the ampl itude
() AL
of the second ha rmonic generated w ave as a
function of propagation length
L
. 32
2 2
33 0
2
e1
( ) .
i kL
i
A L d A
k c i k
(2.1.16)
With the intensit ies given by 32
0
22
0 0 0 0
2 ( ) , 2 I n c A L I n c A
(2.1.17)
where
n
is t he refractiv e index for th e second harmonic wav e and w ith the
following relations
12 Theoretical bac k ground
2 22
2 2 2
2
e1 sin c a nd ,
2
i kL n
kL
Lk
i k c
(2.1.18)
we obtain the following expression for the intensity of th e second harmonic wave.
2
4 22
2
0
33 0 0
23
2 22
2 2 2
0
33 0 0
22 2 22
33
0
32
00
2 e1
()
2 sinc 2
sinc .
22
i kL
n
I L d A A
k c i k
kL
d A A L
nc
d kL
IL
c n n
(2.1.19)
From equation (2.1.19) we see that for a w ave v ector mismatch
0 k
and all other
values held constant, the propagation len gth dependence of the second harmonic
intensity follows a normalized sinusoidal function (see Figure 2-1 ). From Figure 2-1
it is clea r that in order to continuously in crease th e intensity of the second harmonic
wave, the wa ve vectors of the driving a nd induced waves have to be matched
( 0) . k
C ommonl y , the optical birefringence of non linear polar materials is
exploited to achieve phase matching, however the birefr in gence in III - Nitrides is
week and other phase matching techniques a re necessary, such as q uasi phase
matching (QPM) or modal dispersion phase matching (MD PM) .
Fig u re 2-1: Intensity o f the second harmonic generated wav e as a function of
propagation l ength. Highlighted in r ed is the coherence length distance lc , which is
the length in which the wave ve ctors of the driving and induc ed wave accumulate a
phase- shift of π.
0.0
0.5
1.0
c
l k
3 kL
Propagation length L (arb. un its)
I 2 ( L ) (arb.units)
kL
22
2 ( ) si nc 2
kL
I L L
Second Order Nonlinear Optical Processes 13
Additionally, equation ( 2.1.19) indicates that the int ensity o f the second harmonic
wave (or a lternativel y, the conversion efficiency ) is directly proportional to the
square of the nonli near susceptibility co efficient
33
d
of the nonlinear cr y stal. Being a
constant material propert y , its value will determine the potential conversion
efficie n c y that can b e achieved for a given non linear cr ystal material. In fact, the
quantity
22
2
/
xy
d n n
is often used as a figure of merit to classify the potential
conversion effi ciency of nonli near cr ystal materials. Table 2-1 displ a y s t he se cond
order nonlinear coefficients for the most prominent nonlinear crystals used for SHG
in the UV-C spe ctral range. It is cl ear th at AlN has the potential for an order o f
magnitude grea t er conversion efficienc y , when compared to other nonlinear cr ystals.
14 Theoretical bac k ground
Table 2-1: Nonlinear properties of prominent nonlinear c r y st als used for S HG in the
UV -C spectral range and AlN for comparison. 36 – 41
Material
Second order
Nonlinear
coeff i cient
(pm/V)
Refractive
index @ 275
nm
Refractive
index at 550
nm
22
2
/
xy
d n n
β -BaB 2 O 4
d 11 = 1.84
1.75
1.67
0.69
CsLiB 6 O 10
d 36 = 0.95
1.54
1.5
0.26
KBe 2 BO 3 F 2
d 11 = 0.8
1.52
1.48
0.19
KH 2 PO 4
(KDP)
d 36 =0.46
1.55
1.51
0.06
AlN
d 33 = 7.4
2.32
2.16
5.06
In the followin g section s, first, the theory d escribing the propagation of elec tro -
magnetic waveguide modes will be presented, followed by a brief discussion of
modal dispersion phase matching (MDPM). Th en a mor e detailed descr iption of
quasi-phase matchin g ( QPM) will be presented, being the more relevant phase
matching technique f o r this work.
2.1.2 W aveguide Modes
The intensit y of second harmonic generation can be described b y equatio n (2.1.19),
when des cribing the p ropagation of electromagnetic wave s in bulk material.
However if wav eguide structures are employed, i t is necessary to consider the
propagation of transverse-electric (T E) a nd tra nsverse-ma gnetic (T M) modes. I n
AlN and GaN, the second order nonline ar susceptibili ty (
2 ( ; , )
l m q ij
) alon g the c-
axis exhibits the largest value. This translates i nto higher conversion efficiencies for
TM modes when compared to TE modes. For thi s reason, this section will focus on
describing the propagation of TM modes . L it erature with a broader and more
detailed description of coupled-mode theo r y for guided wave optics is av ailable. 34 ,42 –
46
Second Order Nonlinear Optical Processes 15
Fig u re 2-2: Schematic of planar waveguide structure used to describe the
propagation of TM ele ctromagnetic modes. Thr ee la y ers with different refrac tive
index
i
n
are displayed.
TE polarization refers to electromagnetic wave s where the only non -zero electric
field components is alon g th e y-axis (see Figure 2-2 ) while TM pol arization re fers
to electromagnetic wav es where the only non -zero magnetic field components is
along the y-axis. He nce, from Maxwell’s wave equation in vacuum, the
electromag n etic field components of the TM waves are reduced to: 34
()
( , , ) ( ) e ,
i t z
yy
H x z t x
H
(2.1.20)
()
0
( , , ) ( ) ,
i t t
xy
r
E x z t x e
H
(2.1.21)
0
( , , ) .
y
z
r
H
i
E x z t x
(2.1.22)
Note that
( , , )
x
E x z t
, the relevant field component for SHG , is directl y proportional
to the magnetic field amplit ude
()
y x H
which varies as a function of x .
()
y x H
is
different for each of the three la y ers des cribed in Figure 2-2 . From continuit y
requirement at the la ye r boundaries, an expression for
()
y x H
can be derived for
each of the layers with four unknowns (
C
,
q
,
p
and
h
). 34
− ℎ
𝑞
𝐶 𝑒 − 𝑞𝑥 , 0 ≤ 𝑥
ℋ 𝑦 = 𝐶 [− ℎ
𝑞
cos ( ℎ𝑥 ) + sin (ℎ𝑥)] , −𝑊 ≤ 𝑥 ≤ 0 (2.1.23)
𝐶 [ ℎ
𝑞
cos ( ℎ𝑊 ) + sin ( ℎ𝑊 )] 𝑒 𝑝(𝑥 +𝑊 ) . 𝑥 ≤ −𝑊
16 Theoretical bac k ground
C
is a norm alization constant and t he parameters
q
,
p
and
h
can be expressed in
terms of the unknown pr opagation constant
. This is done by subst ituting each of
the ex pressions for ℋ 𝑦 (x) in (2.1.23) into (2.1.20) and rea rran ging the wa ve
equation (2.1.24) whic h must be satisfied.
∇ 2 𝐻
= 𝜀 (1)
𝐶 2 𝜕 𝐻
𝜕 𝑡 2 . (2.1.24)
The following relations are determined:
𝑞 = (𝛽 2 − 𝑛 1
2 𝑘 2 ) 1
2
𝑝 = (𝛽 2 − 𝑛 3
2 𝑘 2 ) 1
2 (2.1.25)
ℎ = (𝑛 2
2 𝑘 2 − 𝛽 2 ) 1
2
where
𝑘 ≡ 2𝜋
𝜆 , 𝑝 ≡ 𝑛 2
2
𝑛 3
2 𝑝 𝑎 𝑛𝑑 𝑞 ≡ 𝑛 2
2
𝑛 1
2 𝑞 (2.1.26)
Here
is the vacuum w avelength of the prop agat ing electromagnetic wav e and
i
n
is the refr active index of the respective la y er s. Additionall y, from the requirement
that
y
x
H
at
xt
is continuous, a transcendental equation can b e deriv ed for th e
unknown variable
which must be satisfied. 34
tan ( ℎ 𝑊 ) = ℎ (𝑝
+𝑞
)
ℎ 2 −𝑝
𝑞
. (2.1.27)
Since only the case for total internal reflection is considered, t he value of th e
propagation constant
is limited by the surro unding la yer with the largest
refractive index and the refr active index of the waveguiding la y er , with:
32
, kn kn
(2.1.28)
Equation (2.1.27) can b e solved graphicall y or numericall y, where a discrete number
of solut ions for the value of the propagation co nstant
m
are obtained. From the
solutions
m
a relation describing an e ffective refractive index
m
eff
n
can be derived
with
m
m
eff
n k
. (2.1.29)
In summar y, we r ealize that the bounda r y conditions of the wave guiding la y er, do
not allow for
to take any arbitrar y value which satisfies the condition in (2.1.28).
Only valu es are allowe d which also satisfy the transcendental e qu ation (2.1.27)
Second Order Nonlinear Optical Processes 17
giving rise to the multiple TM modes. Note that the allowed modes are dependent on
the waveguide la y er thickness
W
, the refrac tive ind ex
i
n
of the three layers an d the
vacuum wavelength
of the propagating electromagne tic wave.
2.1.3 Mo dal Dis persion Phase Matc hing
As determined in section 2.1.1, the int ensity of th e second harmonic g ener ated wav e
will not mono tonically i ncrease as a function of the propaga tion length if the wave
vectors of the drivin g a nd induced w aves are mismatched (Figure 2-1 ). I n moda l
dispersion phase matching (MDPM) the dispersion relation of the material in
combination with the different propagation constant values
m
for the different
waveguide modes m is uti lized to match the wa ve vectors of the driving and the
induced second h armonic waves. Using th e expression (2.1.21) which describes the
electric field along the x -direction in waveg uid es, equation (2.1.16) is modified to
0 0
0
0
2
2 2 ,
,
2 2 2
0
e1
( ) ( ) ( ) ,
m
s iL
m
s s m
y eff y
s
i
A L x d A x
n c n i
HH
(2.1.30)
where
s
and
0
m
are the waveguide mod es for the second harmonic a nd the
driving waves respectivel y and
0
2
. I n general
0 ,
, ( ) ( )
m
s
yy
xx
HH
and the
amplitude
() AL
of the second harmonic electric field , will depend on the overlap
integral
0
,
between the dr iv ing and second harmonic waves, with:
0
0
0
2
2 2 2
22 0
,
2 e1
()
m iL
sm
ef f
ss
n i
A L d A
n c i
(2.1.31)
and where
0 , ,
0
, ( ) ( ) .
m s
yy
C x x dx
2
HH
(2.1.32)
C
is a normalization constant referenced to a perfect ove rlap between
()
y x
H
and
0 ()
y x
H
. The ex pression for the intensit y
() IL
of the second harmonic wave can
then be derived with:
0
0 0
4
2 22
2 22
0
2
2 3
0
0
,
2
( ) si nc .
2
2
m
ef f
s sm
d L
I L I L
c n n
(2.1.33)
Again,
is the wave vect or mismatch betwee n the driving an d second harmonic
waves with:
18 Theoretical bac k ground
0
2,
ms
(2.1.34)
where it is possible to find values for
0
2 m
and
s
, such that
0.
More details on
how to determine
0
, , , and W s m
such that
0
2
sm
are d escribed elsewhere. 47 I n
that case, the intensity of the second harmonic wa v e simply follows
2
2
0
( ) . I L L I
(2.1.35)
Note that in thi s section MDPM is onl y considered for equal prop agation modes of
the driving w aves
0
m
A
, where
0
2 ms
. However, it is possible to achieve
phase matching when different propa gation modes m and p of the driving waves
0
m
A
and
0
p
A
are found so that the condit ion
00 0
m p s
is satisfied. More
details on MDPM for mixed modes of the fundamental waves are detailed in a work
by Tr oh a et. al. 47
In summar y, phase m atching is accessible throu gh MDPM and some experimental
results will be presented in section 7. The dr awback of this technique lies i n that the
mode order numbers s and m require d to achieve equal propa gation constan ts for the
driving and second harmonic wave s, in general, lead to small overlap integ rals
which decrea s e the conversion efficiency.
2.1.4 Q uasi-Phase Matchi ng in III -Nitride W aveguide Struct ures
An alternative for achieving phase matchin g be tween the driving and t he second
harmonic waves was pro posed in 1962 b y Armst rong et al. and is now commonl y
addressed as the quasi-phase matching (QPM) t echnique. 48 A detailed theore tical
analysis of QPM is described b y Fejer et al.. 49 I n this approach the sign of the
second order nonli near coefficient
2
is inverted after a propagation distance
c
l
,
called the coherence le ngth, b y inverting th e nonline ar cr ystal (equivalent to
inverting the polarit y of t he III -Nitride film). The coherence l ength
c
l
is the distance
for which th e drivin g wa ves and the second harmonic wave accumulate a phase shift
value of
, with
.
c k
l
(2.1.36)
Second Order Nonlinear Optical Processes 19
For a phase shift larger than
(
2 c k l
), the electric field amplitude
()
s
AL
of
the second harmonic wave decreases as the c ardinal sine function ( Figure 2-3Figure
2-1 ). Inverting the nonli near cr ystal after ever y c oherence length
c
l
and with it, the
sign o f the nonli near susceptibilit y coefficient , effectivel y corrects t he phase
mismatch betwee n the driving and s econd harmonic wav es allowing for the
amplitude of the second harmonic wave to contin ue increasing . M athematicall y , this
translates into a propa gation length (z -direction) dependence of the nonlinear
susceptibility coefficient
( 2 ) () z
. For a square- wave m odulation of the nonlinear
susceptibility co efficient (equivalent to a periodic ally poled III-Nitride cr ystal) from
( 2 )
to
( 2)
with duty c y cle
D
, it follows 49,50
( 2 )
33
2
( ) sin( ) .
m
iK z
m
z d D e
m
(2.1.37)
where
l
D
,
2 ,
m
m
K
is the period of the modulation and
l
(not to be
co nfused with
c
l
) is the le ngth o f the defined posi tive direction o f the cr ystal (i.e
domain len gth of Al-polar se ction in AlN LPS). Equation (2.1.31), which describes
the amplitude
()
s
AL
of the second harmonic wa v e, is thus modified to:
0
0
0
2
2 2 2
2 33
22 0
,
2 2
( ) si n( ) si nc ,
2
r KL
i
sr
ss
n i K L
A L i e d D A L
n c m
(2.1.38)
where
0
2 rs
m
KK
.
m
K
represents an extra pa rameter, dir ectl y re lated to the
periodicity of the late ral polar structur e, whi ch can be modified to achieve
0. K
Note that as in MDPM we are considerin g the allowed propagation TM modes r and
s in the waveg uide, as w ell as the overlap integral between the driving and second
harmonic waves. In contrast to MDPM, in QPM using waveguides, it is p ossible to
find
0
r
and
s
so that th e overlap inte gral
0
,
is unit y. If the parameters are
chosen so that
0 K
, equation (2.1.38) is reduced to
0
0
0
2
2 2 2
33
22
2 2
( ) si n( ) .
r
sr
ss
n i
A L d D A L
n c m
(2.1.39)
The intensity
() IL
of the TM polarized second harmonic wave then follows
𝐼 𝜔 ( 𝐿 ) ~ ( 2
𝑚𝜋 𝑠𝑖𝑛 ( 𝜋𝐷 ) ) 2 𝑑 33
2 |𝐼 𝜔 0 | 2 𝐿 2 . (2.1.40)
20 Theoretical bac k ground
From equation (2.1.40) it can be se en that the conversion efficienc y in QPM is
decreased b y the factor
2
2 sin( ) D
m
when compared with pe rfect phase matchin g.
It is e as y to see that the l argest conversion efficiency is achieved for m =1 (first order
QPM) and when the dut y c y cle is
0.5 D
. Note that m here is not the waveguide
mode number. For this case
() IL
is reduced to:
𝐼 𝜔 ( 𝐿 ) ~ ( 2
𝜋 ) 2 𝑑 33
2 |𝐼 𝜔 0 | 2 𝐿 2 . (2.1.41)
This corresponds to appr oximatel y 40 % conversion efficienc y compared t o an ideal
case (see Figure 2-4 ). Alternatively, high er or der QPM ( m > 1) is also possible,
allowing fo r flexibilit y when choosing th e periodi city of the nonline ar c r y stal lateral
polar structure ( III-Nitride L PS). Surprisingl y als o for even number ed QPM orders,
SHG can b e achieved if the dut y c y cle
0.5 D
and is most efficient for
0 . 2 5 o r 0 . 7 5 , DD
as can be deduced fr om equation (2.1.40).
In summar y , the theor y describing the QPM approach to achieve second harmonic
ge n eration is pres ented, where the phase mi smatch between the d riving and the
second harmonic waves is periodic all y correc ted through inverting the nonlinear
crystal ever y coherence length distance. Detail s on the fabrication of periodic
structures necessary for t his ap proach are presented and discussed in section 4 and 5 .
Furthermore, results showing QPM second harm onic generation of UV l aser light
are presented and discussed in section 7.2.
Second Order Nonlinear Optical Processes 21
Fig u re 2-3: El ectric field amplitude of the second harmonic wav e as a function of
propagation length for th ree different phase matching scenarios.
Fig u re 2-4: Intensity of the second harmonic wave as a function of propaga tion
length for three different phase matching scena rios .
-2
0
2
4
6
8
10
( ) si n c 2
s kL
A L L
() 0 .6 3
s
A L L
()
s
A L L
3 kL
Propagation length L (arb. un its)
Electric fie ld amplitud
of SH wa ve A s
(L) (arb.units)
kL
0
10
20
30
22
( ) si n c 2
kL
I L L
2
() 0 . 4 I L L
2
() I L L
3 kL
Propagation length L (arb. un its)
I ( L ) (arb.units)
kL
22 Theoretical bac k ground
2.2 Surf ace Kinetics in III -Nitride G rowt h
An ex tensive stud y relating the vapor supersaturation to the grow th mode and
morphology of cr y stal su rfaces w as published in 1950 b y Burton, Cabrera a nd Frank
(BCF). 51 The B CF model has been used extensively to describe the growth of
semiconductor mate rials. 52 – 55 This section will brie fl y describe the concepts relevant
to this work and relies heavily on the work published by Mita et al. and Bryan et al.
29,54,55
Chemical vapor epitaxial proc esses are non -equi librium processes with a driving
force tow ards the rmodynamic equilibrium of the system. The drivin g force for
growth is determined by the cha n ge in the Gibbs free energy
G
where
l n( 1 ) . G R T
(2.2.1)
Here, R is the ideal gas constant, T is the temperature and
is the vapor
supersatura tion. For t y pical growth conditions of III-Nitrides in m etal organic
chemical vapo r deposition (MOCVD), the deposition reaction is governed by th e
supersatura tion of th e III metal species. The vapor supersaturation is defined by
0
,
III I II
III
PP
P
(2.2.2)
where
0
III
P
is the input partial pressure of the III metal species and
III
P
is the
equilibrium vapor pressure of the III spe cies ove r the III-Nitride cr y stal at growth
conditions. To obtain the vapor supersaturation value
, it is necessary to ca lculate
0
III
P
and
III
P
. I n MOCVD, met al-organics a re used as precursors for the III metal
species (i.e. trieth ylgallium (TEG) for Ga and tr i meth y laluminum (TMA) for Al).
The metal-organics a re kept at constant temperature in an enclosure (t ypica ll y
referre d to as th e bubbler). A carrier gas is flowed through the bubbler to “ carry” the
metal-organic mole cules into the growth chamber. The emplo ye d m etal-organics
have a low p y r ol ysis te mperature ( <400 °C) an d t ypical growth temperatures are
above 1000 °C, thus the assumption of Al vapor i n the growth r eaction is justified.
The input partial pressure of the III species,
0
III
P
, can be calcula ted from the vapor
pressure o f the III m etal precursor
II I pr ec urs or
p
in the bubbler, the carrier gas flow
Carrie r
f
, the total reactor gas flow
To tal
f
and the total chamber pressure
To tal
P
. With
10 ,
Pre curso r
Q
D T
II I prec ursor
p
(2.2.3)
Surface Kinetics in III-Nitride Growth 23
where D and Q are the experimentall y d etermined constants of the v apor pressure
equation (see Table 2-2 ) and
Pr ec ur so r
T
is the temperature of the III sp ecies precurs or
in the bubbler.
Table 2- 2: Experimentally determined v apor pressure equation constants for the
metalorganic prec u rsors trimethylaluminum (TMA) and triethylga llium (T EG).
Vapor pressure equation constants
D
Q
TMA
8.224
2134.83
TEG
8.083
2162
The III sp ecies flow
III
f
into the growth c hamber is calculated from
,
ca rr ier III p re cu rso r
III
pr ec urs or
fp
f P
(2.2.4)
where
pre curso r
P
is the pressure inside the precursor en closure. Aft er obt aining
III
f
,
0
III
P
can be calcula t ed from
0 ,
Total III
III
Total
Pf
P f
(2.2.5)
where
Total
P
is the total chamber pressure and is set by the experimental conditions.
The equilibrium vapor pressure
III
P
can be obtained b y considering the following
chemical reaction at or near the growth surface:
32
3
( ) ( ) I I I - ( ) ( )
2
I II g N H g N s H g
(2.2.6)
The corresponding equilibrium equa tion is
2
3
3 / 2
10
B
A
III N H C T
III N
III NH
aP
KT
PP
( 2.2.7)
where
III N
K
is the equilib rium constant,
2
H
P
and
3
NH
P
are th e equilibrium vapo r
pressures of H 2 and NH 3 respectively and
III N
a
is the activity of the III-Nitr ide.
Koukitu et al. calculated the equilibrium constants for AlN, GaN and InN where the
coeff i cients A, B and C for equation (2.2.7) are given in Table 2-3 . 56
24 Theoretical bac k ground
Table 2-3: III -Nitrides coefficients for the equilibrium constant equation in (2.2.7).
Equilibrium constant coefficients
A
B
C
AlN
14.2
3.17 x 10 4
2.33
GaN
12.2
1.78 x 10 4
1.79
InN
13.1
1.13 x 10 4
2.29
The relevant gasses for the reaction are H 2 , NH 3 , and III( g ), therefore, the total
pressure is composed by their respective equilibrium partial pressures with:
32
Total III NH H
P P P P
(2.2.8)
The molar conserva tion c onstraints dictate that
33
00
I II I II NH N H
P P P P
(2.2.9)
where
3
0
NH
P
is the input partial pressure of NH 3 . Ex pre ssions for
3
NH
P
and
2
3/ 2
H
P
can
be obtained fr om (2.2.9) and (2.2.7) respectivel y with
33
00
N H II I II I NH
P P P P
(2.2.10)
33
2
22
00
33
()
II I N III NH II I N III I II II I NH
H
II I N II I N
K P P K P P P P
P aa
( 2.2.11)
with
1
III N
a
, subst ituting (2.2.11) and (2.2.10 ) into (2.2.8) leads to a 4 th orde r
polynomial equation for the e quilibrium vapor pressure o f the II I met al species
with: 54
23
4 3 2 2
2 2 2 2
8
2 12 6 0 ,
II I II I II I III
II I N II I N II I N I II N
B B B
P A P A P P
K K K K
(2.2.12)
where
3
00
a nd B .
N H II I T ot al
A P P P A
(2.2.13)
III
P
is the onl y unknown in equation (2.2.12 ) whi ch can be solved numerically.
Once the values for
III
P
and
0
III
P
are known the vapor supersa turation
can be
calculated.
The vapor supersaturation can then be used to describe a vari ety of growth modes
including diff erent types of step bunc hing, bilay er step flow, spira l growth, 2D
Surface Kinetics in III-Nitride Growth 25
nucleation and a mixed growth mode of the 2D nucleation and step flow growth. 55
In this work w e are inte rested in the transition from 2D nucleat ion growth to step
flow growth and its re lation to the vapor supersaturation since the latter growth
mode leads to a reduce d nitrogen polar surface roughne ss (see section 5.1.2).
The BCF theor y st ates that for a “perfec t ” c ryst al surface, free of steps and
dislocations, growth will onl y proceed when the vapor supersaturation exceeds a
critical value
*
for which the formation of 2D nucl ei is favored. Fo r 2D nu clei to
form, the cha n ge in Gibbs free energy
2 D
G
must be favored with
2
2 2
Ds
r
G rh A
(2.2.14)
where
r
,
h
,
s
,
A
and
are the nucleus radius, nucleus heig ht, surface free
energy of the step, proj ec ted area of an adatom and chan ge in chemical potential,
respec tivel y.
2 ()
D
Gr
increases with
r
reachin g a m aximum at a critical r adius
* r
where the for mation of nuclei bec omes stable. F or larger values of r ,
2 ()
D
Gr
decreases and th e form ation of 2D nuclei becomes more favorable. The critical
radius
* r
is related to the critical surface supers aturation
*
s
(not to be confused
with the vapor supersaturation
) by
*
*,
l n( 1 )
s
Bs
hA
r kT
(2.2.15)
from which a n expression for the c ritical free energy for 2D nu cleation can be
derived. 29
22
2 *
* ln( 1 )
s
D
Bs
Ah
G kT
(2.2.16)
For the growth mode and the corresponding surface morpholog y , thi s translates into
mixed step flow and 2D nucleation growth fo r surface supersaturation values above
this critical value and solel y step flow growth for values lower than
*
s
. An
expression for
*
s
can be derived
2 *
2
22
*
65 l n( ) ,
BD
s
s k T R
hA
e
(2.2.17)
where
*
2 D
R
is the critical nucleation rate and is related to
2 *
D
G
by 55
2 *
65
*
2 .
D
B
G
kT
D
R e
(2.2.18)
26 Theoretical bac k ground
In general, the surf ace s upersaturation varies as a function o f its position in relation
to the step ed ges. The max imum value of the surfa ce supersaturation is relat ed to the
vapor supersaturation through
, max
0
1
1,
cosh 2
s
s
(2.2.19)
where
s
is the surface diffusion length of the ad-atoms and
0
is the terrace w idth.
This ex pression shows the relation between the input growth parameters (containe d
in
) and the surface sup ersaturation. The grow th parameters can then be modified
to decrease the surface supersaturation and prom ote step flow g rowth. Th is leads to
a significant reduction of the nitrogen polar surface roughness as it will be shown
and discussed in section 5.1.2.
The relation presented in equation (2.2.19) is repr esentative of the m aximum value
that the surface supe rsa turation can take, however it does not account for pre-
reaction or other possible loss es. Alternativel y , the effective value of
, max s
can be
described by the growth rate
R
with 55
0 0 0
, m ax
0
ta nh ,
24
s
s
ss
S
Rn
hn
(2.2.20)
where
s
is the mean residence ti me of the adatom at the surfac e,
0
n
is the adatom
site densit y and
h
is the monolay er step heig ht. The expression in (2.2.20) is used to
highlig ht the f act that pr e-reaction losses, whi ch lead to a redu ced growth rate
R
,
also imply a decrease on the surface supersaturation. In section 5.1.2 results showing
pressure and temperature dependen t pre-reactio n losses in AlN growth will be
presented, indicative of a lower surface supersaturation value than the calculated
vapor supersaturation.
In summ ar y, a m ethod f or calculating th e Al vapor supersaturation with a given s et
of grow th conditions is described. Th e v apor supersatura tion is related to the
maximum value of the surface supersaturati on. Finally, a critical surface
supersatura tion value describing the transition from step flow growth to mi xed 2D
nucleation and step flow g rowth is presented. This theoretical background motivated
the work pr esented in section 5.1.2 and 5.2.2 to achieve smoo ther surfaces of th e
Point Defects 27
epitaxial nitroge n polar thi n films as well as the GaN and AlN latera l pola r
structures.
2.3 Poin t Defects
Ideally, the III -Nitride cr y stals contain onl y III-metal and nit rogen at oms (also
referre d as native atoms) in a 1:1 ratio forming a wurtzit e cry stal structure. In rea lit y ,
the cr y stals contain atoms of other elements which can incorporate in various
manners. Substit utional point defects incorporate by replacin g either the I II -metal or
the nit rogen atom. Ato ms which incorporate in -between oc cupied l attice sites are
called interstitial point defects. Multipl e impurity atoms c an incorpora te in the
crystal formin g a complex with or without native atoms and are t y picall y a ddressed
as point defect complexes . No te that point de fects are not necessaril y compos ed of
foreign elements but can also refer to native atom interstitials, unoccupied lattice
sites (also known as v acancies) and native ato ms occupying anti -sites, which are
typica ll y addressed as nati ve point defects. The materials optoelectronic properties,
such as transparenc y, photoluminescence spectra , mobilit y and carrier concentration,
are d ependent on the concentration and t ype of point defec ts. In this chapter, a brief
overview of the theoretical model uti lized to estimate the point defec t types and
concentration in AlN and their respec tive thermod yna mic transition energ y is
presented. Nex t, the theoretical background fo r relating theoreticall y obtained
thermody n amic transition ene rgies with absorption, photoluminescence and
photoluminescence-excitation spectra under th e F ranck -Condon approximation is
described. Using these t ools, the developed theoretical model ca n then be tested
experimentally by means of optica l characterization.
2.3.1 E nerg y of Formation for Point Def ects
All densit y functional theor y (DFT) c alculations were performed b y Dr. Irving’s
research group in the Materials S cience and Engineering department at North
Carolina State University. In particular, I wo uld like to thank J . Harr is and
Dr. Gaddy, who develop ed the code and carried o ut the calculations. For a thorough
description of the theory and methods, refer to Dr. Gaddy ’s , doctoral dissertation. 57
The energ y of formation for point defects is useful for identifying the point defect
types present in wide bandgap semiconductors. Th is energy is directl y related to the
28 Theoretical bac k ground
likelihood that the point defec t will incorporate in the crystal during growth .
Furthermore, the thermod yna mic transition energies of a point defect can be directl y
extracted from the energy of formation for the dif ferent charged states and compared
with photoluminescence and absorption spec tr a. 58,59
The form ation ener gy
q
X
E
for a p articular point defect
X
in a charge state
q
is
calculated by
( ) ( ) ,
q
DF T q DF T
De fec tiv e Bu lk i i F V q
X i
E E X E n q E E V
(2.3.1)
where
DF T
Bu lk
E
and
()
D F T q
D e fe c tiv e
EX
are the total ground state ener g y o f an ideal cr ystal and
that of a crystal containing a sin gle point defect
q
X
respectivel y. The foll owing
term,
ii
i
n
, describe s the chang e in ene rg y due to the intera ction betwee n the
involved species
i
n
and t heir resp ective chemical potential
.
i
The last term,
()
F V q
q E E V
, describes th e interaction between the charge state
q
of the point
defect
X
and the Fermi level energy
F
E
with respect to the valence band en ergy
V
E
and a potential correction term
q
V
. To mention some details, the He yd, Scuseria
and Ernzerhof (HSE) se mi -local hybrid method is implemented for calculating the
exchange and correlation potential, where a 0.32 fra ction of the Hatree-Fock exact-
exchange was chosen to match the 6.09 eV band gap energy of AlN . 60 The Kohn and
Sham a pproach is then used to obtain a solution for the Hohenberg and Kohn
functional. 61 Using this functional th e g round state energy ca n be calculated as
described b y Hohenberg and Kohn. 62 For all calculations a 96 -atom supercell was
chosen and a pl ane wave b asis set, as implemented in the Vi enna ab initio
simulation package (VASP) was used.
The calculated formatio n energ y o f a point de fect determines the probabil ity o f it
being incorporated into t he cr ystal du ring growth. The point def ect concentration in
the crystal,
q
X
C
, is related to the for mation ener gy by
q
X
B
q
E
kT
s
X
C uN e
(2.3.2)
where
i
N
and
u
are the number of sites and possible configurations respectivel y ,
normalized to counts per unit volume ( cm -3 ). 57 From this relation it is clear that the
lower the formation e nerg y of a point defect, the hi gher its con centration.
Additionally, the formati on energ y of a point de fect varies as a function of the Fermi
Point Defects 29
energy
F
E
(see equation (2.3.1)). It is useful to plot this relation for a point defect
with different charged states q (see ex ample in Figure 2-5 ). The differe nt slopes
repre s ent the dif ferent charged states of the p oint defec t. Comm only, onl y the
charged state with the lowest formation ener gy is displayed for a given Fermi energy
(see Figure 2-6 ).
Fig u re 2-5: Illustra tion of a formation ene rg y diagram of a point defec t
X
for
various cha r ged states q (+2, +1, 0, -1) as a function of Fermi energy r eferenced to
the valence band maximum (the bandgap energy of AlN was c hos en as an example).
30 Theoretical bac k ground
Fig u re 2-6 : Illustration of a formation energ y diagram of a point defect, with its
thermody n amic transition energies highlighted.
The kinks where the c hanges in slope are observed in Figure 2-6 mark the
thermody n amic transitions be tween two cha rge d states of a point defect. The se
thermody n amic transiti o n energies are related to optical spectra and are useful for
identifying the point de fect t y pes present in the c r ystal (section 6 ). I n the next
section (2.3.2) a more de tailed description on how the the rmodynamic transitions are
related to optical spectra is given. I t is important to highlight that DFT calculations
using the HSE h ybrid functional, have been establ ished to estimate thermodynamic
transition levels of im purities within the bandgap of the host semiconductor material
more accuratel y than methods using the local densit y approximation (LDA) method
or the general gradient approxim ation (GGA) 63,64 . The latter significantly
underestimate the bandgap energy as well as the electron/hole loc alization.
Nevertheless, even when using th e HSE h y brid functional, finite siz e correction
schemes for charged def ects lead to inaccurac i es in the calculations. T y pi cal claims
for the accurac y of DF T calculations using the HSE hy brid functional are in the
order of 0.1 eV, 63 however the accurac y varies for different char ged states of the
impurities and a higher error is predicted for native point defec ts such as native
vacancies. 57, 64
Point Defects 31
2.3.2 Franc k -Co ndon Approxim ati on
In th e presence o f point defects, energy stat es wi thin the bandgap of the III - Ni tride
semiconductor ma y exist and thei r energ y l evel is determined b y the therm odynamic
energy required for a point defect to transition from one charged state to another
( Figure 2-6 ). Th ese defe ct energy states can participate in optoelectronic transitions
leading to below ban dga p ener g y absorptio n and luminescen ce b ands. The
transitions include conduction band to defec t state (or vice versa), valen ce band to
defect state (or vice versa) and defect state to defect state (commonl y referred to as
donor acceptor pair transit ions). At equilibrium, the charged state of point defects is
determined by the Fermi leve l. The equilibrium coordina te of a point de fect is
dependent on its charged state, thus the equilibrium coordinate for the ground state
may defer from that of the excited state, leading to ene rg y shifts between the
observed a bso rption maxima and the photoluminescence maxima (see Figure 2-7 ).
Fig u re 2-7: Configuration coordinate dia gra m illu strating the shift in energy between
the peak absorption and emission bands, due to electron-phonon coupling. An
optoelectronic transition involving a point defec t
X
in the -1 charg ed state leadin g
to a free electron in the conduction band and a neutral charged state is shown and the
respec tive recombination process.
In the F ranck-Condon approximation it is assumed that the optoelectronic transition
occurs in a short time s cale, wh en compa red to the nuclear motion of the point
defect, so that the transition probability c an be calculated at a fixed nuclear
coordinate. 65 Assumi ng the initial state is at equilibrium, f rom conservation of
32 Theoretical bac k ground
momentum, the probabilit y of an optoele ctronic transition will be proportional to the
overlap between the 0 th quantum number vibrational wave function in the initial
state with the n th (n = 0, 1, 2, 3 …) quantum number vibrational wave fun ction in the
final state of the point defect. More generall y, Fermi ’s golden r ule s tates, the
transition proba bilit y
Tran
P
is proportional to the square of the transition dipole
moment which under the Franck-Condon app rox imation can be separated into the
electron ic transition dipole moment
e
and a nuclear term
FC
, with 66
𝑃 𝑇𝑟𝑎𝑛 ~ | 𝜇 𝑒 | 2 𝜇 𝐹𝐶 . (2.3.3)
In this section we are interested on the ef fects the nuclear term has on the shape of
the absorption and photoluminescence spectra. For thi s reason, the electronic
transition is assumed to be allowe d , and
e
is normalized and assumed to be
independent of the coordina te position. The transition pro bability
Tran
P
, which
determines the shape of t he spectra, from the 0 th vibrational state of the ground state
in to the n th vibrational state of the ex cited state ca n be described b y the f ollowing
equation: 59
𝑃 𝑇𝑟𝑎𝑛 ( ℏ𝜔 , 𝑇 ) = ∑ 𝑤 ( 𝑇 ) |⟨𝜒 𝑛𝑒 | 𝜒 0g ⟩| 2
𝑛 𝛿 (𝐸 𝑇ℎ𝑒𝑟𝑚 𝑜𝑑𝑦𝑛𝑎𝑚𝑖𝑐 + 𝑛ℏ𝜔 𝑣 − ℏ𝜔 𝑝ℎ𝑜𝑡𝑜𝑛 ) . ( 2.3.4)
here
() wT
is the thermal o ccupation factor of the vibrati onal energy stat e,
v
is the
vibrational frequenc y,
photon
the photon frequency ,
Ther mod y nam ic
E
is the
thermody n amic transitio n energy and
0 ne g
are th e Franck-Condon overlap
integrals of the vibration al wave functions. Assu ming the potential for both charged
states in their respective equilibrium coordinate are identical, then one can assume
the nuclear vibr ational en ergy quanta of th e initial and final state to be equal (ℏ 𝜔 𝑖 =
ℏ𝜔 𝑓 = ℏ𝜔 𝑣 ). I t follows for low tempe ratures: 59,67
2
0 ,
!
ne g
n
S
eS
n
(2.3.5)
where
S
is the electron phonon coupling strength (also known as the Huang-Rh y s
factor). The e l ectron-phonon coupling strength is given b y
𝑆 = | 𝐸 𝑃𝑒𝑎𝑘 − 𝐸 𝑇ℎ 𝑒𝑟𝑚𝑜𝑑𝑦𝑛𝑎𝑚𝑖𝑐 |
ℏ𝜔 𝑣 = 𝐸 𝐹𝐶
ℏ𝜔 𝑣 . (2.3.6)
Point Defects 33
Here
Pe a k
E
is the peak absorption/emission energ y . Thi s difference in energ y
FC
E
is
typica ll y addressed as the Franck -Condon ener gy shift. The energy
Pe a k
E
ca n be
measured b y absorptio n, photoluminescence and photo lum inescence excitation
spectroscopy techniques and
mod Ther y namic
E
is obtained from the energy of formation
diagrams (see section 2.3.1). From this the absorption and PL spectra can b e fitted in
order to obtain a value for
S
and hence the vibrational energy qu anta
v
.
Alternatively, at th ermal e nergies
B
kT
much higher than the vib rational energy
quanta
v
, t he full with at h alf max imum
()
PL
WT
of the photol uminescence band is
a function of temperature with 59
𝑊 𝑃𝐿 ( 𝑇 ) = 𝑊 0 coth ( ℏ𝜔
𝑘 𝐵 𝑇 ) . (2.3.7)
He re
0
W
is the full with at half max imum for T = 0 and
B
k
is the Boltzmann
constant. An expression for
0
W
can be derived with
𝑊 0 = ℏ𝜔 √ 8 𝑙𝑛 (2𝑆 ) (2.3.8)
From temperature dep endent measurements one can obtain the vibr ational energ y
quanta
v
and the Huang-Rhys parameter
S
. 59
In summ ar y, this chapter describes the DFT theoretical model utili zed for
calculating the energ y o f formation of point defects as a function of Fermi level.
From these diagrams, the thermod y namic transition energies of point de fects can be
extracted. The thermod ynamic transition energies can then be t ested experimentall y ,
where the sh ape of the measured P L and absorption bands are d escribed under th e
Franck-Condon approximation. A method for obtaining the electron -phonon
coupling stre n gth and the vibrational frequencies of the point defect is described.
34 Experimental Setup
3 Experimental Setup
3.1 Optical Spect rosco py
3.1.1 Phot oluminescence and Pho tolum inescence Exci tation
Spectrosc opy
The photoluminescence (P L ) setup for above b andgap excitation is displ ay ed in
Figure 3-1 . Two laser sources are available in the setup. A 193 nm emission
wavelength argon fluoride excimer las er s y stem with 5 ns pulse width , where the
repetition can b e tuned f rom 10 Hz to 500 Hz and the energy per pulse from 0. 05 mJ
to 6 mJ . Alternatively a 325 nm emission wavelength helium -ca dmium c ontinuous
wave (cw) laser sy stem i s available with a maximum output power of 50 mW.
Fig u re 3-1: Experimental setup for photoluminescence spectroscopy measurements.
Two different methods f or detecting the sample’s photoluminescence si gnal were
used. In one setup, the sample signal w as coup led into a UV- grade opt ical fiber
cable which is then coupled to the detection monochromator. Altern ativel y the
sample was plac ed insid e a cr yostat chamber and the si gnal was collected usin g a
system of lenses. The cry ostat is cooled b y flowing h elium in a closed c ycle s y stem
using an “F - 70L Sumitomo Helium Compressor” , reaching temperatures a s low as 3
K. The temperature of the cr y ostat is controlled by adjusting the pow er of a heating
element, allowing for te mperature dependent P L measurements up to 350 K. The
monochromator in the d etection s y stem is a 0.75 m focal length “Acton series SP -
Optical Spectroscopy 35
2750” gratin g monochromator. The signal is detected b y a “Pixis - XO: 2KB”
charged couple device ( CCD) with a 2048 x 512 imaging arra y of 13.5 µm by 13.5
µm pixels. The CCD is thermoelectrica ll y cooled to -75 °C.
The photol uminescence excitation spectroscopy measurements were con ducted in a
separa t e setup ( Figure 3-2 ). The ex citation li ght source used is a 450 W x enon arc
lamp, where the light was collim ated with an elliptical mirror . The broadband light
is then coupled to a do uble 0.3 m fo cal l ength monochromator, contai ning UV
blazed 3600 groove s m m -1 gra tin gs, to select the excitation wavelength (energy).
Optical filters a re placed in the optical pa th after the monochromator s to block
second order artifacts. The light is then guided and focused onto the sam ple surface
at a 45°- 60° an gle. Sil ver paste is used to adhere the samp le to a cold finger in a
high vacuum enclosure. The sample is cooled to as low as 6 K by flowi ng liquid
helium through the cold finger. The temperature of the cold finger can be adjusted
between 6 K and 273 K by adjustin g the flow rate of the liquid helium .
Fig u re 3-2: Schematic of the photoluminescence excitation spectroscopy setup.
The sample signal is then collimated with a lens and guided to the detection
monochromator. A filter holder is placed before t he entrance sli t of the
monochromator to allow for filters which blo ck the excitation wavelength and
second order artifacts. A 150 grooves mm -1 diffraction grating is used in the
detection monochromator. The diffracted li ght is then detected b y a liquid ni trogen
cooled CCD detector.
36 Experimental Setup
3.1.2 Seco nd Harm onic Generatio n Spectroscop y
To test the AlN LPS-based waveguides as well as the single polar AlN and GaN
waveguides fo r QPM SHG and MDPM S HG respec tivel y, a tunable wavelength
(600 nm - 1100 nm) 40 femtosecond pulse l en gth laser s ystem was use d with a 1
KHz repetition rate and 30 nm spectral width (FWHM). The energy pe r pulse varied
with the wavelength and ranged from 1 µJ to 100 µJ . A 10 mm focal length lens was
used to focus the laser beam onto the front face of the waveguide, where the beam
diameter at th e waveguide couplin g facet was 10 µm. The polarization was chosen
so that TM modes were coupled into the w aveguide. The SH signal together with t he
remaining fundamental signal was collected from the output waveguide f acet with a
lens. The fundamental signal was filtered allowing to guide the SH si gnal to the
detection s ystem, consisting of a monochromat or and a photon counti ng camera
sync h ronized with the femtosecond laser s y stem . A schematic of the experimental
setup is displaye d in Figure 3-3 .
Fig u re 3-3: Schematic of ex perimental setup used for testing the AlN and GaN
based waveguides for second harmonic ge n eration.
3.1.3 T rans m ission Spectr osco py
Tempera tu re dependent transmission spectroscopy measurements were c onducted
up to 870 °C. The setup employe d for th e temperature dependent me asurements was
built in-house and is displayed in Figure 3-4.
Optical Spectroscopy 37
Fig u re 3-4: Experimental setup for temperature de pendent transmission spectra up to
900 °C.
A turbo-molecular pump is attached to the chamber to keep the pressure below 10 -4
mbar. The temper ature is increa sed usin g a co iled tungsten wire as a resistive
heating element. The current and volt age across the wire is manuall y controlled with
an external power supply where powers up to 200 W are applied. To achieve
temperatures as high as 900 °C, five concentric heat-shields, with circular openings
to allow for the t ransmission of light, were ma chined to r educe the radiative heat
transfer out of the sample enclosure. Not onl y higher temperatures can be achieved
by the introduction of heat -shields, but also a mo re homogenous tempe rature within
the sample enclosure is maintained. The stainless steel vacuum chamber w all is
water cool ed to kee p the ambient temperature constant and to avoid an y dama ge to
vulnerable components due to ove rheating. The sample temperature is measured
using a thermocoupl e w hich is placed in contact with the sample holder inside the
concentric heat-shields. A 150 Watt UV-enhanced xenon arc lamp is used as a broad
spectrum li ght source with an emission spectra r anging from 225 nm to above 800
nm. UV -grade fused sil ica viewports were attached fo r the transmission
measurements. Th e trans mitted light is focused onto the opti cal fiber and coupled to
the detection system described above. A spectra at 800 °C was taken with no
excitation light source to measure the b ackground int ensity due to heat radiation and
determined to be neglig i ble in the spectral range of interest.
38 Experimental Setup
3.1.4 Micr o-photolum inescence Spec troscopy Setup
In this setup an a rgon ion laser s ystem is used as the ex citation li ght source.
Nonlinear cry st als for frequenc y doubling a re available, allowing for discrete
excitation waveleng ths i n the range between 227 nm and 264 nm according to the
laser li nes of the argon ion laser. The laser li ght is guided and focused onto the
sample surface using a UV-compatible micro-objective lens with 1 µm resolution ,
which is positioned nor mal to the sample su rface . The sample is pla ced on a piezo
translation stage allowing for selective nano-posi tioning of the sample. The sample
signal is collected using the same objectiv e lens as the excitation lens, ho wever it is
separa t ed b y placing a beam spli tter in the optical path. An additional beam splitter
can be pla ced allowing for the sample surface to be displ ay ed by a camera on a
scree n. The sample signa l is then guided to a triple monochromator s ystem where it
is spectrall y sep arated and detected b y a liquid nitrogen cooled CCD detector
( Figure 3-5 ).
Fig u re 3-5: Micrometer spatiall y resolved photolumi nesce nce ex citation
spectroscopy se tup.
Growth Setup 39
3.2 Growth Setup
The epitaxial AlN, GaN and AlGaN la y ers investigated in this work are grown via
metal or ga nic ch emical vapor deposition (M OCVD) in a low pressur e (20 – 100
Torr) v ertical showerhead reactor with a water cooled quartz tube (see Figure 3-6 ).
Inductively coupled grap hite susceptors a re used to heat the up to 2-inch subst rates
which are placed at their top surface. Two diff erent material coatin gs of the graphite
susceptors are av ailable, silicon carbide and tantalum carbide , where the latter is
used when temperatures above 1250 °C are required and with which t emperatures up
to 1550 °C can be achieved. For th e III- metal aluminum an d gallium,
trimethylaluminum (TMA) and trieth ylgallium (TEG) metalorganic li quid sources
are us ed as precursors. Ammonia gas is used as the nitrogen precursor. H ydrog en
and nitrogen gas sources are available to serve as the carrier gas and/or as a diluent
ga s es. The reactor b ackground pr essure is in the high 10 -7 Torr range. Epi-read y
LED quality 0.4 mm thi ck c-pl ane s apphire sin gle cr y stals with 0.2 ° of fcut (unless
specified otherwise) were used a s the sta rting substrate material.
Fig u re 3-6: Picture of the metal organic chemical vapor deposition reactor during
vacuum annealing at 110 0 °C (left). Clockwise st arting at the top left, pict ure of the
cooling s ystems containing the metalor ganic source s (TMA and TE G), liquid
nitroge n tank which provides the N 2 gas sour ce, ammonia gas source and h y drogen
ga s sou rce.
40 Experimental Setup
3.3 Laser Interferen ce Lithograph y
For the l aser inte rference lithograph y, a Lloyd’s mirror con figuration setup was
employe d, developed b y A. Bagal ( Figure 3 -7 ). 68 In this setup, a helium -cadmium
laser is focused onto a pinhole to obtain a wave f ront of parallel plane waves with a
Gaussian intensit y profil e as a function of the radial distance from the optical ax is. If
the sample is then placed at a lar ge e nou gh d i stance (>1 m), a nea rl y uniform
intensity across the samp le is obtained. The sample is paced adjacent to a mi rror at a
90° angle. The angle of incidence can then be rotated to obtain the desir ed
periodicity .
Fig u re 3-7: Llo y d's mirror configuration setup.
La s er Interference Lithography 41
Fig u re 3-8: Laser interference intensit y profile at the sample surface.
The periodic intensit y of the laser at th e sample s urface is a result of the phas e-shift
between th e two incid ent waves with wave vectors 𝑘
1 and 𝑘
2 ( Figure 3 -8 ). Since
both waves originate fro m the same li ght sou rce, the ir wave vecto r comp onents i n
the y and z direction are equal. Onl y the dir ection of the wave vector in the x -
direction is opposite while the magnitude is equa l with
𝑘
1 𝑒 𝑥 = 𝑘 1𝑥 = −𝑘 2𝑥 = −𝑘
2 𝑒 𝑥 . (3.3.1)
The magnitude of the w ave vector in the x -direction
1 x
k
will be a function of the
incidence angle with
|𝑘
1 | sin ( 𝜃 ) = 2𝜋𝑛
𝜆 sin(𝜃 ) (3.3.2)
Where
n
is the refractive index of the medium. The total pha se -shift
accumulated at the sample surface a fter a translati on distance r alon g the x -direction
will be
1 2 1 1 1
( ) ( ( )) 2 .
x x x x x
r k r k k r k k rk
(3.3.3)
The period is g iven by the tr anslation distance at whic h a phase-shift value o f
2
is accumulated. From (3.3.2 ) and (3.3.3) i t follows the relation between the
ang l e of incidence
and the interfere n ce period
, with
11
2 2 2
xx
rk k
(3.3.4)
and
1
2 .
2 2 s in( )
x
kn
(3.3.5)
42 Experimental Setup
With the waveleng th
and refractive index
n
known, it is straight forward to
calculate the angle of incidence
necessary to obtain the calcula ted periodicit y
required for quasi-phase matched frequenc y doubli ng in the UV-sp ectra (section
2.1.4 ).
Historical Perspec tive 43
4 Polarity Control
As discussed in section 1.1, the II I-Nitrides se miconductors are polar materials.
Epitaxial lay ers can exhibit either nit roge n polarity, III-metal polarit y or mix t polar
growth where both pola rities grow side b y side simultaneousl y ( Figure 4-1 ). This
section fo cuses on how the polarit y of III -Nitride epitaxial films can be controlled in
MOCVD systems, when using c-plane sapphire substrates.
Fig u re 4-1: Schematic displa y in g the crystal structure for different pol ar growth
directions and mixed polar growth
4.1 Histo rical Perspect ive
Single cr y st al AlN and GaN epitaxial la yers on sapphire substrates by chemical
vapor deposition, were reported for the first time b y Yim et al. 12 and Maruska et al. 11
respec tivel y . Their optical and electrical properties as well as their cr y st al structure
were characterized, however no studi es on the polarity of the grow n film s were
performed. Yoshida et al. 69 reported on the first epitax ial AlN layers on sapphire b y
reactive mol ecular beam epitaxy (M BE) . In 1983 Yoshida et al. usin g reacti ve MBE
showed that if an AlN la y er is deposited prior to the deposition of a GaN layer, the
surface roughness is si gnificantly reduced and the electrical and opti cal pro perties of
the GaN la y er are signifi cantly improved. The stud y, relate d the result to the reduced
lattice mismatch and ther mal expansion mismatch between GaN and Al N compared
to that of sapphire. 70 Similarly, in a later stud y b y Amano et al. using metal organic
44 Polarity Control
chemical vapor deposition , superior quality GaN layers were achieved by prior
deposition of an AlN la yer under ad equate growth conditions and was also relate d to
the reduced lattice and th ermal expansion mismatch . 71,72 I t is now assumed that the
improved quality of the reported GaN films , was likel y due to uniform Ga-polar
growth as oppos ed to N -polar or mixed-polar growth. In 1988, Sasaki and
Matsuoka, reported on MOCVD GaN epitaxial films using SiC polar substrates,
where both the C-fa ce and the Si-f ace of the ( 0001) plane were used as well as
sapphire substrates. 73 The work sho w ed that p reviousl y observ ed differen ces in the
surface morpholo g y ( atomicall y smooth Vs hex agona l hil locks) an d optical
properties of GaN epitaxial films arise due to polarity dependent growth surface
kinetics and impurities incorporation. The stud y showed n earl y identical
photoluminescence spect ra and surface morpholog y (hexa gonal hillocks) for GaN
films grown dire ctly on sapphire substrates and on the C -face of the SiC substrates.
Meanwhile, the prop erties of the GaN film grown on the Si -fac e of SiC were sim ilar
to the GaN films grown on AlN la yers on s apphire subst rates reported b y Yoshid a et
al, and Amano et al.. The results b y Sasaki and Matsu oka, unco vered the
implications of different polar growth directions, however the polarit y of the films
remained unknown. Nakamura and Mukai, simil arly to Amano et al. and Yoshida et
al., observed an improvement on the optical and struct ur al qualit y of I nGaN
epitaxial lay ers on s app hire when introdu cing a low temperature (500 °C) GaN
buffer la yer prior to the I nGaN depositi on. 74 It wasn’t until 1996 that Daudin et al.,
using ion chann eling di ffraction and conver gent beam ele ctron diffr action (CBED),
determined th at MOCVD GaN la yers ex hibiting a smooth surface were uni forml y
Ga -polar and that films exhibiting hexagonal hilloc ks at the surface were
predominantly N -polar with a high densit y of narrow Ga -polar domains. 75 The study
highlig hts the importance of an optimized low temperature GaN buffer layer in
obtaining uniform G a-polarit y . In p arallel, Hwang et al. studied the effect of
nitridation of the sapphire surface prior to depos iting the GaN film and concluded
that under certain conditions , nitridation of the sapphire sur face leads to films
exhibiting a rou gh surface cove red with hexagonal hillocks , now kno wn to be
typica l for N-polar G aN films . 76 Dimitrov et al. reporte d that a low temp erature AlN
nucleation layer leads t o Ga-polar GaN films (similar to the GaN buff er la yer
reported b y Daudin et al.), while direct growth on sapphire leads to N -p olar GaN
films. 77 Collazo et al. developed a process for controlling the polarity of Ga N
III -Polar AlN and GaN 45
epitaxial layers usin g MOCVD, where N-pol ar films are a chieved by p roper
nitridation of the sapphir e substrate prior to growth of the GaN la yer and Ga -polar
films are achieved b y int roducing a low temp erature AlN nu cleation layer which is
properly annealed. 78 An extensive review summarizing growth techniques, growth
procedures and the resulting pola rity of th e G aN film was reported b y S umi y a and
Fuke. 79 The epitaxial proce sses dev eloped over th e past decades which use an AlN
or GaN nucleation la yer, to control the polarity of the III -Nitride film, have been
empirically established with no detailed d escription available on t he precise
mechanism leading to a particular polarit y. A recent stud y b y Mohn et al. has shone
light on th e subject, where hi gh r esolution transmission electron microscop y
measurements of the AlN low temperature buffer layer, indicate that a rhombohedral
aluminum-ox y nit ride interla y er is responsible for the polarit y inversion from the “N -
polar” AlN of th e nitridated sapphire surface to the Al-polar face AlN. 80
As an alternative to controlling the polarit y of III-Nitride epitaxial films , there are
reports demonstrating po larity inversion from the III -polar face to the N-polar face
through high concentration magnesium doping in both GaN and AlN. 81,82 This
polarity control process scheme has been emplo yed to fabricate submicron GaN and
AlN late ral polar structures with limited success. 82,83 This approa ch has proven
successful in a chieving periodic poling of GaN, while little success has been
demonstrated for p eriodic poling of AlN, t ypically r esulting in no gro wth at the
interfaces between the polar domains , inhibiting th eir us e in nonline ar opti cal
applications. In thi s work we emplo y the previousl y described polarity c ontrol
process scheme, where a n AlN nucleation layer is used (or not) to achieve III-polar
(N -polar) grow th of th e III-Nitride film and is described in d etail in the following
section.
4.2 III -Polar AlN an d GaN
As described in the former subsection ( 4.1) III-Polar III - Nitride epitax ial films can
be achieve on sapphire substrates by d epositing an optimiz ed AlN or GaN
nucleation la y er. In this subsection the process developed b y Collazo et al. where an
AlN nucleation layer is used to ac hieve uniform III -polar films is described.
46 Polarity Control
An L ED qualit y c-plan e sapphire substrate with a 0.2° offcut towards the m -plane is
introduced to the MOCVD s y st em described in section (3.2). The reactor is pumped
down to a pressure in th e order of 10 -6 Torr to high 10 -7 Torr. The subst rate is then
vacuum annealed at 1100 °C for 10 minutes and subsequentl y ba ckfilled with a 1:1
ratio of 1 slm H 2 and 1 slm N 2 to a total chambe r pressure of 20 Torr, where it is
annealed for additionall y 7 minutes. Following, ammonia is introduced to the reactor
at a flow rate of 0.3 slm together with 1 slm of N 2 diluent gas for 4 minut es at 950
°C. Next, the 20-30 nm AlN la y er is deposited b y flowing 5.5 µmol/m in of TMA
in to the reactor fo r 3 mi nutes at 650°C under 3 slm flow of N 2 and 3 sl m flow of
NH 3. Next, the AlN nucleation la y er is annea l ed at 1040 °C for 15 mi nutes under 1.6
slm flow of N 2 and 0.2 slm flow of NH 3 . A t y pical temperature profile of the growth
run for an AlN nucleation lay er is displa y ed in Fi gure 4-2 .
Fig u re 4-2: Growth run temperature profile of an AlN nucleation layer.
In Figure 4-3 the surface morphology of a typical AlN nucleation lay er as measured
by AFM is display ed .
III -Polar AlN and GaN 47
Fig u re 4-3: AFM image of the surface of a typica l AlN nucleation layer.
For single polar films, instead of cooling down and removing the sample from the
reactor (step V II in Fi gure 4-2 ), the growth of the GaN (AlN) film is started . The
subsequent grow th conditions for the III-Nitride la y ers depend strongl y on the
objective at hand. There are however stand ard growth runs for Ga N and AlN layers,
which are us ed to troubleshoot the MOCVD s ystem. I n a “ standard ” growth run for
a 1.2 µ m thick GaN la yer, following the annealing o f the AlN nucleation at 1040 °C
(step V I in Figure 4-2 ), TEG is flown into the reactor at a flow r ate of 36 µmol/min
for 33 minutes in a mixture of 0.3 slm of NH 3 and 6.9 slm of N 2 at 20 Torr total
chamber pr essure. The growth is then finished by stoppin g the TEG flow and the
reactor is cooled down under NH 3 atmosphere. For a “ standard ” 300 nm AlN la y er,
following the annealing of the AlN nucleation lay er , the tempe rature is increased to
1150 °C where growth i s started b y flowing 7.1 µmol/min of TMA for 6 minutes
under 10 slm of H 2 and 0.3 slm of NH 3 . Under continued growth and otherwise
constant conditions, the temperature is increase d to 1200 °C and left there for 24
minutes followed b y an a dditional temperature increase to 1250 °C fo r 15 minutes of
additional growth. The growth is then terminated b y stopping the TMA flow and the
reactor is cool ed unde r NH 3 atmosphere. The su rface morpholo g y of a “ st andard ”
III -polar GaN and AlN film is displa y ed in Figure 4-4 .
48 Polarity Control
Fig u re 4-4: AFM measurements of the surface mo rpholog y of a Ga -polar GaN (left)
and Al-polar AlN (right) epitaxial la y er.
Typical III -polar GaN fil ms g rown as described a bove, exhibit step flow growth, are
highly resistive (>MOhm) and are inert to KOH wet-etching . T ypica ll y p oint defect
concentrations (mainl y carbon) in the high 10 17 cm -3 to low 10 18 cm -3 is measured
for these films. Standard III-polar AlN films also exhibit step flow growth, are inert
to KOH etching and have point defec t con centrations in the low 10 18 cm -3 .
4.3 N-Polar AlN and GaN
To obtain Nitro gen pol ar III -Nitride films , the first three steps are identic al to those
used for the deposition of an AlN nucleation la y er ( s ection 4.2). The sapphire
substrate is vacuum an nealed at 1040°C, followed b y annealing in H 2 and is
subsequently annealed in NH 3 at 950 °C as described in the previous section (section
4.2). Following th e ann ealing st ep in NH 3 , the substrate tempe rature is increased to
the desired growth temperature at which the III-Nitride la y er is to be deposited.
Typical starting growth temperatures for GaN a nd AlN are 1040 °C an d 1100 °C
respec tivel y. AFM m easurements of th e surface o f N -polar GaN and AlN are shown
in Figure 4-5 .
N-Polar AlN and GaN 49
Fig u re 4-5: AFM measurements of the surface morpholog y of N -polar GaN (left)
and AlN (right) respectively with hi gh (top) and low (bottom) mag nificatio n.
In contrast to III -polar GaN, N-polar GaN exhibits 2D nucleation growth leading to
a rough sur face morph ology with a high densit y o f hexagonal hillocks with
diameters r eaching tens of mi crometers. The unintentionally inco rporated o x yge n
impurities, reach concentrations in the order of 6 x 10 19 cm -3 and account for the
majority of the point defects, leading to conduc tive n -ty pe GaN l a yers. 84 The N-
polar AlN fa ce, is react ive to KOH wet-etchin g and more d etails on th e polarit y
dependent etching will be described in the next sub -section (4.4). The surface of the
N-polar AlN epitax ial la y er also ex hibits a rough surface with a high de nsit y of
columnar-like hexagonal hillocks in contrast to Al -polar AlN. The diam eter of the
columnar hexagonal hillocks is t y pi call y in the hundreds of nanometers, where an
aspect ratio in the range 0.3 to 0.6 is measured, significantl y hi gher than the rang e
measured fo r GaN of 0. 03 to 0.1 . The concentration of ox y gen im purities in the
epitaxial N-polar AlN layers is in the high 10 19 cm -3 to l ow 10 20 cm -3 range, how ever
in contrast to GaN the fil ms are hi ghly resistive . The ox yge n im purit y as a nitrogen
substitutional point defect in AlN is expected to have a stable DX - state at 550 meV
below the conduction band, explaining the highly resistive natur e of the N -polar
AlN lay ers, ev ent at such high oxygen concentrations. 57
50 Polarity Control
4.4 Polarity Dep endent Wet Etch ing in KOH
The pola rity of epitax ial GaN and AlN films grown via MOCVD under t he pro cess
conditions described above, has been extensivel y studied using convergent beam
electron diffraction (C BED), conventional tr ansmission electron microscop y
(CTEM) and scanning transmission electron microscopy (STEM). 85 , 86 These
character iz ation techniques require complex sample preparation procedures making
it impractica l for chara cterizing a lar ge number o f samples. Alternative techniques
have been developed to determine the polarit y of the films includin g reflection high
energy electron diffraction (RHEED), X -ray photoelectron spectroscop y (XPS ) and
chemical stability anal ysis in alkali solut ions. 79 The latter is found to be the most
convenient techniqu e, where the pol arit y depend ent chemical p roperties of the III -
Nitrides are used to determi ne the polarit y o f the f ilms. 87 In this work the p olarity o f
the epitaxial films or that of particular polar domains in the s ample s, is determined
by wet etching in KOH solutions. I n Tabl e 4-1 th e polarit y dependent etch rates fo r
AlN and GaN are summarized as deter mined b y Guo et al.. 87
Tabl e 4-1: Etch rates o f N - and III -polar G aN and AlN crystals in 1wt% KOH
solution in deionized water a t 70 °C. 87
Etch rate (nm /min), 1wt % KOH @ 70 °C .
Material
N-polar
III- polar
Etch selectiv ity (N-polar/III -polar)
GaN
40
1.9
~20
AlN
1400
1.6
~900
As can be seen from Tabl e 4-1 the etch rat e for the N-polar surf ace is around one
and three ord ers o f ma gnitude lar ger than th at of the III-pola r surf ace, for GaN and
AlN respective l y . From cross sectional SEM measurements before and afte r wet
etching , the polarit y of t he films can be determi ned based on the established etch
rates. In addition, the III- polar surface remains ato mically smooth after wet etching,
with the exception of regions containing pit s where the etch rate of the exposed r (1 -
102) and s (1-101) plan es (and possibl y othe rs) is lar ger , leading to in creased pit
sizes. I n contr ast, the N-polar surface roughness significantly inc reases after wet
etching in alkali solution, leaving a hig h de nsit y of he x agonal hillocks ex posed
( Figure 4-6 ). 87 Often, examining the sample surface with an optical m icroscope
before and after wet etching is sufficient to estimate the pola rity of the sample. In
Polarity De p endent Wet Etching in KOH 51
Figure 4-6 the chemically et ched N-polar and III-polar sur face of a G aN and AlN
layer a re presented for comparison. The III-polar surface for both GaN and AlN
remains featureless, while the N -polar surface of both GaN and AlN ex hibit a rou gh
surface filled with hexagonally shaped p yra midal features.
Fig u re 4-6: Tilted cross section SEM image displaying the etched surface of a III -
polar (top) and N-polar (bottom), GaN (left) and AlN (right) epitaxial layer.
The ch emical reactions l eading to the formation and diss olution of III- Nitrides into
III -oxides and ammonia when submerged in a KOH solution is well known with: 88 –
90
KOH
2 2 3 3
KOH
2 3 3
KOH
2 2 3 3
KOH
2 3 3
2Ga N + 3H O Ga O + 2NH
Ga N + 3 H O Ga (O H) + N H
2A lN + 3H O A l O + 2 NH
A lN + 3H O A l( OH ) + N H
(4.1.1)
Guo et al. 88 calculated a Gibbs free energy for the latter chemical reactions of 1399
KJ/mol, 723 KJ/mol, -350 KJ/mol and -334 KJ/m ol respectivel y indicating the mor e
favora bl e formation of Al -oxide/-h y d roxide over Ga -ox ide/hydroxide, which is
reflected in the increased etch rates for AlN over GaN. Th e polarit y etch selectivit y
favoring the N-pol ar fa ce over the III-polar f ace, has been attributed to the different
52 Polarity Control
number of nit rogen dan gling bonds for the respective polarities, where th e N -polar
face will exhibit three nitrogen dangling bonds, shield ing the III-atoms from reacting
with the OH - molecules, while the III-polar face will onl y exhibit a single nitrogen
dang lin g bond allowing for a reaction with the O H - molecules. 89 However, none of
the studies consider polarization induced charge compensation and it s relation to
polarity dependent oxidation potential, which may a lso pla y a role on the etch
selectivity betwee n th e polarities of the III -Nitride s.
In summar y , the polarit y control process is described in detail for III- and N-polar
GaN and AlN thinfil ms deposited via MOCVD on sapphire. Th e surface
morphologies for the res pective polar films are characterized via AFM, where step
flow growth is observe d for both III-polar III-Nitrides and a rou gh surface is
measured for both N-po lar III-Nitrides plagued with hexagonal hillocks. The etch
behavior for both polarities in a KOH soluti on at 70 °C is presented where the III -
polar films are inert and the N -polar films a re etched, exhibiti ng a high densit y of
hexagonal hil locks at the surface after wet etching. This method for determining the
polarity of the III -Nitri des is practicle when characterizing a large number of
samples, and is the main characterization techni que emplo y ed for the lateral polar
structures fabrica t ed in this work.
AlN Lateral Polar Structure s 53
5 Lateral Polar Structures
5.1 AlN L ateral Polar Structures
A novel concept fo r devices based on late ral pol arity struct ures was introduced b y
Stutzman et al., where Ga -face and N-fa ce GaN films were deposited
simultaneously sided b y side. 91 For thi s, an MBE s y stem was us ed, wh ere a low
temperature AlN layer deposited on a sapphire substra te w as lithographicall y
patterned le aving alterna ting regions of ex posed sapphire substrate and AlN. The
subsequently d eposited GaN films were N-pol ar on the regions where the sapphire
substrate was exposed and Ga -polar on the regio ns where the AlN la ye r r emained.
Similarly , C ollazo et al. demonstrated polarity control via MOCVD and realized
GaN late ral polar struct ures b y lithographicall y patternin g a p reviousl y deposited
AlN buff er la y er. 92 Using the same concept, MOCVD g rown AlN latera l polar
structures w ere demonstrated b y Kirste et al.. 93 I n this work, we emplo y the
procedure d escribed b y the latter stud y to fabricate III -Nitride lateral polar
structures.
The AlN lateral polar st ructures are fabricated u sing a multi -step process. First an
AlN nucleation la ye r is deposited on an LED qualit y c -plane sapphire substrate as
described in section 4.2. The substrate coated wit h a 20 -30 nm AlN nucleation layer
( Figure 4-3 ) is then rem oved from the reactor a nd spin -coated with a 3 µ m thick
positive photoresist layer (S1813). A photolit hog raph y m ask was designed for the
growth and study o f lat eral polar stru ctures and is displ aye d in Figure 5-1 . The
photoresist la y er is exposed to 130 mJ / cm 2 using the mask displa y ed in Figure 5-1
and developed for 1 min in MF-319 developer. After rinsing the s ample with
deionized water and blo w dr y in g it with N 2 , the pattern is trans ferred to the III -
Nitride epitaxial laye r b y R IE in a Cl 2 and BCl 3 anisotropic plasma in a “Try on
Minilock II” RIE s ystem. The sample s are etched at an RF po wer of 100 W in a 1:1
ratio gas mixture of 25 sccm of Cl 2 and BCl 3 at a 75 mTor r total reactor pres sure.
54 La t eral Polar Structures
Fig u re 5-1: Schematic of mask design used f or photol ithography. The mask
contains 8 different regions of 1 cm 2 areas with different stripe structures. The stripe
structures are composed of equall y spaced covered and uncovered stripes. The
periodicity of the s tripe structures are 10, 20, 40 and 100 µm. Every periodic
structure is available in two orientations at a 90° angle from each oth er in order to
study th e influence of the subst rate orientation o n the grown structures. The center
region is half cove red and half uncovered to achieve 0.5 x 1 cm 2 s ingle polar
domains and compare with the corresponding polar domains in the lateral polar
structures.
The remaining photoresist residue was then removed b y submer ging the sample in
heated N-Meth y l-2-P y rr olidone (NMP) followed b y isotropic O 2 plasma in a PM -
600 s y stem. An A FM image at the 20 µm periodic structure r egion of a patterned
substrate, is displa yed in Figure 5-2 . Th e patte rned substrate is th en int roduced to
the MOCVD reactor, which is pumped to a pressure in the high 10 -7 to low 10 -6
Torr. The sample is vacuum annealed at a temp erature of 1040 °C for 1 0 minutes
and then backfilled with 1 slm of H 2 and 1 slm of N 2 at a total chamber pressure of
20 Torr where it is k ept for 7 minutes. Next, the temperature is lowered to 950°C
and the sample is exposed to a mixture of 1 slm N 2 and 1 slm NH 3 for 4 min. The
substrate tempe rature is then increased to 1100° C where the AlN grow t h is started
by flowing 6.7 µmol/min of trimethy lalumini um (TMA) and 0.3 slm NH 3 for 10 min
using N 2 as the precursor carr ier gas and 10 slm of H 2 as a diluent gas in a reactor
total pressure of 80 Torr. Finall y , the temperature and the TMA flow are increased
to 1250°C and 13.4 µ mol/min, respectively. In this proce ss, N -polar AlN grows on
AlN Lateral Polar Structure s 55
the exposed sapphire regions and Al -polar Al N on top o f the AlN nucleation
layer 93,94 .
Fig u re 5-2: AFM ima ge of a 20 µm periodic st ripe pattern of an AlN nucleation
layer deposited on a sap phire substrate with color coated height scale (left). L in e
scan across the periodic structure showin g the height profile.
Figure 5-3 displa ys th e surface morpholog y of an AlN lateral polar structure at a 20
µm periodically patterne d region, wh ere on e N - polar domain can be se en in the
center region surr ound ed b y two Al-pol ar domains at each side.
Fig u re 5-3: AFM image of a 20 µm periodic AlN lateral polar structure
56 La t eral Polar Structures
An expanded view of the Al-polar domain (bottom right in Figure 5-3 ) shows a
smooth surface with an RMS value of 0.3 nm, sim ilar to that shown in Figure 4-4 .
In contrast a rough sur face, exhibiting hex agonal hil locks is observed for the
expanded view of the N-polar domain (top ri ght in Figure 5-3 ), like the N-polar
surface shown in Figure 4-5 . To confirm the polarit y of the respective domains, the
samples were submer ge d in a 1 molar KO H solution in DI w ater at 70 °C . I n Figure
5-4 , D I C optical mi croscope image s of a 100 µm periodic AlN L PS before and after
30 seconds of wet etching in KOH are presented for compar ison.
Fig u re 5 -4: D IC optical microscope images of a 100 µm periodic AlN LPS as grown
(left) and after wet etching for 30 sec onds in 1M K OH at 70 °C.
In Figure 5-4 the c hange in roughness at the N-polar re gions, b efore a nd after
etching is obse rved. The N -polar region seemingl y becom es smooth after etching.
This is due to the fact that the etch time was suff icient to remov e the N-polar film
and ex pose the smooth surface of the sapphire s ubstrate as determined f rom cross
section SEM measurements. For comp arison SEM measurements of an AlN L PS
before and after wet etching are shown in Figure 5 -5 . Note that the displa yed images
are taken fr om dif ferent patterned areas of the same sample.
AlN Lateral Polar Structure s 57
Fig u re 5-5: SEM im age s of a 10 µm periodic AlN L PS as grow n (le ft). On the right
a 100 µm periodic AlN LPS after wet etching in a 1M KOH solution in DI water at
70 °C for 30 s.
A more detailed inspection of the wet etched sample reveals that while the majorit y
of the N-polar film has been removed, leavin g a large area of expose d sapphire
surface, a hi gh densit y of hexagonally faceted p yramids of AlN domains remain on
the surface ( Figure 5-6 ). These features can b e divided in to two categories. A lower
density of large p yramids with heights in th e r ange between 300 - 500 nm and
widths of 500 – 1000 nm, can be observed. S econdly, a higher densit y (~3 x 10 9 cm -
2 ) of hexagonall y faceted p y r amids of significantly smaller size with heights ranging
from 5 - 100 nm and widths between 50 nm and 200 nm remain on the surface.
Fig u re 5-6: SEM measurements of a wet etched 100 µm periodic AlN LPS. (Left )
The wet etched N-polar domain where the remaining low d ensit y of large conical
features are hi ghlighted. (Center) high magnification of the inversion domain
boundary with hig hli ghted high densit y of conical features.
The origin of the residue material is unclear. O n one hand, a stud y b y Guo et al.,
showed that wet et ching the N-polar sur face of P VT grown AlN single cr ystals,
where no inversion doma ins are expected and hav e a low dislocation density (~ 10 3 -
58 La t eral Polar Structures
10 4 cm -2 ), leads to a rough surface full of hexagonall y faceted p y ramids with a
density ~ 10 7 cm -2 , suggesting that the remaining residue is li kely the result of an
inhomogene ous etch rate. 87 However, the observed d ensit y of remaining
hexagonally faceted fe at ures in Figure 5- 6 is two to thre e orders o f mag nitude
higher than the densit y observed in the latter study . A more likel y scenario based on
a study b y Husse y et al ., is the prese nce of a high densit y of Al-pola r inversion
domains. 86 Throug h cross sectional high resolution TEM measurements on N-polar
AlN samples in combination with l ow molarit y KOH wet etchin g ex periments, the
study determined an inv ersion domains densit y ~ 10 9 cm -2 , in agre emen t with the
estimated densit y of the smaller features observed in thi s work. Figure 5-7 shows a
high ma gnification SEM image of a low molarit y and short ti me wet- etched N-polar
AlN domain, exhibi ting vertically aligned AlN wires of var y ing widths between 5 –
40 nm located at the top of the hexag on ally faceted pyramids.
Fig u re 5-7 : S EM image of a w et etched N-polar AlN film in a 0.5 M KOH solution
in D I water for 20 s at 70 °C. The appare nt Al -polar inversion domains are
encircled.
The density of the vertically aligned AlN wires i s estimated to be ~ 3 x 10 9 cm -2 in
agreement with the densit y measured by Husse y e t al. , as well as with the measured
widths of the inversion domains. From these ob servations, a li kely scenario is that
the p y ramidal shape of the base surrounding the Al -polar wir es is g ive n by the
etching natur e of N-polar AlN film s as described b y Guo et al., however, contrar y to
AlN Lateral Polar Structure s 59
the case of AlN sin gle crystals, the hexagonal p y ramids are pinned at their center b y
Al -polar inv ersion domains explaining the two to three orders o f ma gnitude hi gher
density observed. No te that such inversion domains have also been me asured in N -
polar GaN films on sapphire subst rates. 75 Husse y et al. showed that regardless of the
grown III-Nitride polarit y , voids are formed at th e sapphire surface int o the sapphire
substrate and suggest th at these are formed durin g the H 2 and NH 3 annea ling steps
where H 2 participates in the sapphire decomposition. In addition the stud y shows
that in both N-polar and Al-polar growth, these voids promote the growth of Al -
polar domains, however the precise mechanism leadin g to Al -polar growth remains
unexplained.
Fig u re 5 -8: A FM ampli tude image s of the patt erned AlN nucleation lay er on a
sapphire substr ate p rior t o the growth of an AlN LPS (Top images). SEM images o f
wet etched AlN LPS showing a se ries of aligned Al -polar inversion domains in a
similar pattern to the polishing sc ratches (Bottom images).
Takeuchi et al. has shown that a low densit y of large AlN h exagonal p y r amids ma y
remain on the sapphire s urface even aft er prolon ge d wet etching in 10% wt. KOH
60 La t eral Polar Structures
solution in DI water at 60 °C and attributes them to Al -polar inversion domains that
may originate from re sidual polishing scrat ches on the as r eceived sapphire
substrates. 95 The top im ages in Figure 5-8 display two different patterned AlN
nucleation la y ers deposited on sapphire substrat es, where the s apphire su rface with
residual polishing scratches can be observed. The bottom images are 60° tilted SEM
measurements of a wet etched AlN LPS s ample where rows o f aligned Al-polar IDs
in the N-polar domains are highlighted. In partic ular, two rows of aligne d Al -polar
IDs continue after crossing an entire Al -polar domain (bottom left image in Figure
5-8 ), indi cating that the IDs originate from residual po lishing scratches in agreement
with the conclusion made by Takeuchi et al. An SEM imag e of the large I Ds related
to residual polishing scratches is presented in Figure 5-9 , showing that ve rtical AlN
wires extending from the top of the hex agona l pyramids are also present. A possible
explanation is that the residual polishing s cratches act as voids, sim ilarly to
decomposed sapphire, and promote Al -polar growth as suggested b y Hussey et al. 86
Fig u re 5-9: SEM image display in g a magnified view of the residual hexagonal
pyramids after wet etching. Vertical AlN wires located at the top of the hexagonal
pyramids are hi ghlighted.
In summary, AlN L PS can be obtained usin g the process described in thi s section.
Uniform Al-polar growth of AlN is obtained in the regions where an AlN nucleation
layer remained. Predomi nantly N-pol ar growth can be achieved in the areas where
the sapphire surf ace is exposed, however a d ensity ~ 10 9 cm -2 of Al -polar inversion
AlN Lateral Polar Structures 61
domains is estimated. The inversion domains are measured to be 5 – 40 nm in
diameter. Assumin g a 10 nm diameter av erage of the Al-polar inv ersio n domains,
this corresponds to <1% of the material volum e which is not expected to
significa ntl y de crease the conversion efficienc y in quasi -phase matching.
Nevertheless, a detailed study on the influence of H 2 and NH 3 annealing in the
decomposition of sapphire and how the y p romote Al-polar growth, is necessary for
developing a process to achieve a reduced density of Al-pola r inversion domains in
N-polar AlN films . Finall y , it is critical that t he starting surface of th e sapphire
substrate is epi-re ad y, free of any re sidu al polishing scra t ches, to mini miz e the
density of A l -polar inversion d omains in the N-polar AlN reg ions.
5.1.1 N ano m eter Scale AlN Lateral Polar Struc tures
For fr equenc y doubli ng of laser light into the UV spectral range via quasi-phase
matching usin g AlN lateral polar structures, domain sizes in the nanometer scale are
necessary. The coheren ce length (see se ction 2.1.4) in bulk materi al can b e
calculated with
00
0
2
,
4( )
c
l k n n
(5.1.1)
and is presented in Figur e 5-10 as a function of the fundamental wavelength, whe re
the S ellmeier dispersion relation coefficients were taken from the literature. 96 I t can
be observed that for f requenc y doubling from 530 nm to 265 nm in bulk AlN, the
coherence len gth is 645 nm, setting the periodicit y of the required AlN LPS at 1.3
µm to achieve 1 st order QPM.
62 La t eral Polar Structures
Fig u re 5 -10: Calculated coherence length in bulk AlN sin gle cr y stal as a function of
fundamental (driving) wavelength.
Figure 5-10 gives an idea of the required per iodicities for QPM in bulk AlN,
however as discussed in section 2.1.4, wh en us ing waveguide stru ct ures, the
propagation of TM modes need to be considered which lead to sli ghtly different
periodicities for 1 st order QPM structures. Th e condition determined in section 2.1.4
0
2
20
rs m
K
can be rearra n ged to the form
0
0
,, ,
2
r eff s eff m
nn
(5.1.2)
where
0
0
0
,
r
r eff
n k
and
,
s
s eff
n k
are the effective refractive index of th e r th mode of
the fundamental (driving) wave and the s th mode of the second harmonic wave.
0
,
0
k
and
k
are the v acuum w avelength and w ave vectors for th e r espective wave
freque n cies
0
and
. Using a W olfram Mathematica code, both sides of equa tion
(5.1.2) were plotted for a given waveguide dimension ( Figure 5-11 ). In Figure 5-11
only the 0 th TM modes for both driving and second harmon ic waves were
considered, the QPM ord er w as set to m =1 and a 550 nm thick AlN L PS waveguide
with 1.2 µm periodicity was assumed.
AlN Lateral Polar Structure s 63
Fig u re 5-11: Both side s of equation (5.1.2) are plotted. In red, th e effective
refractive index for the 0 th order mode of the fundamental wave. In purple, the
effective refrac tive index for the 0 th order mode of the second harmonic wave
reduced a ter m given by the periodicity of the AlN L PS with Λ =1.2 µm.
Standard, available, mas ked photolithograph y is lim ited to featu res in the order of 2
µm in size, making other patternin g techniques necessar y to achieve the periodicities
required for QPM SHG i n the UV -C spectral range. For this reason a nov el process
is developed, which use s lase r interference lithograph y in combination with the
previously established p olarit y control p rocess scheme, to achieve sub- micrometer
periodically poled Al N lateral polar structures (L P S) ( Figure 5-12 ).
64 La t eral Polar Structures
Fig u re 5-12: N anoscale polarit y control process scheme. Step 1: MOCVD
deposition of AlN nucleation la y er on c -plane sap phire. Step 2: Photoresist and ARC
are spin coated onto the substrate. Step 3: P hotore sist la y er is ex posed to the laser
interference periodi c pattern and developed. Step 4: Pattern is transferred t o the AlN
nucleation la yer b y reactive ion etching. Step 5: The residu al photoresist and ARC
are removed by O 2 plasma. S tep 6: The patterned substrate is reinserted in the
MOCVD chamber, where the AlN film is deposited leading to the AlN periodic
lateral polar structure . 97
A low temperature nucleation la y er as d escribed in section 4.2 is deposited on an
LED-quality c-plane sapphire substrate with 0.2° offcut towards the sa pphire m-
plane. The substrate is then removed from the r eactor and spin -coated with a 100 nm
thick anti-reflection coating (Brewer Sci ence i-CON-16, n=1.72 -0.04 j ) and a 630 nm
thick photoresist la y er (Sumitomo PF I-88). The la ser int erference pattern is obtained
using a L lo yd’s mirror configuration setup (section 3.3), developed by Ba gal et al. 98 ,
resulting in a highl y periodic sub -micrometer pattern across the entir e subst rate. A
He -Cd laser focused ont o a pinhol e is used as a monochromatic point light source.
The sample is placed adj acent to a fixed mi rror at a 90° ang le, acting as the second
light source with the same incidence angle 𝜃 . The periodicity, 𝛬 , of the int erference
pattern is then defined by th e angle of incidence 𝜃 with respect to th e normal of the
sample, the wavelength 𝜆 of the light sourc e and the re fractive index 𝑛 of the
medium as follows:
2 sin n
(5.1.3)
AlN Lateral Polar Structure s 65
From this relation, the refractive index of air being
1 n
and the wavelength of the
laser
325 nm
, the ang le of incidence to achieve a 1.2 µm periodicity (necessar y
for 1 st order qu asi phas e matching at 2 80 nm) c an be calculated, wh ith
7.78
.
The sample was exposed to a tot al en ergy o f 47 mJ and was developed for 1 mi nute
( Figure 5-13 ).
Fig u re 5-13 : Differential interfere nce contrast o ptical microscope image of 1.2 µ m
periodic pattern of the photoresist layer.
In addition to the standing wave intensit y pr ofile along the sample surface , a
standing wave no rmal to the sample surface is created which deteriorates the
sidewall profile of the exposed photoresist la y er . 99 To suppress the vertical standing
wave and a chieve vertic al sidewalls of th e patte rned photoresist, an additional la ye r
between the sample and t he photoresist la ye r is introduced t ypically addressed as the
anti- re flection coating (ARC) layer. Th e purpose of the ARC la yer, is t o suppress
the vertica l standin g w ave by d estructive int erference between the r eflected li ght at
the sample-ARC interfa ce and the r eflection at the ARC -photoresist interface. For
more details on t y pes of ARC la yers and th eir workin g principle, refer to the
dissertation of M. Walsh. 99 I n thi s work, a comp uter program, which con siders the
complete la ye r sta ck and their re spective refra cti ve indices (substra te, t hin film,
ARC, photoresist and air), is used to calculate the ARC thickness which wil l lead to
66 La t eral Polar Structures
the max imum suppressio n of the vertical standing wave (see Figure 5-14 ). From the
program, the optimal ARC thickness of 100 nm was obtained.
Fig u re 5-14 : Reflected intensit y at the ARC -photoresist interface as a fu nction of
ARC thickness.
The patterned obtained f rom developin g the ex posed photoresist la y er is transferred
to the ARC la ye r and then to the epitaxial layer in a two-step reactive ion etching
(RI E ) process . First the s ample is int roduced in a “Semigroup 1000TP” R IE s ystem
and is exposed to an anisotropic ox yge n plasma f or 3 minutes at an RF power of 54
W, in 30 sccm of O 2 flo w and 30 mTorr total pressure. In a second step, the pat tern
is transferred to the III-Nitride epitaxial la yer by R IE usin g the same co nditions as
described in the previous section ( 5.1). The remaining photoresist residue was then
removed using heated NMP, followed by isotropic O 2 plasma. An AFM image ,
displaying such a p atterned substrate is displa y ed in ( Figure 5-15 ).
AlN Lateral Polar Structure s 67
Fig u re 5 -15: Atomic force microscop y image and height p rofile line s can of the
patterned substrate, displ aying domains of 25 nm thick AlN layers and do mains with
the sapphire substra t e exposed.
The patterne d substrate is then placed in the re actor and the AlN latera l polar
structures are grown a ccording to the procedure described in the previou s section,
where both polarities grow simultaneousl y . A FM images of a patterned substrate
before and after the Al N film deposition are s hown nex t to each othe r in Figure
5-16. Alternating stripes of low temperature AlN nucleation layer and bare sapphire
substrate c an be observed in Figure 5-16 (left). Figure 5-16 (right) shows an AFM
image of the surface of a n AlN film deposited on t he patterned substrate. Two
different domains of similar width to the initial pattern are observed and i dentified
as Al- and N-polar domains from their char acteristic surf ace morpho log y . The
surface morpholo g y for the Al-polar domains is smooth with a surface r oughness
RMS value of 0.3 nm, while columnar hexagonal structures are observed for the N -
polar AlN with surface roughness RMS values in the order of 30 nm, which are
typica l surface mo rphologies fo r the respective polarities at thes e g rowth
conditions. 93 The I DB between the Al- and N-polar domains is well define d and
parallels the shape o f the patterned Al N nucleation layer, which demons trates the
ability to control the polarit y of the AlN la y er down to the sub -micron regime using
laser interference litho graphy.
68 La t eral Polar Structures
Fig u re 5-16: Hei ght profile AFM images of th e patterned subst rate b efore (left) and
after the AlN thi n film growth (right). In th e ri ght image, domains with a rough
hexagonal columnar su rface, characteristic of the N -polar domain, is observed as
well domains with a smooth (sub-nanometer RM S roughness) Al-polar su rface with
similar domain sizes as the patterned substrate, pointing at the vertical inversion
domain boundaries.
To unambiguousl y ident ify the Al -polar and N- polar domains, KOH etching and
subsequent SEM charac t erization were performed ( Figure 5-17 ). The figure shows
tilted cross-section SEM images o f the AlN LPS film as grown (a) and the same
sample after etching in a 1M KOH solution in deionized water for 1 minute at 70°C .
For the wet etch ed sample, the N-polar dom ains were completel y r emoved while the
Al -polar domains remained unchanged, the reby confirming the polarity of the
respec tive domains. Some lateral etchin g is observed at the Al -polar domains,
however no vertica l top -down etching is observed.
Fig u re 5 -17: Tilted view S EM image of the AlN LPS as grown (a) and after being
submerged in a 1 molar KOH solution in deionized water for 1 minute a t 70 °C (b).
AlN Lateral Polar Structure s 69
In a growth series, the d eposition times were v aried, to determine if ther e is mass
transport betwe en the po lar domains leading to an increased deposition rate of one
polarity over the other, and to est ablish if polari ty over grow th takes plac e at these
growth conditions. Fro m cross-section s econdary electron m ic roscopy (SEM)
image s ( Figure 5-18 ) , ta ken in a “Verios 460 L FEI s y stem” , equal growth rate for
both polarities is deter mined and vertical growth with no polarity overgrowth is
observed. Mor e significantly, full y coalesced inversi on domain boundaries are
observed, essential for the propagation of li ght, since an y air gaps at the interface
will lead to large scattering loss es and/or r eflection at eac h IDB inhibiting their use
for second harmonic generation of laser light. The 20-30 nm patterned low
temperature AlN nucleation la y er can also be observed, which as expected, is
present directly b elow the plateaus of the Al-polar domains.
70 La t eral Polar Structures
Fig u re 5-18: Cross-s ectional SEM im ag es of AlN L PS samples with varying
thicknesses. The inversi on domain boundaries a re highli ghted with yellow dashed
lines. Complete coalescence at the IDB s is obse rved.
Using laser inte rference lithography w ell d efined polarity control is demonstrated
down to 600 nm do m ain siz es with full y coalesced inversion domain int erfaces and
equal g rowth ra tes for both polarities. Howe v er, sca tterin g losses at t he surface
roughness remains a concern, p articularly at th e N-polar AlN sur face. For QPM
SHG, the ex citation and second harmonic light will travel in th e AlN w aveguides
and scatterin g losses will depend on surface roughness. Scattering loss es due to
random deviations at the waveguide bounda ries have been investigated in
detail. 46,100 Under the Ra y l eigh criterion, a surf ace ma y b e considered as opticall y
smooth for
AlN Lateral Polar Structure s 71
,
8 cos ( )
s
(5.1.4)
where
s
is the RMS surf ace roughness, λ is the wavelength in the material and 𝜃
the angle of inciden ce with respect to the surface normal. When considering the
propagation of TM mode s in AlN LPS-based waveguides, ever y mode r w ill have a
corre spondin g an gle of incidence
r
and is related to the mode’s propagation
constant value
r
by
s in ( ),
r
r
kn
(5.1.5)
where
k
and
n
are th e vacuum wave ve ctor and the re fractive index of AlN at
freque n c y
re spectively. The propagation constant values
r
a re obtained b y
graphica ll y solving equati on (2.1.27) as described in section 2.1.2. Considering an
RMS surface roughness value of 30 nm (t y pi cal measured value for AlN LPS), a
650 nm thick waveg uide and uti lizing the method described by Tien et al., 46 the
calculated attenuation coefficient p er unit len gth
r
at 550 nm wavelength for the
0 th order TM mode is 102 cm -1 . I t is clear that the scattering losses for such a
surface roughness will not allow efficient propagation of the driving and second
harmonic waves along the wave guide and thus efficient QPM SHG of UV laser
light. Hence , it is nece ss ar y to reduce the surface roughness o f the AlN LPS. One
possible solut ion is to reduce the surfac e roughness b y m echanical polishing.
Figure 5-19 displa y s an AFM image of a 1.2 µ m periodic AlN LPS before and after
mechanical polishing. Alumi na particles of 0.3 µm in size dissolved in D I water
were used as a polishing vehicle squi rted on a “ TexMet P” soft pad platform. The
mechanically polished samples showed significantly improv ed RMS surface
roughness values of 10-15 nm. Furthe r r eduction of the roughness seemed
challenging as lon ger pol ishing times did not lead to further improv ement. This may
have been related to th e polarity-dependent etching du e to the pH of the poli shing
vehicle. However a more detailed stud y on mechanical polishing using various
particle siz es and materials as well as different pH solutions may lead to further
improvements of the surface roughness.
72 La t eral Polar Structures
Fig u re 5 -19: AFM ima ge of a 1.2 µm periodic AlN L PS before (top left) and after
(bottom left) mechanical polishing with comparable sclaes. The respective hei ght
profile linescans across the periodic structure a re shown on the top right a nd bottom
right.
Nevertheless, the a chieved RMS roughness v alues of 10 nm lead to a c alculated
attenuation coefficient v alue,
r
, for the 0 th order TM mode of 11 cm -1 at 550 nm
wavelength and 6 cm -1 for the SHG wave at 275 nm. These v alues predi ct that the
fabricated AlN LPS are s uitable for SHG in the UVC spectrum [1] [2].
Waveguides were etch ed into a mechanica ll y poli shed AlN LPS sample using
standard masked photol it hogra ph y and RIE, to test the AlN L PS for second
harmonic genera tion. For this , a 3 µm thick negative photoresist (NFR 016 D2) la y er
was spin coated onto the sample and exposed to 110 mJ of UV li ght. After light
exposure the sample was submerged in MF -319 developer for 1 min. The sample
was subsequentl y placed on a 90 °C hot plate for 10 min to harden the ph otoresi st.
Following, th e pattern is transferred to the AlN LPS by R IE for 50 minutes with 2.5
minutes of pause in between 2.5 minutes of etch time to avoid overheating of the
photoresist, and using the same etchin g conditions as for the low temperature AlN
nucleation layer (described in section 5.1).
AlN Lateral Polar Structure s 73
Fig u re 5-20:SEM ima ges showing the AlN LPS- basded wave guides at a low (left)
and high (right) magnification re spectivel y..
These w aveguides were tested for QPM SHG, where more det ails are presented in
section 7.2.2.
5.1.2 Prom o ting Step Flow Growth throu gh Control o f Al Va por
Supersatura tion
An alternative to mechanical polishing fo r reducing th e surface roughness of the
AlN L PS is to promote step flow g rowth for both AlN polarities . The Burton,
Cabrera and Frank (BCF) theor y of cr y st al growth has been used to d escribe the
growth kinetics le ading to distinct surface mo rph ologies of p rominent epitaxial
semiconductor materials. 51 – 53,55,101 I n epitaxial N-polar GaN thin films a hi gh density
of hexagonal hil locks a re frequentl y observ ed. Th e formation of hillocks in G aN can
be suppress ed b y promoting step flow growth. I n general, this is achieved b y
decreasing the surface supersaturation
s
below a critical value
*
S
as describe d in
section 2.2. 52,53,55,101 Studies have demonstrat ed the growth of smooth N- polar GaN
thin films b y MOCVD either b y in creasing the off-cut angle of the substrate with
respec t to the (0001) sapphire plane, substituting the nit rogen diluent ga s with
hydrogen or increasin g the V/ III ratio of the precursors under nitrogen d iluent gas,
all resulting in a reduce d surface supersaturation
s
directl y or indirectly through a
reduction of the vapor phase supersaturation
. 101 – 104 I n analog y to previous work
done on N-polar GaN, the vapor phase supersaturation is reduce d in order to
promote step flow growth at th e N-polar surface of the AlN thin films . For this , a
growth series was conducted where th e Al vapo r supersaturation
was decreased
step wise by in creasing the growth temperature ( Figure 5-21 ).
74 La t eral Polar Structures
Figure 5-21: Surface m orpholog y of N -pol ar AlN thin films grown at different
temperatures. The grow t h temperatures for the di splayed samples is 1250 °C, 1400
°C, 1500 °C and 1550 °C for a) -d) respectivel y.
For the sample g ro wn at the highest vapor supersaturation (1250 °C), the typica l
rough surf ace morphology ex hibiting a high density of hexagonal hillocks is
observed. As the vapo r supersaturation is de creased, the hillock aspect ra tio
decreases as well as the surface roughness RMS value (22 nm at 1400 °C ). Also the
AlN nuclei in crease in siz e and decrease in densit y , and step t erraces becom e
resolvable with AFM ( Fi gure 5-21 - b) ), indicating a mixed growth mode o f step flow
and 2D nucleation. Further decreasing the surface sup ersaturation , results in a
drastic decrease of the R MS surface rou ghness va lue to 1.6 nm. I nterestingl y, 30-50
nm wide and ~10 nm tall columns with a densit y of ~ 3 x 10 9 cm -2 can be observed
( Figure 5-21 -c)) in agreement with the previously established densit y of Al -polar
inversion domains in epitax ial N-polar films (section 5.1). For the r egions in
between the columns, the surf ace rou ghness is below 1 nm indicating step flow
growth. Finall y, the N-polar film grown at the lo west vapor supe rsaturation ( Figure
5-21 -d)), clearl y displays step flow grow th, where the sur face rou ghness RMS value
is measured to be 0.5 nm. Here a densit y of ~ 3 x 10 9 cm -2 of the 30-50 nm diameter
wide columns can also be observed, however thei r height onl y ranges from 0.5 nm
to 1 nm.
AlN Lateral Polar Structure s 75
Fig u re 5-22: Al vapor supersaturation as a function of growth temperature
From these observations, the estimated Al vapor supersatura tion ne cessary for step
flow grow th of N-pola r AlN is ~10 4 or lower. Note that the critical surface
supersatura tion will depend on the surface diffu sion length of the adatoms . In this
temperature ran ge, the diffusion length is expected to decrease with temperature.
Since we observe a transition from 2D nucleation to step flow growth with
increasing temperature, it is evident that the vapor supe rsaturation plays a
dominating role. Also, the calculated Al vapor supersaturation values ( Figure 5-22 )
do not include pre-reaction or other transport losses specific to the reac t or design
and represent the maximum expected vapor supersaturation values. I t is mor e likel y
that the critical surface supersaturation is actuall y low er than the estimated value
from the calcul ated Al vapor supersaturation values , because pre-reactio n losses of
TMA are significant in AlN MOCVD growth, a s can be seen in Figure 5-23 . As
determined in section 2. 2, the surface supers aturation is directly proportional to the
growth rate (see equation (2.2.20)), thus from Figure 5-24 , where an inc rease in the
total reactor pressure is expected to lead to a hig her Al vapor supersaturation, but
actually a reduced growth rate is measured ( Figure 5-23 ), it is clear that the vapor-
phase reaction of TMA is significant and leads t o a lower surface sup ersaturation
than the calculated Al vapor supersaturation , since in the mass transport li mited
regime, the growth rate i s not ex pected to change if the TMA flow is kept constant .
Figure 5-23 shows that at 1250 °C growth tem perature, v ar y in g the total re actor
pressure from 20 Torr to 80 Tor r and otherwise maintainin g equal growth
76 La t eral Polar Structures
parameters, results in a d ecreased growth rate b y a factor of ½. S imilar observations
have been reported in th e literature, where vapor-phase p re-reaction between TMA
and NH 3 are studied. 105 – 107
Fig u re 5-23: Temperatur e and pressure dependen ce of measured growth rates for Al -
and N-polar AlN epitaxial films.
Fig u re 5-24: Al vapor supe rsaturation as a function of total pressure inside the
growth chamber.
AlN Lateral Polar Structure s 77
Also, increasing th e temperature from 1250 °C to 1550 °C resulted in a decrease d
growth rate b y an additional factor of ½ , refl ecting the temperature dependence of
the pre-reaction of NH3 with TMA.
In summar y , step flow growth of N-polar AlN can be achieved b y de creasing the Al
vapor supers aturation, w here the critical sur face supersaturation
*
S
is estimated to
be <10 4 at a growth tem perature of 1500 °C. Th e surface ro ughness RMS value is
reduced by two orders o f magnitude from 50 nm to 0. 5 nm. I n addition, a pressure
dependent vapor-phase reaction between NH 3 and TMA is measured where an
increase from 20 Torr to 80 Torr leads to a decrease in g rowth rate b y a fa ctor of ½.
Similarly at 80 Tor r reactor pressure, the vapo r -phase rea ction of TMA with NH 3 is
measured to be dep endent on temperature, where an increase from 1250 °C to 1550
°C leads to a decrea s e in growth rate by a factor of ½.
5.1.3 Mas s Transport betw een Polar D omains
Having a chieved step flo w growth for N-polar AlN at low supersaturation values, a
growth series was conducted where the supers aturation was ste pwise de creased,
through in creasing the growth temperature, to achieve smooth AlN LPS ( Figure
5-25 ).
78 La t eral Polar Structures
Fig u re 5-25: AlN LPS for a series of growth runs, where the growth temperatur e
was varie d to reduce the Al vapor supersaturation.
AlN Lateral Polar Structure s 79
In contrast to the AlN LPS grown at 1250 °C ( Figure 5-16 and Figure 5-18 ), a
temperature dependent growth rate dif ference is observed for the alternati ng polar
domains in Figure 5-25 . At 1250 °C growth temperature, simil ar deposition rates are
measured for both polarities ( Figure 5-18 ). Increasing th e temperature leads to an
increased deposition rate at the Al-polar domains compared to the N-polar domains ,
reaching a maximum growth rate difference bet ween 1400 °C and 1450 °C. For
growth temperatures above 1450 °C the growth rate of th e Al -polar domains
decreases reaching a crossover temperature a round 14 75 °C, where sim ilar growth
rate for both polar domains is de termined. For hig her temperatures the N-polar
growth rate exceeds that of the Al -polar domain s. The polarities of the respective
domains were confirmed b y KOH etchin g an d subsequent AFM and/or SE M
character iz ation. Amplitude AFM im ages of sample s before and after KOH etchin g
are displaye d in Figure 5 -26 and Figure 5-27 .
Fig u re 5 -26: Amplitude AFM images of a grown AlN LPS sample b efore (top left)
and after (top ri ght) KOH etching in a 1M solution at 70 °C for 30 s. (bottom )
Heig ht p rofile line scans for the corresponding a m plitude AFM image.
80 La t eral Polar Structures
Fig u re 5-27: Amplitude AFM images of AlN LPS before (top left) and after (top
right) KOH etching in a 1M concentrated solution at 70 °C for 30 s.
Figure 5-26 displa ys an AlN L PS with smooth Al-polar domains with surface
roughness RMS values ~3 nm and relativel y rou gh N-polar domains with V-shaped
valley s within the polar domains. I n contrast Figure 5-27 displa y s smooth N-polar
domains with ~3 nm RMS values and rough Al-polar domains with V-shaped
valley s. Regardless of the surface morpholo g y , in both cases the N -polar domains
are completel y etched a wa y while the Al -pol ar domains remain unaltere d. Vertical
sidewalls are revealed after KOH etching, whi ch is critical for th e fabricati on of
QPM structures. Deviations from vertical growth will lead to dut y c y cle variations
and in extreme cas es, to polarity over grow th, r esulting in a r educed QPM SHG
conversion efficiency.
Because t he measured growth rates for sin gle polar AlN film s are i ndependent of
polarity ( Figur e 5-23 ), the g rowth ra te differences observed in Figure 5-25 are
attributed to mass transport between the adjacent and opposi te pola r dom ains. This
conclusion is also suppor ted b y the fact that the to tal volum e is conserved when the
volume of both polar domains is added, which is equal to that measured for single
polar AlN films. To date, there is no theoretical model detailing the mechanism
leading to polar domain thickness differences in III-Nitrid es. Experiments indi cate
that the mecha nism is r elated to multiple growth para met ers includin g temperature,
the choice of dil uent gas, V/III ratio and tot al chamber pressure, suggesting a
dependence on the Al vapor supersaturation. Furthermore, thickness di fferences
AlN Lateral Polar Structure s 81
between th e polar domains are dependent on the distance relative to the inversion
domain boundary, exten ding up to tens of µm, hinting towards mass transport in the
vapor-pha s e. A mor e detailed stud y is nec essar y to develop a theo retical model that
precisely de s cribes the ex perimental observa tions .
Fig u re 5-28: Polar domain thickness difference and Al vapor supersaturation as a
function of temperature .
Figure 5-28 display s the measured thickness differe n ce between the polar domains
as a function of temp erature. The corresponding Al vapor supersatur ation values are
superimposed for comparison. The v alues are obtained b y measuring the 10 µm
periodic AlN L PS and taking the difference betwee n the ave rage value of the
respec tive polar domains. For the error ba r, the sum of the RMS values for the
respec tive polar domains is taken. Similar growth rates for both polar domains are
achieve d at 1500 °C growth temperature or pe rhaps more re levant , at Al va por
supersatura tion values
4
1 3 x 1 0
as can be observed in Figure 5-25 . The
measured AlN LPS surface roughness RMS value for 10 µm periodic AlN LPS
grown at 1500 °C is 11 nm over a 90 µm 2 area. Additionall y, the surface roug hness
corre l ation length is obviousl y lar ger compared t o that of AlN LPS where the N -
polar surface ex hibits a high densit y of hex agonal hillocks. A larger correlation
length in addition to the reduced surface rou ghness RMS will lead to lower
scattering losses for the propaga tin g laser light. 550 nm thick and 250 nm thick, 10
µm periodic AlN L PS were grown at 1500 °C and ~5µm wide waveguides were
82 La t eral Polar Structures
etched into the film, using masked photol ithography and RIE ( Figure 5-29 ). W hile
such large periodicities cannot be used for 1 st order QPM SHG, lower efficiency
higher order QPM SHG ca n be achieved as it will be demonstrated in section 7.2.1.
Fig u re 5-29: (left) AFM images of 550 nm thick (top) and 250 nm thi ck AlN LPS -
based waveguides with 10 µm periodicity. (right) Height profile line sc ans across
and along the wa v eguide corresponding to their respective AFM images.
Growing AlN LPS with shorter periodicities , to achieve 1 st o rder QPM SHG in the
UV -C spectral range (i. e. 1.2 µm periodicit y), at low Al vapor supersaturation
values (
4
1 3 x 1 0
) , necessar y for equal deposition rate at both polar domains and
step flow growth at the N -polar domains, results in a highl y pitted sur face and mix ed
polar growth within the polar domains . An AFM image of such an AlN L PS is
displaye d in Figure 5-30 . For comparison, an opti cal DIC image of the sampl e after
etching in a KOH solution for 30 s at 70 °C is displa y ed.
AlN Lateral Polar Structure s 83
Fig u re 5-30: (le ft) AFM image of 1.2 µ m periodic AlN LPS grown at 1500 °C .
(rig ht ) Optical D I C image of t he sam e sample after bein g submerg ed in KOH,
displaying inhomogeneo us etching, indicatin g th at the AlN LPS contained mixed
polar domains.
A higher magnification ampl itude AFM image, highli ghting the su rface morpholog y
of 1.2 µm periodic AlN LPS grown at 1500 °C, is displayed in Figure 5-31 .
Fig u re 5-31: Amplitude AFM image of 1.2 µm AlN L P S s amples grown a t 1500 °C.
Regions where one polar ity is overgrowing the neighboring polari t y are encircled. A
few inv ersion domain boundaries (IDB’s), as d etermined b y t he surface
morphologies characteristic of the re spective polarities, are marked with y ellow
dashed lines.
Regions where one polar domain has overgrown the neig hboring opposite -polar
domain are encircled. Moreover, th e Al-polar domains are plag ued with a hig h
density of pits with depths up to 200 nm as well as with protrusions of up to 150 nm
in height. The scattering losses for such a rough structure will not allow for the
propagation of laser li ght inhibit ing their use for QPM SHG. Additionally, for QPM,
alternating polarit y domains are necessary, hence polarit y over grow th will not allow
for the phase mismatch correction of the driving and second harmoni c waves at
84 La t eral Polar Structures
every coherence length distance and QPM will not take place. Polarit y overgrowth
seems mainly a concern for growth conditions leading to simil ar growth rates for
both polarities (
4
1 3 x 1 0
). This conclusion is based on the fact that if the growth
parameters are selected, such that one pola rity has a si gnifica nt l arger deposition rate
compared to the opposing polarit y ( Figure 5-28 ), no polarity overgrowth is observed
as well as vertical grow t h at the r espective polar domains ( Figure 5 -32 ). It is worth
noting that, thus far, polarity overgrowth in 1.2 µm periodic AlN L PS has onl y been
observed for geometries where the IDBs are placed parallel to the cr y st allographic a -
plane of the AlN. However a more detailed stud y is necessar y to make a
substantiated conclusion.
Fig u re 5-32: AFM hei ght images fo r 1.2 µm AlN LPS grown at
3
5 1 0 x 10
(left)
and
5
1 x 1 0
(right) Al vapor supersaturation values.
To circumv ent the iss ue of polarit y ov ergrowth, a growth process w as developed
where different growth modes are combined. First the 1.2 µm p eriodic AlN L PS is
grown at high Al vapor supersatura tion values, where well defined I D B’s and po l ar
domains are obt ained ( Fi gure 5-16 ), until the d esired film thickness is achieved. In a
second step a “capping” AlN layer is deposited , where th e Al vapor supe rsaturation
is decreased (i.e. b y increasing the temperature) t o promot e step flow growth at the
N-polar surface and reduce its surface roughness. At this point, polarity ov ergrowth
will onl y influence a thin lay er near the surface of the AlN LPS, which will not
significa ntl y affect the QPM SHG c onversion efficiency, since the electric field
amplitude of the wave- guided TM 0 mode is predominantl y confined in the center
AlN Lateral Polar Structure s 85
region of the waveguide. Figure 5-33 shows AFM height images of the s urface of a
series of 1.2 µm AlN LPS, grown in a two -step temperature process, where the
temperature of the second step was varied fr om 1 400 °C to 1550 °C.
Fig u re 5-33: A FM h eight ima ges of 1.2 µm AlN LPS grown b y a two -step
temperature process. The first step growth t emper ature for all samples was 1250 °C.
In the se cond step the te mperature w as increased to 1400 °C (top), 1500 °C (center )
and 1550 °C (bottom) in order to achieve a smoo th surface morpholo g y of the 1.2
µm AlN LPS.
A clear decrease in th e domain height di fference is observed as th e tem perature is
increased for the secon d growth step, in agreement with previous obse rvations
( Figure 5-28 ). A representative tilted S EM imag e o f a 1.2 µm periodic AlN L PS
grown in a two-step tem perature process, after K OH etching is presented in Figure
5-34 .
86 La t eral Polar Structures
Fig u re 5-34: Tilted SEM image s of a KO H w et -etched 1.2 µm AlN LPS sample
grown in a two-step temperature process.
The two step temperature process can also be implemented in separa te growth runs.
Figure 5-35 shows two different AlN LPS where thicker Al -polar domains
compared to the N-polar domains are measured.
Fig u re 5-35: AFM height (top) and amplitude (bottom) image of two different 1.2
µm periodic AlN LPS, where thicker Al -polar domains compared to the N -polar
domains are measured.
After characterizing the s amples, the y we re cleaned in an ultrasou nd bath in acetone,
methanol and deioniz ed water and subsequentl y subjected to an acid clean in a 5%
HF solut ion in deionized water followed b y rinsi ng with only d eionized water. The
samples were then int roduced to the MOCVD reactor where the y were va cuum and
Al N Lateral Polar Structures 87
H 2 annealed following the standard procedure d escribed in section 5.1. Following
the annealing steps, the s amples were h eated up t o 1550 °C at 80 To rr total chamber
pressure, 10 slm and 0.3 slm flow of H 2 and ammonia respectivel y . AlN was then
deposited for 30 minutes by flowin g 13.4 µ mol/min of TMA. The calculated vapor
supersatura tion for these grow th parameters is σ = 5x10 3 , where higher d eposition
rates at the N-polar domains are establishe d ( Figure 5-28 ).
Fig u re 5-36: AFM hei ght (top) and amplitude (bottom) image of the 1.2 µ m periodic
AlN LPS displayed in Figure 5-35 after r egrowth at x temperature for x minutes,
where higher deposition rates for the N -polar domains compared to the Al -polar
domains were determined.
Figure 5-36 shows AFM height and amplitude images of the AlN L PS samples after
regrowth. In both samples the thickness difference between the oppo site polar
domains has virtuall y disappeared while sti ll maintaining the polarit y of the
respec tive domains. The N -polar domains are evident from the m -plane faceted step
flow morpholog y, as well as the inversion domains with a densit y ~10 9 cm -2 . As
evident in Figure 5-36 thi s method can be used to achieve 1.2 µ m p eriodic AlN L PS
with a smooth surface morpholog y . Additionall y , the possibilit y to control
deposition rates for the respective pola rities when grown side b y side will be useful
for other applications.
88 La t eral Polar Structures
In summa r y , when g rowing AlN LPS at v apor supersaturation values
< 10 8 , mass
transport between the opposite polar domains is observed as the Al vapor
supersatura tion
is decrea sed. For
84
10 3x 10
mass transport from the N-
polar to the Al-polar do mains, leads to thicker Al-polar domains. For
4
1 - 3x 1 0
similar g rowth rates for both polarities is measured, indicating no net ma ss transport
between the adjacent po larities. Finall y, for
4
1 0
mass transport from th e Al -
polar to the N-pola r domains is measured leading to thicker N-pola r domains. For
AlN LPS with periodicities
1 .2 µm
, polarity overgro wth takes places when
grown at Al vapor supersaturation values where si milar growth rates a re de termined.
Alternatively, a two-step temperature p rocess can be utiliz ed to avoi d polarity
overgrowth and achieve 1.2 µm periodic AlN LPS with a 6-10 nm surface rou ghness
RMS value. Finally, 5 µm wide waveguides w ere etched into 10 µm AlN L PS
waveguides o f two differ ent thicknesses (550 nm and 250 nm) to test them for QPM
SHG in the UV spectral range.
5.1.4 Inf lu ence of Crystallogr aphic Orientat ion on the IDB
A closer examination of the IDB with AFM, re veals that the IDB’s pre fere ntiall y
facet along the cr ystallographic m -plane of A lN, giving rise to diff erent IDB
patterns for LPS with different crystallographic or ientations ( Figure 5 -37 ). For AlN
LPS with the I DB aligned along the cr y stal’s (11 -20) plane, a jigsaw pattern for the
IDB can be observed. In contrast, the AlN LPS w here the IDB is aligned with the
crystal’s (10 -10) plane, the I DB is virtuall y a s traight li ne. These r esults are in
agreement with IDB’s predicted and obs erved for GaN, where first principle
calculations predi ct a co mparabl y small formation energ y fo r an IDB along the m -
plane and shifted along t he c-direction b y a magnitude of c/2 = 2.6 Å. 85,108
AlN Lateral Polar Structure s 89
Fig u re 5-37: A FM amplitude images of the I DB in AlN LPS samples with
periodicities along the a- direction (top) and along the m-direction (bottom). The left
image s, are taken from a sample where the stri pe pattern is well aligned with the
crystallographic orientations and the samples on the ri ght are tak en from a sample
where the stripe pattern is slightl y misaligned with respect to the crystallographic
orientations.
This was later confirmed in a study through hi gh resolution TEM characterization
showing the expected shift along the c-direction at the IDB. 109 Fr om these
observations, it is evident that in order to achieve an ab rupt IDB along the
periodicity of the AlN L PS, it is nece ssar y to alig n the IDBs with the (10 -10)
crystallographic plane. Note that the qualit y of the I DB will also depend on the
sidewall roughness of the patterne d AlN nucleation layer which is used to
selectively grow Al-polar AlN. For AlN LPS where the IDB is ali gned the (11 -20)
plane, where the IDB is not abrupt but rather displays a jigsaw pattern, the position
of the I DB is measured t o vary in a range thinner than 50 nm. While it is not ideal,
small changes in th e dut y c ycle of the periodic structure will not have a s ignificant
impact on conv ersion efficienc y , b ecoming mor e relevant as the pe riodicit y of th e
AlN L PS decreases.
90 La t eral Polar Structures
5.2 GaN Lateral Pola r Structures
In contrast to AlN bas ed L PS, numerous studi es on GaN based LPS h ave been
published. 78,84,85, 91,110 – 115 In pa rticular, the doctor al dissertation of S. Mita and M.
Hoffmann, 84,114 have a detailed descriptio n of studies on GaN based LPS with
periodicities
5 µm
using the s ame polarit y control process scheme as d escribed
in section 4. The focus o f this section includes pr omoting step flow grow t h at the N -
polar GaN surface to achieve smooth GaN LPS and avoid polarit y ove rgrowth for
GaN LPS with 1.2 µm periodicit y. It will be shown that the effec ts observed and
described in section 5.1 for AlN LPS, largel y parallel those obse rved in GaN LPS,
only shifted towards lower temperatures.
Like fo r AlN and as described in section s 4 and 5.1, patterned low temperature AlN
nucleation la y ers deposited on sapphire substrates are used to control the polarit y of
GaN epitaxial la y ers and fabricate GaN LPS, where the onl y difference lies in the
growth conditions for the GaN layer deposited on the patterned substrate. Afte r
vacuum annealing the p atterned substrate at 104 0 °C , followed b y H 2 anneal and
NH 3 anneal at 1040 °C (section 5.1), the GaN growth is started b y flowing 133
µmol /min of TEG and 0.6 slm of NH 3 ( equivalent to a V/ III ratio of 250) i n 6. 6 slm
of N 2 diluent gas. These growth conditions were chosen as a sta rting point , based on
results presented b y Hoffmann et al. 1 16 , which show similar growth rates for both
polarities and the smalles t polar domain hei ght difference. Figure 5-38 , sho ws AFM
image s of a 2.4 µm thick GaN LPS grown unde r the conditions described above.
While n o polarit y ove rgrowth is observed, and th e avera ge height values for the N -
polar and Ga -polar domains differ from each other b y 50 nm , the surface r oughness
RMS value for the N-polar domains is measured to be 85 nm. Such high valu es for
the surface roughness, would lead to significant scattering loss es in GaN LPS -based
waveguides, inhibiting their implementation for QPM applications. Note that while
the surface rou ghness of the GaN LPS is critical for L PS -based w aveguides, it has
no im plications for thick bulk GaN LPS whe re waveg uidin g modes need not be
considered.
GaN La t eral Polar Structures 91
Fig u re 5-38: AFM im age with corresponding height profile l ine-scans of a GaN LPS
grown at a V / III ratio of 250.
The surface roughness can be reduced, as wit h the AlN L PS, b y m echanical
polishing with alumina p articles of 0.3 µ m in size diss olved in D I water, s quirted on
a “TexMet P” soft pad platform. A sequ ence of o ptical DIC microscope images of a
GaN LPS after diffe rent polishing times is presented in Figure 5-39 .
Fig u re 5-39: DIC optical microscope images for a GaN L PS before (top le ft) and
after different polishing times.
92 La t eral Polar Structures
Polishing times longer t han 75 mi nutes did not result in a further reduction of the
surface roughness RMS value. The surface of a 75 minute long me chanically
polished GaN L PS sampl e was studied in more detail by AFM.
Fig u re 5-40: 75 min long mechanically poli shed GaN LPS with 0.3 µm alumina
particles in DI water solu tion.
Throug h mechanical polishing the GaN L PS surface roughness R MS value was
reduced from 66 nm to 25 nm. A constant heig ht differe n ce between the polar
domains of 40 nm is measured independent of further poli shing times. As suggested
for AlN LPS, the reason for the obtained hei ght differences after polishing, m a y be
related to polarity dependent etching du e to the pH of the poli shing solut ion. Further
polishing studies are necessar y to d etermine the mechanism leadin g to the polar
domain height dif ferences measured. Some parameters that could be modi fied
include, differe nt pH poli shing vehicles, the poli shing particles t ype and size and the
polishing pad. However, there are a variety of other parameters that can be studied.
In this work an alternative approach is pursued where the surface rou ghness of the
GaN LPS is reduced b y promoting step flow growth at the N-polar domains during
growth with the goa l to eliminate the n eed for p ost-processing steps to reduce the
GaN LPS surface roug hn ess (section 5.2.2).
5.2.1 N ano m eter Scale Ga N Lateral Polar Str uctures
For first order QPM SHG us ing GaN LPS in the UV-visi ble spectral range ,
periodicities below 10 µm are required ( Figure 5-41 ).
GaN La t eral Polar Structures 93
Fig u re 5-41: Calculated coherence length for bulk GaN as a function of fundament al
wavelength.
Figure 5-41 displa y s th e calculated coherenc e length for bulk GaN as a f unction of
the driving (fundamental) wave. The fundamental absorption ed ge of GaN limits
QPM SHG to photon energies above 3.47 eV (360 nm wavel en gth). Whil e QPM
SHG into the UV-C sp ectra is not accessible f or GaN LPS, there are interesting
potential applications including down conversion from InGaN-based high power
LD’s into the I R communication wavelengths. Th e lower coherence length limi t for
QPM SHG in GaN LPS, from 720 n m to 360 nm , requir es L P S with peri ods in the
order of 1.2 µm. Figure 5-42 shows AFM im ages of an intended 1.2 µ m GaN L PS ,
before and after KOH e tching. From th e surf ace morpholo g y , it is cl ear that Ga -
polar GaN has partiall y overgrown the N -polar GaN domains whi ch is then
confirmed b y the AFM height im age of the KOH etched sample. Moreover, tilted
cross-section SEM images of a 1.2 µm GaN LPS ( Figure 5-43 ) shows electron
charge accumulation in t he sapphire subst rate, localiz ed below the N -polar domains.
This is t y pi call y observed in epitaxial N -polar GaN and is likel y related t o the fact
the N-polar GaN is intrinsically conductive due to its hig h ox yg en incorporation in
contrast to the intrinsicall y insulating Ga -polar G aN. Th e obs erved polarit y
overgrowth for pe riodicities 𝛬 ~ 1.2 µ𝑚 parallels the observations made for 1.2 µm
periodic AlN LPS grown at Al-vapo r supe rsaturation values (
4
1 - 3x 1 0
) wh ere
similar grow th r ates for both polar domains was determined.
94 La t eral Polar Structures
Fig u re 5-42: (left) AFM amplitude image of a 1.2 µm periodic GaN L PS showing
N-polar GaN b eing over grown b y Ga -polar GaN . (ri ght) AFM hei ght image wh ere
the N-polar GaN areas that have been etched awa y are highlighted.
Fig u re 5 -43: Tilted cross -section S EM ima ge of a 1.2 µm GaN L PS b efore (left) and
after (right) we t etching in a KOH solution.
Clearly polarit y overgro wth is also a challenge i n GaN when the periodi city of the
GaN LPS is ~ 1.2 µ m. The Ga vapor super saturation value fo r the growth
conditions used for the GaN L PS describe d in Figure 5-43 is σ ~ 5 x 10 3 . In the nex t
section, it will be shown that for Ga vapor super saturation values σ ~ 10 0, polarity
overgrowth can be avoided and similar growth rates for both polar domains are
achieve d.
5.2.2 Pr om o ting Step Fl ow Growth f or Sm ooth GaN L PS
Numerous studies hav e demonstrated step flow growth of N -polar GaN. 1 01 – 104 This
has been achieved by in creasing the off-cut angle of the substrate, substituting the
nitroge n diluent gas with h ydrogen or b y increasing the V/ III ratio of the precursors
under nitro gen diluent gas, all resulting in a reduced su rface sup ersaturation
s
GaN La t eral Polar Structures 95
directl y or indirectly thr ough a reduction of the Ga vapor supersaturation
. As a
guide, Figure 5-44 and Figure 5-45 display the calculated G a vapor supersaturation
for multiple g rowth conditions with the goa l to illustrated gene ral tre nds when
varying specific growth parameters, such as tem perature, pressure, V/ III ratio and
exchanging the N 2 diluent ga s with H 2 .
Fig u re 5-44: C alculated Ga vapor supers aturation as a function of temper ature. For
comparison the values are calculated for H 2 and N 2 diluent gas (left) and for
different total reactor pressures (right).
Fig u re 5-45: Calculated Ga vapor supersaturation as a function of V/III r atio for
different tempera tu res under N 2 diluent gas (left) and under H 2 diluent gas (right).
To achieve a smooth surface morpholog y for N-p olar GaN thin films , in this work,
sapphire substrates with 2° off-cut towards the m -plane are used. Following the
standard substrate annealing steps in vacuum, H 2 and NH 3 (section 4.2 ) a GaN
nucleation la y er is deposit ed at 950 °C by flowing 133 µmol /min of TEG and 6 slm
of NH 3 under 1.2 slm of N 2 diluent ga s fo r 30 seconds at 20 Tor r total re actor
pressure. Th e GaN nu cleation la y er is annealed for 6 mi n at 1100 °C under the same
conditions, with the ex ce ption that no TEG is flown into the reactor. S ubsequentl y
the growth of G aN is commenced, where TEG is reintroduced into the reactor at 133
96 La t eral Polar Structures
µmol/min, the N 2 diluent gas is exchanged with 4 .2 slm of H 2 gas and th e ammonia
flow is decre ased to 3 slm to maintain a constant total flow rate of 7.2 slm. The
calculated Ga va po r supersaturation for these growth conditions is
100
.
Fig u re 5-46: AFM hei ght im age o f the surface of an N -pol ar GaN thi nfilm grow n
under the conditions described in the text. A scan area of 5 x 5 µm 2 (left) and 90 x
90 µm 2 (right) is prese nt ed.
Fig u re Figure 5-46 shows AFM h eight images of an N -polar GaN film grown using
the conditions described above. Clear step flow growth is observed and a surface
roughness RMS value of 2 nm over a 90 x 90 µm 2 area is achieved. Using the same
parameters for the grow t h of GaN L PS , leads to a significant improvem ent of the
surface roughens, where step flow grow th is clearl y observ ed and an RMS value of
36 nm over a 50 x 50 µm 2 area is achieved ( Figure 5-47 ).
Fig u re 5-47: AFM height (left) and amplitude (rig ht) ima ge of a G aN L P S grown at
relatively low Ga v apor supersaturation values (
100
).
GaN La t eral Polar Structures 97
Cross section SEM images of the GaN LPS show a fully coalesced film and equal
polar domain height at t he IDB’s ( Figure 5-48 ). Charge accumulation is observed
below the N-polar GaN domains, in agree m ent with previous observations . L ow
scattering loss es at the surface interface ar e expected for th e propa gating wave,
allowing for their implementaion in QPM SHG applications.
Fig u re 5-48: Cross section SEM image s displa y in g a GaN LPS grown at a Ga vapor
supersatura tion valu e of 100.
Furthermore, in contra st to 1.2 µm periodic Ga N L PS g rown at hig h Ga vapor
supersatura tion v alues ( Figure 5-42 ), at a Ga vapo r supersaturation v alue o f 100, no
polarity overgrowth is observed as evidenced from the AFM height images
presented in Figure 5 -49 for a 1.2 µm G aN LPS before and after etchin g in KOH
etching .
98 La t eral Polar Structures
Fig u re 5-49: AFM amplitude im ages (top) and h eight pro file linescans (bottom) of a
1.2 µm periodic GaN LPS grow n at a Ga vapor superseaturation of 100 before (left)
and after (KOH) e tchin g.
From Figure 5-49 it can be seen that the surface morphology of the Ga -polar
domains remains unaltered after submerging the sample in KOH for 3 minutes at
80 °C in a 3M conce ntration solution , while 320 nm to 520 nm of etch depth is
measured at the N-polar domains, confirming the polarit y of the respective domains.
In summar y, the GaN p olarity control process scheme, which utiliz es a patterned
low temperature AlN nucleation layer, is extended to the nanometer scale b y means
of laser interference li thograph y. A smooth surface of the GaN LPS is achieved b y
inducing step flow growth at the N-polar surface throu gh controllin g surface
supersatura tion. At the s ame time, polarit y overgrowth in 1.2 µm periodic GaN L PS
is prevented by growing at low supersaturation values, where step flow gro wth at the
N-polar domains is observed.
PVT Grown AlN Bulk Single Crystals 99
6 Point Defects in AlN
For an ideal wurtzite AlN single cr y stal with a b andgap ener gy of 6.2 eV and optical
phonon energies in the order of 0.1 eV, 12 ,117 transparenc y is ex pected in the 205 nm
– 12 µm spectral range. I n r ealit y , impurities are present in the AlN crystals, which
introduce b elow bandgap energy absor ption bands. These absorption bands are
detrimental (in some cases even hinder) to a pplications where transparenc y is
necessary, including UV L EDs desi gned in a ge o metry where the li ght is ex tracted
through the substrate. Moreover, unint entionall y introduced impurities, lead to
doping compens ation, below bandgap en erg y luminescent bands and a reduced
mobilit y as w ell as thermal conductivity, resulting in an infe rior performance of
AlN-based optoele ctronic devices. To im prove the optical and electrical properties
of the AlN cr y stals, it is critical to identif y the impuriti es prese nt in the cry s tal and
understand their incorpo ration mechanism. This chapter will foc us on id entify in g
point defec ts leadin g to below bandgap energy lumi nescent bands and a commonly
observed UV-C absorpti on band in AlN single cr ystals grown via ph y si cal vapor
transport (PVT). A novel approa ch is prese nt ed to determine the impurities t y pe a nd
concentrations in single cr y stal s, where P L, P LE, absorption spectra and SIMS data
is used in combination with a DFT based defec t s olver program , which accounts for
charge balance in the crystal and formation energies of the defec ts.
6.1 PVT Grown AlN Bu l k Single Crysta ls
6.1.1 H istorical Perspect ive
After ini tial reports, where AlN was incidentall y s y nthesized as a b y product when
attempting to p roduce aluminum carbide b y Briegleb and Geuther in 1 862 , 1 AlN
ga in ed si gnificant int erest in the earl y 1900’s because it could be obtained using
bauxite as the source material and dec omposi ng it in alkali solutions produced
aluminum oxide, aluminum hydroxide and ammonia , resulting in a series of patents
by Ottoka r Serpek 1 18,119 . However, the high ener gy r equired to prod uce AlN,
inhibited its commercialization as a pro cess to p roduce ammonia. It later regained
interest as a refractory material inert to reactions with aluminum at high
temperatures (~ 1800 °C). 120 Fa brication methods to obtain AlN single cry stals
continued to be developed, where aluminum powder was he ated up in a nitrogen
100 Point Defects in AlN
atmosphere le ading to th e reaction of aluminum vapor with nitrogen g as, forming a
high densit y of small Al N single cr ystals 12 0,121 T y pical heatin g methods to reach
temperatures above 1500 °C involved either arc lamp furnaces or resistive/inductive
heating of a graphite crucible 1 20 – 122 Further developments included the
implementation of finely grinded AlN powd er as the starting material in a
sublimation condensation pr ocess. 123 Seede d growth on AlN sing le cry s tals wa s
introduced resulting in increased single cr ystal siz e and reduced disl ocation
densities. 124,125 Addition all y , Herro et al. determined that seeded growth on the
nitroge n polar fac e results in a more stable growth mode and allows for a more
relaxed para m eter window. 126
Currently , state o f the art AlN bulk crystals are grown via ph y sical vapor transport
(PVT) in inductively heated vertical rea ctors, w here the N-polar sur face of AlN
single cr ystals are i mplemented as seeds. 1 27,128 For nitride based UV- C
optoelectronic d evices, single crystal AlN is the ideal substr ate material. AlN
substrates with disl ocation densities in the low ~ 10 3 cm -2 are availabl e. 1 27,128 The
latter and the low lattic e mismatch to th at of high aluminum content AlGaN thi n
films of the hi ghest qu ali ty . 129 However, point defects in the crystal le ad to li ght
absorption at energies l ower than that of the bandgap ener gy which hinder their
implementation in applic ations where transparency is necessar y . In early studies the
measured absorption and luminescence bands hav e been attributed to ox y gen. 130,13 1
Strassburg et al. and Bickermann et al., in separate studies, performed glow
discharge mass spe ctrometry analysis on various PVT grown AlN sin gle cr y stals
and concluded that ox yg en alone cannot explain the absorption and luminescent
bands present in such sa mples. 132,133 Carbon impurities in concentrations similar to
that of ox yge n were consistentl y measu red in th e AlN single cr y st als indic ating th at
carbon must pla y a significant role in the optical properties of the cry s tals. A
particularly stron g absorption band centered at 4.7 eV is commonl y m easured in
PVT grown AlN sin gle cr y stals ( Figure 6-3 ). 130,131,134 – 139 The presence of
photoluminescence peaks at 2.7 eV and 3.9 eV is observed in samples displaying th e
strong absorption band at 4.7 eV ( Figure 6-3 ). 134 – 137 The absorption band centered at
4.7 eV with an onset at 4.2 eV is onl y observed in AlN cr ystals w hich contain
carbon c on centrations higher than or comparable to the amount of oxyge n and
silicon. 134 – 137,1 39 Hartmann et al determined that the ox y gen to carbon con centration
ratio needs to be equal or large r than 3 in orde r for the absorption band to be
PVT Grown AlN Bulk Single Crystals 101
completely suppressed. Additionally, the absorption coefficie nt at 4.7 eV decreases
with total concentra tion of C + O for a given concentration ratio of the t wo. 128,135
These results clearl y sh ow that c arbon impurities are present in PVT grown AlN
single c r y st als a t sig nificant concentrations and lea d to the commonly observed
absorption band at 4.7 eV. This is in contrast to t he conclusions mad e b y Sla ck et al
(2002) whe re the in crease of the absorption coefficient at 4.7 eV is attributed to an
increase in the ox ygen i mpurities. 131 However, in the latter stud y no oth er extrinsic
impurities are considered such as carbon, and the ox y gen concentration
measurements are limite d to one sample. Collazo et al , attribute thi s absor ption band
to the prese nce of negatively ionized carbon im purities which incorpora tes as a
nitroge n subst itutional ( C N - ) 135 . This conclusion is based on the calculations of
defect formation energies as well as thermod ynamic and optical transitions using
density functional theory (DFT) which are in agreement with absorption and
photoluminescence spectra as well as secondar y ion mass sp ectroscopy (SIMS)
measurements. 135, 136
6.1.2 A bsorption, PL an d PLE Charact erization
To identify point defect s, it is necessary to con sider the form ation energy of all
plausible point defects and defect complexes , while accounting fo r charge b alance
conserva tion. According to Van de Walle and N eugebauer, the chemical potentials
can be related to p artial pressures when growth conditions are ne ar equili brium. 1 40
This assumption is valid for AlN sin gle cr ystals grown via ph y sical vapor transport
where growth temperatures ar e near the decomposition point of AlN. The partial
vapor pr essure of aluminum over AlN at 2100 °C under t ypic al grow th conditions is
in the order of 50 mbar which is clos e to the Al v apor pressure over liquid aluminum
of 120 mbar at the same temperature. 141,142 Consequently, growth is expected to take
place under aluminum rich conditions and accordingl y assumed for the calculation
of the formation e nerg y of point defects in P VT grown AlN. A more detailed
description on how the formation energies are calculated is discussed in section
2.3.1. If the concentratio n of the main impurities ( i.e. carbon, ox yge n and silicon in
PVT grow n AlN) in the cr ystal is known (i.e. via S I MS or GDMS), it is possible to
estimate the concentration and t ype of point defects and defect complexes, based on
charge balance conservation and their form ation energ y. These calculations were
102 Point Defects in AlN
performed in the research group o f Dr. I rving at North Carolina S tate Uni versity and
details on the methodology used for these calculations are published in part in the
doctoral dissertation of B. Gaddy, 57 and the remaining details will be published in
the doctoral dissertation of Joshua Harris. The larger the amount of possible point
defects and defect complexes that are consi dered, the more representative the result
of the actual AlN cr y stal. For the calculated def ect concentrations in this work, a
bulk of defect complexes are considered including, native point defects ,
substitutional carbon, oxy gen and silicon in both Al and N latti ce sites, and all first
nearest neighbor complexes including the latter mentioned point defects (i.e. C N -C Al ,
C N -O Al , Si Al -O N , O N -V Al , etc…). The calculated po int defect concentrations are listed
in Table 6-1 , where a fix ed concentra tion of 8 x 10 18 cm -3 o x ygen, 7 x 10 18 cm -3
silicon and 2 x 10 19 cm -3 carbon is assumed as measured b y S IMS. O nl y defect
concentrations above 1 x 10 17 cm -3 are listed since lower concentrations are not
expected to contribute significantl y to the optical properties o f the cr y st al compare d
to defects in con centrations as hi gh as 1 x 10 19 cm -3 . The r esults indicate that the
main compensator for carbon point defects are ox ygen and nitro ge n vacancies,
further supportin g the conclusions made by Gaddy et al. 136 which attributed the 2.7
eV Luminescence to a D AP transition invol ving carbon and a nitro gen vac ancy . The
conclusion b y Gadd y e t al. is based on DFT calc ulations that show a relatively low
formation energy of the nitrogen va canc y c om pared to other impurities and its
charge compensa tin g nature to the ionized carbon impurity. 136
Table 6-1: Calculated p oint defect con centration ac counting for charge balance
conserva tion and for a given measured concentration of C, O and Si.
C N
V N
O N
Si Al
Si Al + C N
Defect Concentration
( x 10 19 /cm 3 )
1.98
0.6
0.8
0.6
0.06
Theory predicts the presence of carbon on a nitrogen sit e (C N ), nitrogen vacancies
(V N ), sil icon on an aluminum site (Si Al ), ox y gen on a nit rogen site (O N ) and a
complex between carbon on a nitroge n site and silicon on an aluminum site (Si Al +
C N ). The c alculated formation energ y for the dominant point defec ts a nd defect
complexes are displ ayed in Figure 6-1 as a function of Fermi level energ y . The
charge state o f the defect is represented b y the slope and onl y th e ch arge state with
PVT Grown AlN Bulk Single Crystals 103
the lowest energy of for mation for a particular defect at a given Fermi level ene rg y
is displayed.
Fig u re 6-1: Point defect formation energy as a function of fermi level energy for
various likely point defects present in PVT grown AlN.
From Figure 6-1 , t he t hermod y namic transition energies fo r the respec tive point
defects can be extracted, which correspond to the ener gy values, where c hanges in
the slope of the formation energy are observed. Perhaps fo r a more intuitive
perspec tive, the thermo dyna mic tr ansition energies c an be represented as energy
states within the bandgap as illustrated in Figure 6-2 .
Fig u re 6 -2: Schematic displa y in g the thermodynamic transition ene rg y sat es for th e
respec tive point defect s, as horizontal li nes, refe renced to the valence band
maximu m.
104 Point Defects in AlN
In Figure 6 -2 a bandgap energy of 6.1 eV is assumed for AlN and the c alculated
thermody n amic transition ener gies for C N - C N 0 and V N 0 V N - are 1.8 1 eV and
5.02 eV above the valence band maximum (VBM) respectivel y . From F igure 6-2 it
is clear that the onl y ba nd to defect transition wit h an en erg y difference close to 4.2
eV is the transition invol ving C N - to C N 0 and the conduction band minimum (CBM).
Figure 6-3 displa ys t he absorption coefficient spectra overlapped with the
photoluminescence sp ectra of the studied PVT grown AlN sin gle cry s tal . An
absorption band centered at 4.7 eV is revealed with an onset at 4.2 eV. The
absorption coefficient plateaus at 4.5 eV unti l 4.8 eV wh e re it then d ecreases until
5.1 eV. For photon energies l arger than 5.1 eV the absorption coefficient increases
again. An ex citation energy of 6.4 eV is utili zed to record the photol uminesce n ce
spectra displa y ed in Fig ure 6-3 . Two main luminescence bands centered at 3.9 eV
and 2.7 eV are obs erved. W hen fitti ng the as y m metric band centered at 2.7 eV an
overlapping lower ene rgy lumines cence band centered at 2.5 eV is estimated. An
additional luminescent band centered at 4.5 eV is also present, wh ere th e i ntensity is
significa ntl y smaller in magnitude and will be discussed in more detail later in this
section.
Fig u re 6-3: Photoluminescence spectra (black) overlapped with the absorption
spectra (red) of a PVT grown AlN single cry stal.
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
10 3
10 4
10 5 PL spectra
Fit Peak at 2.7 eV
Fit Peak at 2.5 eV
Cumulative Fit Peak
PL intensity (arb. u.)
Photon energy (eV)
Excitation energ y: 6.4 eV
Zero phonon line transition
C -
N + 4.2 eV photon --> C 0
N + e
C 0
N + e --> 4.2 eV photon + C -
N
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
0
200
400
600
800
1000
1200
Absorption spectra
Photon energy (eV)
Absorption coefficient (cm -1 )
PVT Grown AlN Bulk Single Crystals 105
The minim um photon ener gy for the excitation of a point de fect in a particular
charged state and the maximum photon ene rg y for the respective radiative
recombination o f the generated electron hol e p air are ex pected to be equal to the
thermody n amic transitio n energ y o f the point de fect and it is t y picall y addressed as
the zero phonon line (ZPL) energ y (section 2.3.2 and Figure 2-7 ). 67 According to the
Franck-Condon approximation, the probabilit y for the optoelec tronic transition at
this energy is proportional to the overlap between the 0 th quantum number
vibrational wave functions of the ini tial and final states at their e quilibrium
coordinate position. 65 For differing equilibrium coordinate positi ons of the initial
and final state, the vibrational wave function overlap is expected to be small
between the two char ged states of a poin t defect in AlN, leading to a significantly
reduced emission and absorption probability at this energ y . When comparin g the
absorption with the PL spectra in Figure 6-3 , indeed the estimated high energ y edge
of the P L band centered at 3.9 eV matches th e calculated thermodynamic transition
energy of 4.2 eV for the C N - point defect as w ell as the onset of the absorption band
centered at 4.7 e V. I n spite of these strong l y suggestive observations, it is not
possible to make a defi nite conclusion based o n the above band gap excitation P L
spectra and th e measured absorption spectra du e to the large number o f possible
defects and their overlapping electro -optical transition energies. To prec isel y
determine the electro-optical d y n amics between the luminescence and a bsorption
centers, photoluminescence excitation spectrosc op y me asurements were conducted.
In Figure 6-4 a color coded lo garithmic intensit y contour map is shown where the
horizontal axis represents the dete ction ener gy o f the sample ’s photol uminescence
ranging from 1.95 eV to 4.5 eV while the vertical axis describes the energy of the
excitation light source which spans from 3.6 eV to 5.5 eV. The P LE spectra shows
the onset of the luminescence band centered a t 3.9 eV at an ex citation energy of 4.2
eV. This is in excellent agreement with the model where C N - is the point defect
responsible for the UV absorption band as well as the luminescence band centered at
3.9 eV. This is more e asil y observed in Figure 6-5 where single spectra were
extracted from the contour map. The vertical li nes in Figure 6-4 correspond to the
red P LE curves in Figure 6-5 while the horizontal li nes in Figure 6-4 are display ed
in black/gre y curves in Figure 6-5 and represent the P L spe ctra for a given
excitation energy . L ooki ng at the P LE spectra with the detection energy fix ed at
3.93 eV in Figure 6-5 , an exponential increase in the intensit y is observed when the
106 Point Defects in AlN
excitation energ y reaches 4.2 eV and p eaks at 4.5 eV wh ere it plateaus. Furthermore
the P L spectra with 4.5 eV excitation energy sho ws that the high en ergy edge of the
luminescence b and centered at 3.9 eV matches the onset of the P LE sp ectra with
3.93 eV detec tion ener gy a t 4.2 eV. This is ex pected unde r the Frank -Condon
approximation as previousl y des cribed. These r esults are direct evidence li nking the
3.9 eV P L b and and t he 4.7 eV abso rption band to a common de fect with a
thermody n amic transition energ y of 4.2 eV.
Fig u re 6-4: Color coded logarithmic intensit y 2 D map photoluminescence ex citation
spectroscopy measu rements of an Al N single crystal recorde d at 5 K. The vertical
lines correspond to P LE spectra for a fix ed detection energy and are displa y ed as red
curves in Figure 6-5. Horizontal lines correspond to P L spectra at a fix ed excitation
energy and are displayed in Figure 6-5 as black curves.
PVT Grown AlN Bulk Single Crystals 107
Fig u re 6-5: Photoluminescence spectra (black) for various excitation ene rgies,
overlapped with photoluminescence excitation spe ctra ( red) for various detec tion
energies.
The P L E m easurements show that C N - is also involved in the radiative transition
leading to the luminescence band centered at 2.7 eV. This is evident from the PL E
curve in Figure 6-5 with fixed detection energ y at 2.95 eV which shows an identical
excitation channel to that of the 3.9 eV luminesc ence band. The d etection energ y o f
this PLE spectr a was purposely shifted from the peak emission at 2.7 eV to 2.95 eV
in order to avoid an y intensit y ori ginatin g from the overlapping lum inescence
sideband with pea k emi ssion at 2.5 e V a s is o bserved in the PLE sp ectra with
detection energy at 2.75 eV. The onset excitation energy for th e 2.5 eV
luminescence band is me asured at 3.6 eV excitation energ y , obtained from the PL E
spectra with detection en ergy at 2.45 eV. The origin of this luminescence band is not
clear and further studies are n ecessar y . From the PL spe ctra in Figure 6-5 with 4.5
eV ex citation energy, the ZPL energy of the 2 .7 eV lum inescent band is estimated at
3.1 eV. Assuming the nature of this PL b and to be a dono r acceptor pa ir (DAP)
transition involving carbon, a deep donor state at 5.0 eV above the valence band
maximum is predicted based on the energy l evel of the C N - acceptor state at 1.9 eV
2.0 2.5 3.0 3.5 4.0 4.5 5.0
10 3
10 4
10 5
10 6
10 7
10 8
10 3
10 4
10 5
10 6
10 7
10 8
Carbon inv olving
DAP transition
PL at 5 K
Excitation energy :
3.93 eV
2.95 eV
2.75 eV
2.45 eV
4.5 eV
4.3 eV
4.2 eV
PLE intensity (arb. un its)
PL intensity (arb. units)
Detection ener gy (eV)
PLE at 5 K
Detection energ y:
Zero phono n line (4.2 eV)
C N
- --> C N
0
C N
0 --> C N
-
b) 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Excitation energ y (eV)
108 Point Defects in AlN
above the VBM. From t he thermod y namic transi tion energy diagram ( Fi gure 6-2 )
this is in good agreement with the calculated the rmod y namic transition energ y state
at 5.0 e V for th e nitro gen vacanc y (V N ) from V N + to V N 0 . F urtherm ore, pow er
dependent P L measurem ents reveal the presence of a luminescence band c entered at
4.5 eV ( Figure 6-6 ). As the pulse peak power d ensit y is increased and defect states
are saturated a P L ba nd centered at 4.5 eV appears , where the highest energy ed ge of
th is band is estimated at 5.0 eV in agreement wit h the predicted deep don or ener gy
state involved in the DAP luminescence ba nd centered at 2.7 eV.
Fig u re 6-6: Power dependent photolum inescence measure ments for abov e bandgap
excitation.
In summary, the UV abs orption band at 4.7 eV a nd the luminescence bands at 2.7
eV and 3.9 eV are linke d to the same defect stat e with a thermod ynamic transition
energy o f 4.2 eV throu gh photoluminescenc e excitation spectroscop y (P LE). Power
dependent photoluminescence (P L) measurements revea l the presence of an energy
state within the bandgap with a 5.0 eV th ermod y n amic transition energ y in
agreement with the predicted energy state for the donor ac ceptor pair transition
(DAP) leading to the 2.7 eV luminescence b and and the calculated thermod yna mic
transition energ y for the nitrogen vacancy (V N ). A novel approach is presented to
determine the impuriti es ty pe and concentrations in the cr y stal where PL , P LE,
absorption spectra and S IMS data is used in com bination with a DFT bas ed defect
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
10 3
10 4
10 5
C 0 + D 0 -->
3.1 eV photon + C - + D +
Zero phonon lin e
transition energy @ RT
D 0 --> 5.0 eV photon + D +
4.6 4.8 5.0 5.2
Photon energy (eV)
Zero phonon line
transition energy
20 KW/cm 2
200 KW/cm 2
800 KW/cm 2
80 MW/cm 2
Intensity (arb.u.)
Photon energy (eV)
Excitation Energy: 6 .4 eV
Pulse peak power de nsity:
700 600 500 400 300
Wavelength (nm)
PL @ RT
PVT Grown AlN Bulk Single Crystals 109
solver program which accounts for charge b alance in the cry stal and formation
energies of the defec ts.
6.1.3 H igh Tem peratu re A bsorption Spec tra
As part of m y PhD program, I was responsible for building a setup for temperature
dependence transmission spectroscopy, allowi ng for tempe ratures from room
temperature up to at least 900 °C. A detailed d escription of the s etup i s given in
section 3.1.3. The setup however, is not limited to transmissi on spectroscop y , but
can also be used for tempera tur e dependent photoluminescence spec tros copy .
6.1.3.1 GaN Epitaxial Layers
As an ini tial test of the ex perimental setup and to confirm the band gap value of GaN
near growth temperatures, a GaN epitaxial film deposited on a sapphire substrate
was characterized. One interest in measurin g the absorption edge ener gy of GaN
near growth temperatur es (1040 °C), was in establishing the viabilit y to use an
InGaN laser diodes with 445 nm (2.8 eV) emission waveleng th (energy) for point
defect reduc tion via defe ct quasi Fermi level control. 1 43 – 145 Figure 6-7 display s the
measured lamp spectra when placing a GaN thi n film sample in the optical path,
where the temperature of the GaN sample is varied in the rang e f rom room
temperature to 874 °C . The interference fringes expected for a het eroepitaxial thin
film are observe d and the a bsorption edge at room tempera ture near 3.4 eV i s
measured. From the int erference fringes a film thi ckness of 2 µm is calculated, in
agreement with growth rate calculations. Using t he film thickness, the tra nsmi ssion
spectra and the dispersion relation for GaN, the absorption coefficient can be
calculated and plotted for different temperatures as a function of wav elength ( Figure
6-8 ).
110 Point Defects in AlN
Fig u re 6-7 : Spec tra of a UV-e nh anced Xenon Ar c lamp measure d after passing
through an epitaxial GaN layer deposited on a sap phire substrate as a function of the
GaN temperature .
Fig u re 6 -8: Tempe rature d ependence of absorption coefficient spectra . The spectr a
are not corrected f o r reflection.
PVT Grown AlN Bulk Single Crystals 111
From Figure 6-8 a clear red -shift of the absorption edge can b e observed fo r
increasing temperature following th e V arshni-Shift. 146 An absorption c oefficient
value > 1.6 x 10 5 cm -1 is measured for abov e band gap photon energies. The
measured constant valu e at 1.7 x 10 5 cm -1 is a measurement artifact due to the
background noise level of the detector, indicating the light intensit y fro m the lamp
source was completel y absorbed and does not r epresent a re al absorption coefficient
value. To precisel y determine the GaN temperature dep endent band gap ener gy, the
Tauc relation can be plott ed ( Figure 6-9 ), from which the bandgap energ y can be
extracted from the x-ax is intersec t with ext rapolated li near fit near the band
edge. 147,148
Fig u re 6-9: T auc relation for temperature dependent transmission spectra measured
for a GaN epita x ial thinfilm.
112 Point Defects in AlN
Fig u re 6-10: Bandgap ener gy of a GaN epitaxial film as a function of temperature,
compared with the Varshni model fitted with literature values.
Once the bandgap energy has been determined for each temperature spectra, the
values can be plotted a s a function of temperature. The measured values are in
excellent agreement with the Varshni energy shift model and a gree with previousl y
experimentally established values. A band gap e nergy of 2.77 eV is calculated at
growth temperatures (1040 °C), where an absorp tion coefficient α > 1.6 x 10 5 cm - 1
demonstrating th at a 445 nm (2.8 eV) emissi on wavelength InGaN laser diode can
be used for carrier generation by photoexcitation.
6.1.3.2 PVT AlN Single Crystals
Having established that t he experimental setup is well calibrated, an ex p eriment was
conducted where bulk AlN single cr y stals grown via PVT were investigated. In the
previous section (section 6.1.2), the point defects in AlN single cry st als exhibiting a
strong absorption band i n the UV-C spectra and a high carbon concentration were
investigated. It has been found that by introduci ng silicon and/or ox ygen such that
their concentration exceeds that of carbon, the UV-C absorption ban d can be
suppressed. 128,137,14 9 DFT calculations, have pr edicted that silicon and ox yg en
substitutional point defects have a stable DX - ener gy state which the y po pulate for
Fermi level energies near the conduction band, which is the case for AlN cr y stals
with higher ox y gen and/or silicon concentrations than c arbon. I t has b een argued
PVT Grown AlN Bulk Single Crystals 113
that these states can act as long-lived traps inhibiting the recombination of photo -
ge n erated c arriers f rom t he C N - point defect back to its original state, and thereby
quenching the UV-C abs orption band. In this ex periment a PVT grown A lN single
crystal ex hibiting UV -C transpare nc y with a highe r ox y gen and/or silicon
concentration than carbon, is heated up to 900 °C with the purpose of decreasing the
lifetime of the possible long li ved DX - trap state. If su ch trap states are present in the
crystal, it is expected that with increasing tempe rature the repopulation r ate of the
C N - will incr ease exponentially with temperature and there b y g ivin g rise to the
commonly observed UV-C absorption band. For a silicon in aluminum subst itutional
point defect, an ionization energ y E b of 0.25 eV has been determine d for t he Si DX -
and 0.34 eV calculated for the O DX - state. 57, 150 For these ionization energies, an
increase in temperature f rom 293 K to 1070 K corresponds to an in creased transition
probability by a factor of 1.3 x 10 3 for silicon and 1.8 x 10 4 for ox y gen.
Fig u re 6-11 : Absorption spectra for an AlN s ingle cr ystal with higher ox y gen
concentration than carbon for diff erent temper atures in the ran ge from 295 K to
1063 K. For comparison a “UV non - transparent” sample containing higher carbon
impurities than ox y gen and silicon is displa y ed.
Figure 6-11 displays the absorption spectra for a n AlN single crystal with a higher
ox y gen concentration than carbon. It is clear that t he UV-C absorption band is not
present in the AlN cr ystal with higher ox ygen c oncentration and does n ot appear
with increasing temperature. The se results indicate that a long lived oxyg en or
silicon DX like trap st ate is not responsible for the suppression of the UV - C
114 Point Defects in AlN
absorption band, which is measured in cr ystals w ith a higher carbon concentration
than ox ygen and silicon. Moreover, the r esult su ggests that for hi gh ox ygen and/or
silicon conce ntr ations, where a Fermi level energy n ear the conduction band is
expected, the formation energ y for a diff erent carbon point defect configuration is
more favorable than C N - . However, D FT calculati ons of the formation energ y for
nearest neighbor complexes involving carbon and substitutional point defects in both
lattice sit es, predict hi gher formation energies. Second nearest n ei ghbor complexes
including c arbon remain a possibilit y among a vast pool of possible point defects,
however no DFT calcula t ions for such point defects have been performed to date.
Fig u re 6-12: Abso rption spectra for a n AlN single cr y stal with a higher carbon
concentration than ox ygen and silicon for a temperature range from 296 K to 1070
K.
The absorption spectra f or various temperatures for an AlN singl e crystal with a
higher carbon concentration than ox yge n and silicon, is display ed in Figure 6-12 . At
the high energy edge of t he absorption spectra, the tail of the fund amental absorption
edge is observed and the corresponding Varshni li ke red shift, where a bandgap
energy of 5.2 e V at 1070 K is calculated when using li terature par ameters for the
Varshni shift. 151 A model ex plaining the inc rease in the FWHM of the width of the
absorption band as well as th e broadening towards lower energies of the absorption
PVT Grown AlN Bulk Single Crystals 115
onset is described in the literature . 59 Otherw ise, no significant ch ange in the
absorption band is observed.
In summar y , a transmission spectroscop y s etup was buil t capable of measuring at
temperatures, at least, up to 900 °C. The bandg ap energy of GaN was me asured up
to 874 °C, where the parameters obtained from the measurements for the Vars hni
shift model are in ag reement with li terature. Finall y , hi gh temperature a bsorption
spectra of AlN singl e cr ystals with a higher ox y gen and/or sil icon concentration than
carbon, indicate long liv ed DX - like states are no t responsible for the quenching o f
the UV-C absorption band.
116 UV Laser L i ght as Second Harmonic Generation
7 UV Laser Light as Second Harmonic Generation
La s ers emitting in the ultraviolet spectrum are desired for a variety of
applications, including photochemical labeling, bio -sensin g, nanolithograph y ,
medical sur gery, micromachini ng, Bragg grating s, and man y others. 97 Available UV
laser s ystems are expensive inefficient, stationar y, large, and require frequent
maintenance . Althou gh man y advances have been made towar d the fabrication of
electrically injected AlGaN semiconductor based UV -C laser diodes, doping, c arrier
injection, and defect control are sti ll challenging. 31,143 An alternative approach to
compact UV-C lasers is to exploit frequency doubling via second harmonic
ge n eration (SHG). AlN is an excellent candidat e for the generation of U V-C laser
light via SHG and a variet y of oth er nonlinear opti cal applications due to its large
second order nonlinear susceptibilit y coefficient along the c -axis of 7.7 pm/V, high
thermal condu ctivity (320 W /mK), and a wide tr anspa renc y window (20 5 nm and
above). 13 2,152,153 This e nables the possibilit y for high conversion efficiency, high
power damage threshol d and wide wav elength tunabilit y . Birefringence phase
matching is not accessible in III-Nitrides and other phase matchin g te chniques need
to be emplo y ed. In thi s chapter, SHG results in AlN waveguides using modal
dispersion phase matching (MDPM) and qu asi phase matchin g ( QPM) are
presented.
7.1 Mod al Phase Matc hed SHG
An alternative approach t o birefringence phase ma tching, which is not accessible for
III -Nitrides, is modal dispersion phase matching, as described in section (2.1.3).
Some benefits for employing this phase matchin g te chnique, include the facility to
fabricate, high qu alit y single polar AlN waveguid es, onl y limited b y litho graphy and
dry etching, which are mature technologies. The drawback of this phase matching
technique, lies in the lo wer co nversion efficiency due to t y picall y small overlap of
the wave-guided modes for the fundamental and second harmonic waves (t y picall y
in single digit pe rcent). 47 Figure 7-1 displ a y s a DIC optic al microscope image of
typica l Al -pol ar AlN waveguides, where the AlN film was deposited via MOCVD
as described in section 4.2 and where th e waveguides were fabricated vi a standard
masked photolithography using negative photoresist and reactive ion etchin g in BCl 3
and Cl 2 .
Modal Phase Matche d S HG 117
Fig u re 7-1: DIC microscope image of Al-polar AlN waveguides for MDPM S HG.
The calculated dispe rsion relation for the different waveguide mode s of the
fundamental and s econd harmonic waves in 10 µ m wide and 550 nm thick Al -polar
AlN wav eguides w ere re ported in a publication by T roha et al. and are displa y ed in.
MDPM SHG measurements in the UV spectra l ra nge are displa y ed.
Fig u re 7 -2: Dispersion relation of the fundamental and second harmonic waveguide
modes for a 10 µm wide and 550 nm thi ck Al -po lar AlN waveguide, taken from a
publication by Tr oh a et al.. 47
The corresponding MDPM SHG measurements are displa yed in Figure 7- 3 where a
good agreement between theory and e x periment is measured.
118 UV Laser L i ght as Second Harmonic Generation
Fig u re 7-3: MDPM SHG measurements using a 10 µm wide and 550 nm thi ck Al -
polar AlN waveguide. 47
More details on the MDPM SHG measurements are des cribed b y Troha e t al. 47 and
additional MDPM measurements including in GaN waveguides, will be published in
her doctoral dissertation.
These results demonstrate the fe asibility to empl o y AlN waveguides for UV laser
light generation down to 305 nm, and where theoretical calculations indicate that
MDPM SHG in the UV- C below 300 nm should be allowed in principle.
7.2 Quasi Ph ase Matc hed SHG in AlN LPS Wav eguide s
Quasi-phase matching, where the se cond order nonlinear coefficient of non -
centrosymmetric cr ystals is periodically or aperiodicall y modulated, offers the
widest range of accessible nonlinear int erac ti ons, is the most efficient phase
matching technique an d allows the use of nonlinear m aterials with weak
birefringe n ce. 48 – 50,15 4 This technique had been limi ted due to diffi culties in
fabricating periodicall y inverted nonli near cr ystals with period icities down to the
nanometer scale, and in achieving hi gh quality int erfaces betw een th e inverted
domains. After remarkable advances in lithography and processing technolog y since
the late 1970’s, periodicall y pol ed fe rroelectric oxide crystals are now produced on a
daily bases and periods as short as 1.4 µ m are achieved. 155 – 159 A wealth of quasi-
phase match ed nonlinear interactions h ave been demonstrated using such
crystals. 160 – 163 For integrated optics, thin wave-guiding la y ers, in the order o f
hundreds of nanometers, which can be obta ined using the well -established
semiconductor thinfilm technology are r equired. Progress is being made in
ferroelec tri c oxides to meet these d emands, however it still remains a challenge 164 .
Quasi Phase Matched SHG in AlN L PS Wave guides 119
The III-V compound semiconductors ar e the ob vious alterna tive, since t he y alread y
make up a significant portion of electronics and optoelectronics, and hav e excellent
nonlinear optical proper ties. Being non-ferroele ctric, the main challenge s for this
material s ystem lies in periodic all y inverting the cr y st al while maintaining high
quality interfaces between the alternating polar d omains and achieving an opticall y
smooth surface. AlGaAs has pione ered the fie ld with all -epitaxial periodically
oriented G aAs based waveguides b ein g demons trated nearl y two decades ago b y
Ebert et al. 165 The nonlinear prop erties of III-Arsenides excel in the 1 – 16 µm
spectral r egion where, using thick (> 450 µm) periodically poled GaAs cr y st als,
second-, sum - and difference-frequenc y gene ration have been demonstrated with
efficie n cies up to 50% and an output average power reaching 7.7 W at 100 kHz
pulse repletion rate. 16 6,167 The materi al s y stem is limit ed to photon energies below 2
eV and still faces chall enges in efficient w aveguiding structures inhibiting their
implementation in integrated optics. The III-Nitr ides will provide semiconductor -
based quasi-phase matching structures which c an cover nonli near optical processes
from 14 µm down to 0. 2 µm. 97,112,113 This range covers all wav elength s used in
telecommunication and allows for fre qu ency c o nversion fr om/to waveleng ths as
short as 205 nm which si gnificantly redu ces the siz e li mitation for photonic circuits.
Already, efficiency, ther mal stabilit y and high power are movin g the semiconducto r
industry towa rds AlGaN based electronic devi ces. 168,169 Simultaneously, AlGaInN-
based optoelec t ronics are reaching maturit y and have revolutionized the lighting
industry. I t is reasonable to envision, AlGa InN-based integrated optics where
periodically poled nitride-based waveguides serve as quasi-ph ase matching
structures for nonline ar optical interactions.
In this section, quasi-phase matched UV second harmonic generation at 34 4 nm and
386 nm, using 500 nm and 250 nm thick, and 10 µm periodic AlN lateral pol ar
structure-based waveguides, respectivel y , is demonstrated for the first time. These
results mark the beginning of III-Nitride based waveguide structures for quasi phase
matching applications and is a step towards the r ealization of on -chip and chip- to -
chip optical interconnects.
120 UV Laser L i ght as Second Harmonic Generation
7.2.1 10 µm Perio dicity
The 3D plot ted AFM image in Figure 7-4 shows a small section of the waveg uides
which were etched into a 10 µm periodic AlN L PS grown at 1500 °C (section 5.1.3,
Figure 5-29 ). The waveguides are 500-550 nm thick and ~4 µm wide. The measured
average RMS value f or t he waveguides surface is 11 nm.
Fig u re 7-4: 3D AFM ima ge with color -coated h eight scale of 500 nm - 550 nm thick
and 4 µm wide AlN L PS -based waveguides.
Using a computer code developed b y T. Troha, the dispersion relatio n for the
fundamental and secon d harmonic waves a re calculated for a given waveguide
dimension. Each side of equation (5.1.2) is then plotted to illustrate the conditions
for which QPM is ex pected ( Figure 7-5 ). Theory pr edicts 3 rd and 5 th order QPM
SHG at 340 nm and 473 nm respectively for the TM 0 modes of the fundame ntal and
second harmonic wa ve s in a 10 µm periodic 540 nm thick AlN LPS -based
waveguide and 5 th and 7 th order QPM S HG at 377 nm and 453 nm respectively for a
10 µ m periodic 220 nm thi ck AlN LPS-based waveguide. The model utili zed to
calculate the QPM conditions is according to the theor y described in section 2.1.
Quasi Phase Matched SHG in AlN L PS Wave guides 121
Fig u re 7-5: Dispersion relation for the fundamental (red) and second harmonic
(purple) TM00 wave mode for a 220 nm thick w aveguide.
Fig u re 7-6 shows a top view 2D gra y scale scatterin g intensit y image of the laser
light traveling throu gh a 1 mm long AlN LPS -base d wave guide wit h 10 µm
periodicity . Strong scattering is observed at the coupli ng facet and some appreciable
amount of scattering is evident at the out -coupling f acet. The scattering intensit y
profile along the waveguide is display ed in Figure 7-6 (bottom) for a 100 µm
segment of the 1 mm long waveguide. An obviou s periodic pattern in the scattering
intensity profile along the waveguide is observed matching the Al N LPS periodicity
of 10 µm, which highlights the importance of ach ieving a smooth waveguide surface
122 UV Laser L i ght as Second Harmonic Generation
to minimize scattering losses. The remaining intensit y of the fundamental laser li ght
at the out-coupling facet, is filtered out and the S HG light laser li ght is guided to the
detection sy st em.
Fig u re 7 -6:2D top view gra y scale scattering int ensit y profile of the fundamental
laser light propagating through the 10 µ m periodic AlN LPS -based waveguide
(Top). 1D scattering intensity p rofile fo r a line- scan section alon g the waveguide
surface.
QPM SHG is demonstrated at 344 nm and 471 nm ( Figure 7-7 ) for the 500 nm –
550 nm thick AlN L PS – based wave guide and at 386 nm and 452 nm ( Figure 7-8 )
for the 200 nm – 250 nm thick AlN L PS -based waveguide, in agree m ent with the
calculated v alues ( Figure 7-5 ). The LPS structures will be characteriz ed and
analy zed in more detail, where th e results wi ll be published in the doctoral
dissertation of Tinkara Troha. Sli ght difference s between theory and ex periment
may arise from the difficult y to define a waveguide thickness d ue to the surface
roughness, and from th e planar waveguide approximation, which neglects the
propagation of lat eral modes arising from the finite width of the waveguide . More
significa ntl y , according to theory, second ha rmonic generation for wavelengths
above 375 nm is not accessible throu gh MDP M for the f abricated waveguide
dimentions. 47 Additionally, no MDPM SHG is o bserved experimentall y f or single
polar AlN waveguides of the same thickness at wavelengths above 375 nm,
Quasi Phase Matched SHG in AlN L PS W aveguides 123
confirming the n ature of the SHG measurem ents presented in thi s work to be QPM
SHG. 47
Fig u re 7-7: QPM SHG spectra at two different fundamental wavelengths for a 500
nm – 550 nm thick and 10 µm periodic AlN L PS -based waveguide.
Fig u re 7-8: QPM SHG spectra at two different fundam ental w avelengths for a 200
nm – 250 nm thick and 10 µm periodic AlN L PS -based waveguide.
These results demonstrate the feasibilit y to us e AlN L PS -based waveguides for UV -
C laser generation via frequency doublin g in co mpact integrated opti cs. Numerous
other nonlinear optical processes, which are extensively described in the literature,
may be ex ploited utili zing AlN LPS as the on es p resented in this wo rk. No te that the
fabrication process c an be ex tended to the entire III-Nitride materia l s y stem,
allowing t o design a Nitride based LPS with optimal composition addressing
specific nonline ar opti cal processes. On a broader scale, research towards epitax ial
polarity control in other wide bandgap semiconductors with week birefringence and
promising nonlinear optical properties will be encourage d.
124 UV Laser L i ght as Second Harmonic Generation
7.2.2 1.2 µm Perio dicity
For 1 st order QPM SHG in the UV -C sp ectral range, periodicities in the order of 1.2
µm are required ( Figur e 5-11 ). AlN L PS with 1.2 µ m periodicit y w ere fabricated
according to th e process describe d in chapter 5.1, where surface roughness RMS
values in the ord er of 10 nm or lower were a chieved either b y m echanical poli shing
or two step temperature growth. W aveguides were etched into the 1.2 µm AlN L PS
either by SiO 2 hard mask deposition and sub sequent RIE ( Figure 7-9 ), 97 or by
standard masked photolit hogra ph y using negative photoresist, followed by R IE
(Figure 7 -10).
Fig u re 7 -9: 1.2 µm periodic AlN LPS-b ased w aveguides fabricated via SiO2 hard
mask deposition and subsequent RIE. 97
Fig u re 7-10: 1.2 µm pe riodic AlN L PS -based waveguides fabricated by st andard
masked photolithogra ph y using negative photoresist and subsequent RIE etching.
Quasi Phase Matched SHG in AlN L PS Wave guides 125
For the w aveguides fabricated usin g a SiO 2 hard mask, strait sidewalls were
obtained, however an increase of the sur face roughness at the N -polar domains is
observed, compared to t he AlN LPS prior to the waveguide fabrication. The origin
of the incr eased surfac e roughness at the N -polar domains arises f rom wet etching in
the basic d eveloping solution during the development of the photor esist mask, prior
to the deposition of the S iO 2 hard mask. Hence, if a SiO2 hard mask is desired to
fabricate waveguides, a process needs to be implemented where the surface is not
exposed to the basic developing solution.
For the waveguides fabricated using a ne gative ph otoresist, followed by R IE ( Fig u re
7-10), the surface rou ghness is maintained, however rough sidewalls are observed.
The reason for the observed sidewall roug hness is un clear and a more detailed stud y
is necessary . A possible explanation could be a cry stallo graphic dep endence of the
RIE, where the misaligned waveguide sidewall from a crystallographic plane,
exhibited two different facets, lea din g to a roug h si dewall.
Fi gure 7-11: Top view 2D gra y scale scattering intensit y profile at the coupling facet
of 1.2 µm periodic AlN LPS-based waveguides.
Fi gure 7-11 displa ys a t op view 2D gra ysc ale laser s c attering intensit y im age, at the
coupling facet of 1.2 µm periodic AlN LPS-based waveguides. Significant scattering
intensity is observed, inhibiti ng the coupl ed las er li ght to reach the out -coupling
facet. Clearl y , the wav eguide qualit y for 1.2 µ m period ic AlN waveguide s needs to
be improved for 1 st order QPM S HG in the UV-C spectra l r ange.
In summar y, usin g 10 µm periodic AlN L PS-based waveguides, 3 rd , 5 th and 7 th order
QPM SHG is demonstrated, where wavel engths as low as 344 nm are achieved.
These are the first results demonstrating QPM SHG in AlN L P S -based w aveguides,
126 UV Laser L i ght as Second Harmonic Generation
laying the ground work for QPM nonlinear optics in III-Nitride based waveguide
structures.
Summary a nd Conclusio ns 127
8 Conclusions and Future Work
8.1 Su mmary and Conclusio ns
The theory describing s econd harmonic generation via quasi phase matching and
modal dispersion phase matching is presented. A brief introduction on the densit y
functional theory-based theoretical model utilized for calculating the energy of
formation of point defects a s a function of Fermi level, is g iven. Following, a
description on how the extracted thermod ynamic transition energies c an be r elated
to optical spectroscopy characterization techniques is provided.
A polarity control process is described in detail for III- and N-polar GaN and AlN
thin films deposited via MOCVD on sapphire. T he etch be h avior fo r both polarities
in KOH solution is pres ented and is used for determining the polarit y of the III-
Nitride films fabrica ted i n this work. S tep flow growth of N -polar AlN is achieved
by decreasing the Al vap or supersaturation below values of 10 4 , reducing the surface
roughness RMS value b y two orders of magnit ude from 50 nm to 0 .5 nm. In
addition, mass transport between th e adjacent op posite polar domains is measured
when growin g AlN LPS at vapor supersaturation values
< 10 8 , where a n equal
growth rate for both polarities is established at a vapor supersaturation value of
4
3 x1 0
. A two-step temperature process is utilized to avoid polarity over growth
and achieve 1.2 µm periodic AlN L PS with a 6-10 nm surface roughness RMS
value.
As with AlN L PS, using the same polarit y cont rol process scheme, a smooth surfa ce
of the GaN LPS is achieved b y inducin g step fl ow growth at the N -pol ar surface
through cont rolling surface supe rsaturation and increasing the sapphire off-cut
ang l e.
The optical properties of AlN single cr y stals are investigated, wh ere the UV
absorption band at 4.7 e V and the luminescence bands at 2.7 eV and 3. 9 eV are
linked to the same def ect state with a thermod ynamic transition energ y of 4.2 eV
through photol uminescence excitation spectroscopy (PLE). This therm odyna mic
transition energ y is attributed to ca rbon as a nitrogen subst itutional point defect.
Power dependent photoluminescence (P L) measurements reveal the presence of an
energy stat e within the bandgap with a 5.0 eV thermod y namic transition energ y in
agreement with the predicted energy state for the donor acce pto r pair transition
(DAP) leading to the 2.7 eV luminescence b and and the calculated thermod yna mic
128 Conclusions and Future Work
transition energ y for the nitrogen vacancy (V N ). A novel approach is presented to
determine the impuriti es ty pe and concentrations in the cr ystal where PL , P LE,
absorption spectra and S IMS data is used in com bination with a DFT bas ed defect
solver program which accounts for charge b alance in the cry stal and formation
energies of the defec ts.
While PVT grow n AlN single crystals contain point defect concentrations in the
~ 10 19 cm -3 range , reducing their tr ansparency in the UV-C spectral range, epitaxial
thin films contain point d efect concentrations 2 – 3 orders of magnitude lo wer (10 16 -
10 17 cm -3 ), comparable to HVPE AlN cr ystals, where absorption co efficient values
below 5 cm -1 are measured up to the near band ed ge energ y of AlN. Hence, epitaxial
AlN thin films are expected to be transparent in the UV -C spectral ran ge, allowing
for their implementation as frequency doubling c r y stals for UV-C laser generation.
Modal dispersion phase matched second harmonic generation down to 305 nm is
demonstrated in sin gle polar AlN waveguides, in agreement with theoretical
calculations, showing the feasibility to employ AlN for UV laser light generation.
More significantly, 3 rd , 5 th and 7 th order quasi phase matche d second harmonic
ge n eration is demonstrat ed for the first time usin g 10 µm periodic AlN LPS -based
waveguides, where wavelen gths as low as 344 nm are achieved. These results lay
the groundwork for QPM nonlinear optics in III-Nitride based waveguide structures.
Future Work 129
8.2 Futu re Work
A series of studies are proposed ba sed on the stud ies and conclusions of this work.
While 1.2 µm periodic AlN LPS with surface R MS roughne ss values of 5
nm over a 90 x 90 µm 2 are achieved, second h armonic generation was n ot
measured du e to the scattering losses. A detailed stud y of the ori gin of the
scattering loss es will allow the development of an improved process f or
fabricating waveguide-structures of sufficient high quality suitable for
second harmonic generation in the UV-C spectral range.
A detailed understanding o f the surface kinetics and thermod y namics
leading to mass transpor t between the adja cent opposite polar domains in
III -nitrides LPS, is essential for developing the theoretical framework which
will allow for prec ise co ntrol of the polar domain s thickness differences a nd
achieve th e smoothest surface morpholog y .
Fabrication of AlN L P S using bulk AlN substra tes will a llow for thick
structures ( > 500 µ m), e liminating the n eed for s mooth surfaces, as well as
the need to consider the propagation of waveg uid e modes
A detailed stud y on the mechanism leadin g to the suppression of the UV - C
absorption band at 4.7 eV in bulk AlN sin gle crystals when the ox y g en
and/or silicon impurities concentrations are higher than carbon.
The theory describing no nlinear optical int eractions in quasi phase matchi ng
structures has been extensively studied in the literature . Ex ploring the
possibilit y to emplo y III- nitride L PS for other no nlinear opti cal interactions
relevant fo r integrated optics such as wavelength division multi plexing ,
optical ti me divi sion multiplex ing and optical am plifiers is of great interest.
Initially, the structures di mensions and geometr y necessar y for the particul ar
nonlinear pro cess can be calculated, which can be then fabricated a nd
experimentally teste d.
130 Publications and Conference Contributions
9 Publications and Conference Contributions
9.1 Pub lications
Sections of the presented work includes results which have been published in peere d
review journals and are marked with an asterisk (*). The remaining listed
publications are not directl y related to the presented work but are rather the result of
a wide range of collaborations.
[1]* D. Alden , W . Guo, R. Kirste, F. Kaess, I . Bryan, T. Troha, A. Bagal, P.
Reddy, L.H. Hernandez -Balderrama, A. Franke, S. Mita, C .-H. Cha ng, A.
Hoffmann, M. Zgonik, R. Collazo, and Z. S itar, Fabrication and structural
properties of AlN submicron periodic lateral po lar structures and wave guides for
UV -C applications. Applied Ph y sics Letters 108 , 261106 (2016).
[2]* D. Alden , Z. Bryan, B. Gadd y, I. Bryan, G. Callsen, A. Koukitu, Y. Kumagai,
A. Hoffmann, D. I rving, Z. Sitar, and R. Collazo, On the Origin of the 4.7 eV
Absorption and 2.8 eV Emission Bands in Bulk AlN Substrates. ECS Trans . 72 , 31
(2016).
[3]* T. Troha, M. Rigler, D. Alden , I . Br ya n, W. Guo, R. Kirste, S. Mita, M.D.
Gerhold, R. Collaz o, Z. Sitar, and M. Zgonik, UV second harmonic gen eration in
AlN waveguides with modal phase matching. Optical Materials Express 6 , 2014
(2016).
[4] P. Redd y , S. Washi y a ma, F. Kaess, M. Ha y den Breckenridge, L.H.
Hernandez-Balderrama, B.B. Haidet, D. Alden , A. Franke, B. Sarkar, E. Kohn, R.
Collazo, and Z. Sitar, High temperature and low pressure chemical vapor deposition
of silicon nitride on AlG aN: Band offsets and passivation s tudies. J ournal of Applied
Physics 119 , 145702 (2016).
[5] F. K aess, P. Redd y , D. Alden , A. Klump, L.H. Hernandez-Balderrama, A.
Franke, R. Kirste, A. Hoffmann, R. Coll azo, and Z. Sitar, T he effect of illumination
power density on carbo n de fect configuration in silicon doped GaN. Journal of
Applied Physics 120 , 235705 (2016).
Conference Ta lks 131
[6] Y. Abate, D. S eidlitz, A. Fali, S. Gamage, V.E. Babicheva, V.S. Yakovlev,
M.I. Stockman, R. Collazo, D.E. Alden , and N. Dietz, Nanoscopy of Phase
Separation in In x Ga 1-x N Alloys. ACS Applied Materials & Interfaces (2016).
[7] R. Collazo, I . Bryan, Z. Br y an, M. Bobea, L. Hussey , D. Ald en , S. Mita, B.
Gaddy, J. Tweedie, R . Kirste, D. Irving , and Z. S it ar, Advantages and limitat ions of
UV optoelectronics on AlN substrates. 2015 I EE E Summer Topicals Meeting Series
(SUM). (2015), pp. 135 – 136.
9.2 Co nference Talks
1. D. Alden , T. Troha, R. Kirste, F. Kaess, A. Franke, M. G erhold, A. Hoffmann, M.
Zgonik, R. Coll azo, and Z. Sitar; Second Harmonic Generation of UV Laser Light in
AlN Pe riodic Lateral Polar Structures. I nt ernational W orkshop on Nitride
Semiconductors 2016; Oralndo, FL , USA (Oct. 2 016).
2. D. Ald en , J . Harris, Z. Bryan, I. Br y an, B. Gadd y , G. Callsen, A. Hoffmann,
D. Irving, R. Collazo, Z. S itar ; Detailed Photoluminescence Excitation Study of the
3.9 eV and 2.7 eV Defect Luminescence Bands a nd the Commonly Obser ved D eep
UV Absorption at 4.7 eV. I nte rnational Workshop on Nitride Semiconductors 2016;
Oralndo, FL , USA (Oct. 2016).
3. D. Alden , R. Kirste, T. Troha, W. Guo , F. Kaess, I . Br y an, A. F ranke, M.
Gerhold, M. Zgonik, R. Collazo, and Z. S itar; Sub-micron Polarity Control in AlN
Periodic Lateral Polar Structures . 58 th Electronic Materials Conference, J une 2016,
Newark, Delaware, USA.
4. D. Alden , T. Troha, R. Kirste, F. Kaess, A. Franke, M. G erhold, A. Hoffmann, M.
Zgonik, R. Coll azo, and Z. Sitar; Second Harmonic Generation of UV L aser Light in
AlN Periodic Lateral Polar Structures. 2016 Society o f Hispanic Professional
Engineers Conference. November 2016, Seattle, USA.
10 Refere nces
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11 Acknowledgements
I would like to th ank ever y one who has helped a nd supported me during the course
of my Ph.D. work. I give special thanks to the following pe opl e:
I am ver y grateful to m y advisor P rofessor Axel Hoffmann, for his guidance
and support and for giving me the opportunit y to be part o f an international
collaborative project.
I am deepl y thankful to m y research advisor Prof essor Zlatko Sit ar, also for
his guidance and support, as well as his relentless effort to ensuring the high
quality of my researc h.
I am also eternall y indebted to m y research and thesis advisor Professor
Ramón Coll azo, for his c ont inued motivation, i nexhaustible pa tience and
invaluable mentoring.
I am sincerely thankful to P rofessor Marko Zg onik and Ph.D. candidate
Tinkara Tr oh a, for the collaborative work and many fruitful discussions.
Special thanks to Professor Douglas Irving and Joshua Harris for their
support and collaboration regarding density functional theor y based
calculations.
Thanks to m y research colleagues Alex Fra nk e, Andrew Klump, Biplab
Sarkar, Christian Nenst iel, Felix Kaess, Felix Nippert, Gordon Callsen,
Hayden Breckenrid ge , Isaac Brya n, James Tweedie, J ankowski Nadja,
Lindsay Husse y, Luis H ernandez, Marc Hoffmann, Milena Bobea, Pramod
Reddy, Quiang Guo, Robert Rounds, Ronn y Kirste, S arah Schlichting, Seiji
Mita, Shun W ashiya ma, Stefan Kalinowski, Thomas Kure, Wei G uo, W ill
Mecouch and Zac h ary Bry an.
I am also thankful to Professor Jon -Paul Maria and his researc h group f or
allowing me to use th eir research facilities and for their support.
I am grateful to Professor Chih -Hao Chang and Dr. Abhijeet Bagal, for their
su pport and providing th e laser interference lithography setup.
Also, I would like to acknowledge C ONACYT-Mex ico for their financial support as
well as support from the NSF and ARO.
To my m o ther, this dissertation is dedicated to you, thank you for your love and
support and for making this possible.
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