UNIVERSIDADE DE SANTIAGO DE COMPOSTELA
Cen o Singula de In es igaci´
on en Tecnolox´
ıas da In o maci´
on (CiTIUS)
Tesis doc o al
DEVELOPMENT OF TOOLS FOR THE SIMULATION OF
NANOMETRIC TRANSISTORS USING ADVANCED
COMPUTATIONAL ARCHITECTURES
P esen ada po :
Guille mo Indalecio Fe n´
andez
Di igida po :
An onio Jes´
us Ga c´
ıa Lou ei o
Na alia Seoane Iglesias
San iago de Compos ela, junio de 2016
An onio Jes´
us Ga c´
ıa Lou ei o, P o eso Ti ula del ´
A ea de Elec ´
onica de la Uni e sidad
de San iago de Compos ela
Na alia Seoane Iglesias, In es igado a Pos doc o al del Cen o Singula de In es igaci´
on en
Tecnolox´
ıas da In o maci´
on de la Uni e sidad de San iago de Compos ela
HACEN CONSTAR:
Que la memo ia i ulada De elopmen o ools o he simula ion o nanome ic ansis o s
using ad anced compu a ional a chi ec u es ha sido ealizada po Guille mo Indalecio
Fe n´
andez bajo nues a di ecci´
on en el Cen o Singula de In es igaci´
on en Tecnolox´
ıas da
In o maci´
on de la Uni e sidade de San iago de Compos ela, y cons i uye la Tesis que p esen a
pa a op a al ´
ı ulo de Doc o .
San iago de Compos ela, junio de 2016
An onio Jes´
us Ga c´
ıa Lou ei o
Di ec o /a de la esis
Na alia Seoane Iglesias
Di ec o /a de la esis
Guille mo Indalecio Fe n´
andez
Au o de la esis
An onio Jes´
us Ga c´
ıa Lou ei o, P o eso Ti ula del ´
A ea de Elec ´
onica de la Uni e sidad
de San iago de Compos ela
Na alia Seoane Iglesias, In es igado a Pos doc o al del Cen o Singula de In es igaci´
on en
Tecnolox´
ıas da In o maci´
on de la Uni e sidad de San iago de Compos ela
como di ec o es de la esis i ulada:
De elopmen o ools o he simula ion o nanome ic ansis o s using
ad anced compu a ional a chi ec u es
Po la p esen e DECLARAN:
Que la esis p esen ada po Don Guille mo Indalecio Fe n´
andez es id´
onea pa a se p e-
sen ada, de acue do con el a ´
ıculo 41 del Regulamen o de Es udos de Dou o amen o, po la
modalidad de compendio de ART´
ICULOS, en los que el doc o ando ha enido pa icipaci´
on
en el peso de la in es igaci´
on y su con ibuci´
on ue decisi a pa a lle a a cabo es e abajo. Y
que es ´
a en conocimien o de los coau o es, an o doc o es como no doc o es, pa icipan es en
los a ´
ıculos, que ninguno de los abajos eunidos en es a esis se ´
an p esen ados po ninguno
de ellos en o as esis de Doc o ado, lo que i mamos bajo nues a esponsabilidad.
San iago de Compos ela, junio de 2016
An onio Jes´
us Ga c´
ıa Lou ei o
Di ec o /a de la esis
Na alia Seoane Iglesias
Di ec o /a de la esis
A mind needs books like a swo d needs a whe s one.
Ty ion Lannis e
Ag adecimien os
Jam´
as hab ´
ıa llegado a se doc o si no uese po mi mad e, po que ella me ense˜
n´
o a lee y a
suma . A pa i de ah´
ı ya es ´
acil.
San iago de Compos ela, junio de 2016
x
y la uen e de a iabilidad, de al mane a que compa ando el FSM de a ios disposi i os
ob enemos una elaci´
on en e los p opios disposi i os. Finalmen e, es posible u iliza el FSM
pa a ealiza p edicciones sob e el compo amien o del disposi i o an e un conjun o de pe iles
de pe u baci´
on. Es o pe mi e ob ene una es imaci´
on de los pa ´
ame os del disposi i o sin
ene que llega a simula lo, lo que la con ie e en una p ime a ap oximaci´
on de muy bajo
cos e compu acional y con una p ecisi´
on adecuada.
Cuando se es udia la a iabilidad de disposi i os semiconduc o es a a ´
es de la simula-
ci´
on num´
e ica, nos in oducimos en el campo de los es udios es ad´
ıs icos, en el sen ido de
que end emos una mayo p ecisi´
on en los esul ados a medida que aumen emos el n´
ume o
de simulaciones , es deci la ca ga compu acional de abajo que es amos u ilizando. Es a si-
uaci´
on se da en o os campos de in es igaci´
on, como oceanog a ´
ıa, biolog´
ıa, ingenie ´
ıa ci il,
y no malmen e se esuel e c eando una in aes uc u a adap ada al p oblema conc e o, lo que
conlle a que la soluci´
on es ´
e ligada al p oblema esuel o, no siendo as´
ı aplicable en o os
campos, y gene almen e ampoco se puede adap a a ecu sos compu acionales dis in os. Se
han desa ollado ambi´
en soluciones gen´
e icas que ac ´
uan como un middlewa e o como una
pla a o ma cien ´
ı ica, pe o igualmen e p esen an di icul ades pa a abo da p oblemas nue os,
o pa a se adap adas a ecu sos compu aciones dis in os de los inicialmen e p e is os.
Nues o obje i o es educi el iempo de simulaci´
on, con el in de ob ene los esul a-
dos an p on o como sea posible, pudiendo as´
ı ealiza m´
as simulaciones. En nues o caso de
an´
alisis de a iabilidad, aumen a el n´
ume o de simulaciones nos a a pe mi i ca ac e iza
m´
as adecuadamen e el e ec o de la misma en el disposi i o. La p incipal di icul ad es que,
no malmen e, los ecu sos compu acionales disponibles son incompa ibles en e s´
ı, y po an-
o no se pueden lanza simulaciones en odos ellos de una o ma o almen e inmedia a. Pa a
esol e es e p oblema, hemos c eado cua o he amien as que pe mi en p ocesa e icien e-
men e cien os o miles de simulaciones: el TaskManage as a Se ice, el Gene al Wo kload
Manage , el Au o-calib ado , y la eesc i u a del n´
ucleo del simulado pa a u iliza OpenCL.
Pa a ca ac e iza el TaskManage as a Se ice, hemos u ilizado el en oque que se adop a en
compu aci´
on en la nube, es deci , una axonom´
ıa de modelos de compu aci´
on que com´
unmen-
e consis e en la In aes uc u a como Se icio (IaaS), Pla a o ma como se icio (PaaS) y
So wa e como Se icio (SaaS). En odos es os modelos de compu aci´
on en la nube se p e-
sen a una in e az al usua io, y se abs ae el con enido de las capas in e io es, de iniendo
as´
ı un se icio nue o. Po ejemplo, el IaaS abs ae el ha dwa e de a ios equipos a a ´
es de
las m´
aquinas i uales, y le o ece al usua io la posibilidad de pone en ma cha y adminis a
xi
m´
aquinas i uales. Hemos p esen ado po an o un modelo de compu aci´
on que se adap a a
es a axonom´
ıa pa a man ene un lenguaje com´
un con o os in es igado es.
La idea de ´
as de la TMaaS es aisla el acceso a los ecu sos in o m´
a icos, y o ece al
usua io la posibilidad de de ini y ges iona a eas compu acionales. En cada a ea compu-
acional hay que de ini un conjun o de componen es: el en o no de ejecuci´
on, la aplicaci´
on
que se desea lanza y el conjun o de ecu sos de en ada y de salida. Es os componen es de-
ben se p opo cionados po el usua io pa a que el TMaaS pueda ges iona la a ea de mane a
anspa en e en los ecu sos compu acionales disponibles, sean es os o no homog´
eneos. Po
un lado el TMaaS se enca ga de la comunicaci´
on con el sis ema de colas o sis ema ope a i o
que es ´
e ins alado en cada ecu so compu acional, al igual que del despliegue de m´
aquinas si
se a a de un ecu so de compu aci´
on en la nube, y de la ges i´
on y moni o izaci´
on de la a ea
conc e a. Po o o lado, el TMaaS o ece al usua io el con ol de las a eas, pa a que pueda
ges iona las, independien emen e de la na u aleza de las mismas. De es a mane a esol emos
el p oblema de que la soluci´
on quede ligada a un campo conc e o.
Pa a implemen a y p oba el TMaaS hemos desa ollado el Gene al Wo kload Manage
(GWM). Es a he amien a cumple con los equisi os an es mencionados, y pe mi e al usua io
u iliza los ecu sos in o m´
a icos he e og´
eneos de una mane a anspa en e. El GWM ie-
ne una a qui ec u a clien e-se ido , y u iliza REST pa a comunica ambos ac o es, lo cual
pe mi e descub i las ca ac e ´
ıs icas de la he amien a con acilidad. Como clien e, hemos
desa ollado dos e siones: un clien e de l´
ınea de comandos que pe mi e ges iona el sis ema
comple o desde un e minal UNIX, y un clien e habili ado pa a web que pe mi e al usua io
con ola el compo amien o del se ido desde un na egado web. Es a aplicaci´
on web se ha
cons uido con ecnolog´
ıas mode nas pa a que la comunicaci´
on con el se ido sea m´
ınima,
p opo cionando una expe iencia s´
olida y ´
apida pa a el usua io.
La es uc u a del GWM ha sido dise˜
nada pa a que sea expansible, de al modo que pue-
da p opo ciona sopo e a dis in os ecu sos compu acionales de mane a anspa en e. Me-
dian e es a es uc u a, se han implemen ado m´
odulos pa a el GWM de comunicaci´
on con
a ios shells, como bash, sh o ksh, y pa a comunica se con a ios sis emas de colas, como
PBS/To que o SGE. Pa a ap o echa las soluciones mode nas de cloud compu ing de IaaS,
ambi´
en hemos implemen ado el sopo e con a ios p o eedo es de cloud compu ing, inclu-
yendo CloudS ack, OpenS ack, y Amazon EC2, de al mane a que un usua io puede solici a
la ins anciaci´
on de nue os ecu sos compu acionales en cualquie a de es as pla a o mas, y el
GWM los mues a de mane a anspa en e pa a la ejecuci´
on de las a eas de inidas.
xii
U ilizando el GWM hemos sido capaces de ealiza la mayo ´
ıa de las simulaciones que se
p esen an en es a esis en es cl´
us e es de HPC, que ienen an o el ha dwa e como el sis ema
de colas incompa ible en e si. En cualquie caso, el usua io s´
olo u o que de ini la a ea que
que ´
ıa que se ejecu ase, y el GWM se enca g´
o del lanzamien o y moni o izaci´
on de la a ea
en los ecu sos compu acionales disponibles.
O a de las soluciones desa olladas pa a abo da el p oblema de c´
alculo es un au o-
calib ado . Todas las simulaciones de disposi i os elec ´
onicos p esen ados en es a esis nece-
si an se calib adas con alguna uen e ex e na. Po lo gene al, se u ilizan da os expe imen ales
cuando es ´
an disponibles, pe o ambi´
en se puede calib a con a da os de simulaciones m´
as
p ecisas, como NEGF o Mon e Ca lo. En ambos casos, la calib aci´
on equie e que el usua io
a e ig¨
ue los pa ´
ame os de en ada del simulado median e ensayo y e o . Es e p oceso es
cos oso y len o. Pa a mejo a lo hemos desa ollado un au o-calib ado que u iliza un algo-
i mo gen´
e ico pa a encon a los alo es de los pa ´
ame os que ajus an el compo amien o
del disposi i o a la cu a de calib aci´
on deseada. Es a he amien a u iliza el GWM como in-
aes uc u a pa a desplega los cien os o miles de a eas que se ´
an necesa ios has a alcanza
un calib ado su icien emen e p eciso. Los esul ados ob enidos con es e au o-calib ado han
sido muy sa is ac o ios, con cu as de calib aci´
on m´
as ajus adas que cuando se calib a ma-
nualmen e, y sin in e acci´
on del usua io alguna, m´
as all´
a de de ini el disposi i o, la cu a de
calib aci´
on deseada y los alo es iniciales de los pa ´
ame os.
El simulado que es amos u ilizando es ´
a implemen ado en C, u ilizando MPI pa a comu-
nica los nodos de compu aci´
on de memo ia dis ibuida que se quie en u iliza . Es a imple-
men aci´
on es ´
a muy bien p obada y op imizada, as´
ı que no hay mucho ma gen de mejo a posi-
ble. No obs an e, nue as a qui ec u as como unidades de p ocesamien o g ´
a ico de p op´
osi o
gene al (GPGPU) o acele ado es como el In el Xeon Phi, es ´
an su giendo como una buena
al e na i a pa a alcanza endimien os muy ele ados. Es as a qui ec u as es ´
an m´
as o ien adas
a sis emas con ma ices densas, pues o que el modelo de compu aci´
on de hilos que p esen an
a o ece una ca ga de abajo homog´
enea en e ellos. En nues o caso, dado que u ilizamos
elemen os ini os en los simulado es que ejecu amos, nues as ma ices son dispe sas, lo que
da luga a un p oblema m´
as complicado y no an explo ado. Pa a u iliza es as nue as a qui-
ec u as, hemos implemen ado las ope aciones del n´
ucleo de los simulado es, que es la pa e
m´
as cos osa compu acionalmen e, en OpenCL, un lenguaje que pe mi e ejecu a c´
odigo en
pa alelo en a qui ec u as GPGPU o Xeon Phi, en e o as. Es e abajo es p elimina , pe o
ya hemos ealizado algunas publicaciones con los esul ados ob enidos y se p esen an en la
xiii
bibliog a ´
ıa.
En conclusi´
on, el au o empez´
o es a esis con el obje i o de a anza el conocimien o exis-
en e en disposi i os semiconduc o es nanom´
e icos. Conc e amen e seleccion´
o el an´
alisis de
a iabilidad como un p oblema que exige una combinaci´
on in e esan e de di e sas habili-
dades. Po una pa e, equie e conocimien o de los mecanismos ´
ısicos que a ec an al com-
po amien o de los semiconduc o es, y ambi´
en de los p ocesos de ab icaci´
on, debido a su
impac o en la a iabilidad bajo es udio. Po o a pa e, equie e he amien as po en es pa a si-
mula miles de simulaciones y as´
ı comp ende el e ec o de las uen es de a iabilidad. Du an e
el desa ollo de es a esis se han es udiado dos uen es de a iabilidad dis in as, u ilizando un
simulado de a as e-di usi´
on y o o de ipo Mon e Ca lo. Es as uen es de a iabilidad se han
es udiado en dis in os ipos de disposi i os elec ´
onicos, con dis in as aleaciones y con a ios
ama˜
nos de pue a di e en es. Finalmen e, se han desa ollado he amien as no edosas con las
que pode desplega las simulaciones en ecu sos compu acionales he e og´
eneos y op imiza
el iempo de simulaci´
on.
Con en s
1 In oduc ion 1
1.1 Mo i a ion.................................... 1
1.2 Va iabili ysou ces ............................... 3
1.3 Compu a ionalp oblem............................. 9
1.4 Ou line ..................................... 13
1.5 Lis o publica ions ............................... 14
2 3D Simula ion S udy o Wo k-Func ion Va iabili y in a 25 nm Me al-Ga e Fin-
FET wi h Cu ed Geome y using Vo onoi G ains 19
3 S udy o Me al-Ga e Wo k-Func ion Va ia ion using Vo onoi cells: compa i-
son o Rayleigh and Gamma dis ibu ions 21
4 S a is ical s udy o he in luence o LER and MGG in SOI MOSFET 23
5 Compa ison o Fin Edge Roughness and Me al G ain Wo k Func ion Va iabil-
i y in InGaAs and Si FinFETs 25
6 Gene al Wo kload Manage : a Task Manage as a Se ice 27
7 Conclusion 29
7.1 Fu u ewo k................................... 32
Bibliog aphy 33
Lis o Figu es 41
ii Con en s
Lis o Tables 43
CHAPTER 1
INTRODUCTION
1.1 Mo i a ion
Elec onic echnology has a deep impac in oday’s socie y, as well as in science. Socie y has
in oduced new se e al solu ions in bo h pe sonal and p o essional en i onmen s. Simila ly,
scien i ic esea ch o all kinds ake ad an age o he possibili ies ha echnology p o ides.
Mode n imp o emen s had p o ided science he ools i needs o ad ance a a as e pace.
A ep esen a ion o how impo an his ac o is in mode n socie y and science, is he high
economical impac ha se e al echnological co po a ions ha e in he wo ldwide ma ke .
Mos o hese imp o emen s a e backed up by ansis o s, which a e he main componen
o any digi al elec onic de ice, speci ically o cen al p ocessing uni s (CPUs), g aphic p o-
cessing uni s (GPUs), and ola ile memo y (RAM). Found ies design, manu ac u e and sell
ansis o s as a componen o digi al de ices. These ound ies ely on cu ing edge knowl-
edge o p o ide as e , less powe consuming, smalle o cheape solu ions. To achie e hese
imp o emen s, he e has o be ad ance in he many s eps o he ab ica ion p ocess [1].
In o de o o esee he e olu ion o ansis o s, hence echnology, a g oup o semiconduc-
o indus y expe s publish he ITRS [2, 3], a oad map ha cha ac e izes he e olu ion ha
ansis o s ha e o ollow in o de o main ain he desi ed hy hm o ad ance. P oblems ha
may a ise due o he con inuous minia u iza ion o he ansis o s a e also explained in his
documen . Using he ITRS, esea che s can y o ackle he o eseen p oblems be o e hey
ac ually occu , so hey do no hinde he ad ance o echnology.
Semiconduc o de ice simula ions a e a powe ul ool ha allow scien is s o sa e ime
and money, by being able o p edic how a de ice will beha e wi hou he need o c ea e
2Chap e 1. In oduc ion
he manu ac u ing pipeline [4–6]. In o de o unde s and he beha io o he eal de ice,
he simula ion p ocess has o be as p ecise as possible. The d i -di usion app oach, which
calcula es only he cu en and momen conse a ion o he ca ie s, is a simple bu as solu-
ion. When coupled wi h co ec ions o he quan um con inemen like densi y g adien [7],
his me hod, once calib a ed, is able o accu a ely simula e he sub h eshold cha ac e is ics o
s a e-o - he-a semiconduc o de ices in he nanome e egime. The nex s ep in complexi y
could be he hyd odynamic app oxima ion. This model is simila o he p e ious one, bu
includes ou o equilib ium e ec s ha imp o e he simula ion in ce ain si ua ions. A mo e
complex simula ion me hodology is o use Mon e Ca lo, which conside s he pa icles indi-
idually o as me a-pa icles, and he sca e ing p ocesses along he de ice, o ob ain a e y
good p ecision, specially in he on egime [8–10]. The downside o his app oach is ha each
simula ion is e y cos ly in compa ison wi h d i -di usion. An e en mo e p ecise simula ion
me hod is based on Non-Equilib ium G een Func ions and i sol es he quan um anspo
wi h he Sch ¨
odinge equa ion [11]. As expec ed, his simula o is he mos cos ly o he ones
p esen ed.
One o he p oblems ha we wan o simula e, and hence gi e in o ma ion back o he
scien i ic communi y and ound ies, is he a iabili y sou ces ha appea in he p ocess o
manu ac u ing he nanode ice [12]. This has a e y big impac on he de ices beha io ,
dec easing hei pe o mance o some imes gene a ing ope a ional ailu es [12–15].
In o de o cha ac e ize he a iabili y as well as possible, we ha e o un housands o
simula ions, o ob ain a mo e eliable s a is ical insigh on he na u e and e ec o he a i-
abili y sou ces [16]. The e o e, he selec ed simula ion echnique has o be simple enough
o allow us o deploy as many simula ions as possible while keeping an accu acy le el ha
g an s us meaning ul in o ma ion. In ou case ha will be he d i -di usion simula o wi h
quan um co ec ions, calib a ed agains expe imen al da a when possible.
Ano he p oblem ha we also wan o ackle is he lack o gene al solu ions ha allow a
scien is o easily manipula e he compu ing capabili ies needed in o de o launch housands
o simula ions, o any o he la ge wo kload. The exis ing solu ions a e oo complex, o ailo ed
o ce ain p oblems and limi ed by hei in as uc u e.
In summa y, we wan o ocus ou wo k in wo di e en on s: i) o s udy he a iabili y
sou ces ha a ise in mode n nanode ice a chi ec u es, cha ac e izing hem and hei e ec
on he de ices, and ii) o de elop he compu a ional ools ha we need in o de o be able o
manage housands o simula ions and pos p ocess he esul s.
1.2. Va iabili y sou ces 3
1.2 Va iabili y sou ces
Once he semiconduc o nanode ice is de ined and eady o be p oduced, ce ain de ia ions
om he bluep in s a e o be expec ed. These de ia ions a e andom, and can be o wo ypes:
ela ed o di e en s ages o he building p ocess, o inhe en o he semiconduc o ma e ial
and physics. The e ec o hese de ia ions on he beha io o he de ice is called a iabili y,
and he na u e o he de ia ion is he a iabili y sou ce. These in insic luc ua ions [17],
inc ease when he de ice is scaled down, which agg a a es i s impo ance.
We wan o s udy di e en a iabili y sou ces, and how a e hey ela ed o he scaling o
he de ice. Each a iabili y sou ce unde s udy will ha e an impac on he de ice cha ac e -
is ics, ha will depend on he pa ame e s ha cha ac e ize he a iabili y sou ce. S udying
he ela ion be ween hose pa ame e s and he impac on he de ice cha ac e is ics, we can
conclude which s eps had o be aken in o de o minimize he nega i e e ec o he a iabil-
i y sou ce on he de ice beha io . Simila ly, his allows us o compa e he a iabili y sou ces
be ween hemsel es.
To apply he a iabili y sou ce, conside ing ha hei na u e is he de ia ion om he ideal
de ice, we modi ied he sou ce code o he nume ical simula o o accoun o he di e ence.
Ou app oach has o be as much ealis ic as possible, wi hou modi ying he simula o mo e
han necessa y. All he modi ica ions in he code ha e o be possible o deac i a e, in o de
o es o e he o iginal beha io . Also, because he a iabili y is a s a is ical p ocess, we need
mo e han one simula ion o accoun o he e ec o he a iabili y sou ce. Mo e conc e ely,
conside ing ha some pa ame e s ha cha ac e ize he a iabili y a e no ixed bu also a e
a iables, we may wan o deploy hund eds o housands o simula ions o ha e good s a is ics
and a p ope cha ac e iza ion o he a iabili y sou ce.
The me hodology chosen is common o all he a iabili y sou ces unde s udy: we ana-
lyze he e ec o he a iabili y ia a pe u ba ion p ocess. This pe u ba ion me hodology is
composed o :
1. The pe u ba ion p o ile is any kind o ile o se o iles ha ep esen how he de-
ice has o be pe u bed. This allows o ake he ac ual a iabili y sou ce ou o he
simula o , so a single compila ion o he simula ion can deal wi h di e en ins ances
o pe u ba ions. This pe u ba ion p o ile is gene a ed o se , and deployed wi h he
simula o and he co esponding de ice cha ac e is ics, like he mesh, in o de o ha e
a ull simula ion o he sou ce unde a iabili y.
10 Chap e 1. In oduc ion
capabili ies a ailable will e u n a be e solu ion o hei p oblem. Simila p oblems aised in
o he ields like oceanog aphy o biology, has been sol ed ia c ea ing solu ions ailo ed o a
pa icula p oblem [44–46]. Because o his, he solu ions a e only alid o he co esponden
ield o s udy. Ano he solu ion based on science ga eways is close o sol ing ha p oblem
[47], bu i only p o ides a communi y-speci ic se o ools, and does no allow a scien is o
deploy his code independen ly.
Ou objec i e is he op imiza ion o he simula ion ime, in o de o ha e he esul s as
soon as possible o o ha e mo e simula ions ha allows o a be e esul . The p oblem is
ha ing o use compu a ional esou ces ha a e incompa ible be ween hemsel es. In ou case,
deploying a big amoun o simula ions is a key poin in o de o p ope ly analyze he e ec
o he a iabili y sou ce on he de ice beha io . The e o e, we ha e de eloped ou ools o
e icien ly p ocess hund eds o housands o simula ions, and we b ie ly desc ibe hem in he
ollowing subsec ions: he Task Manage as a Se ice, he Gene al Wo kload Manage , he
Sel -Calib a o , and he OpenCL implemen a ion o he simula o engine.
1.3.1 Task Manage as a Se ice
The cloud compu ing en i onmen has de ined an app oach ha we can adop in o de o
ackle he p esen ed compu a ional p oblem. The axonomy o cloud compu ing se ices [48]
is commonly ep esen ed ia he In as uc u e as a Se ice (IaaS), Pla o m as a Se ice
(PaaS), and So wa e as a Se ice (SaaS). In all hese cloud compu ing models, he e is an
abs ac ion o ce ain laye s o compu a ion, and an in e ace is o e ed o he use so he can
deal wi h hem wi hou knowing hei in e nal de ails. Fo example, he IaaS abs ac s he
ha dwa e o se e al machines ia i ual machines, ha can be launched and managed by he
use .
We p esen he Task Manage as a Se ice, which sol es he a o emen ioned compu a-
ional p oblem. This compu ing model has also been implemen ed in he o m o he Gene al
Wo kload Manage , explained in he nex subsec ion.
The idea behind he TMaaS is o isola e he access o he compu ing esou ces, and o
p esen he use wi h he abili y o de ine and manage asks. We de ine a compu a ional ask
as a se o componen s: he en i onmen , he execu able ha is o be launched, he possible se
o inpu and ou pu esou ces. The TMaaS is a laye ha allows a use o de ine and manage
he li e cycle o asks using he a ailable compu ing esou ces anspa en ly.
1.3. Compu a ional p oblem 11
Once he TMaaS is up and unning, he only in e ac ion o he use wi h he compu a ional
esou ces is he ask. Wi h his uni , i is e y easy o moni o he asks in se e al ways. I also
allows o schedule he asks ollowing di e en scheduling mechanisms ha will adap o he
ime deadlines, he s a us o he compu ing esou ces, o he scien is needs. This compu ing
model does no depend on he ield ha he scien is is wo king on, so i s applicable o he
a o emen ioned cases, and o cou se o ou nanode ice simula o .
1.3.2 Gene al Wo kload Manage
To implemen and es he TMaaS we ha e de eloped he Gene al Wo kload Manage (GWM).
This ool complies wi h he equi emen s men ioned be o e, and allows he use o use he e o-
geneous compu ing esou ces in a anspa en way.
The ool was de eloped ollowing a clien -se e a chi ec u e. A se e is ins alled ha
moni o s some po s o REST pe i ions. By using REST, he applica ion is easy o ex end
and o disco e om he use poin o iew. The clien ha communica es wi h he se e ia
he REST a chi ec u e is con olled by he use . We ha e implemen ed wo di e en clien s
wi h he same capabili ies: one command line clien which allows o manage he ull sys em
om a UNIX e minal, and one web enabled clien ha allows he use o con ol he beha io
o he se e om a web b owse . This web b owse applica ion is de eloped using mode n
echnologies o communica ing wi h he se e , and displaying he s a e, o p o ide a easy,
as and mode n expe ience o he use . Using a Model View Con olle pa adigm, wi h AJAX
in o de o main ain he s a e o he applica ion in he clien , and REST o communica e wi h
he se e , he esul is ha he managemen o housands o asks is no mo e di icul o he
use han ha o an online mail clien .
The GWM is expansible because i has been concei ed as a plugin-based a chi ec u e.
This allowed up o implemen modules o he GWM o communica e wi h se e al shells, like
bash, sh, o ksh. The same plugin-based a chi ec u e is used o acili a e he access o queu-
ing engines, like PBS/To que o SGE, so he use does no ha e o deal wi h he di e ences
be ween hem. Also, he GWM is capable o communica ing wi h se e al cloud compu ing
p o ide s, like CloudS ack, OpenS ack, Amazon EC2, and mo e. So he ins an ia ion o new
compu ing esou ces is done anspa en ly. One o he de eloped schedule s, called in elli-
gen schedule , allows he use o de ine a s opping me ic ha can be calcula ed om he
simula ion esul s, and he GWM will deploy only he equi ed simula ions o ob ain ha
me ic. This is done by calcula ing he alue o he me ic a e each simula ion and using ha
12 Chap e 1. In oduc ion
in o ma ion as eedback.
Using he GWM we we e able o deploy mos o he simula ions ha a e p esen ed in his
hesis. In mos cases, he simula ions we e un in h ee di e en high pe o mance clus e s,
wi h incompa ible ha dwa e and di e en ask managemen enqueuing. In any case, he use
only had o de ine he compu ing ask and he GWM would ake ca e o he ask managemen .
1.3.3 Sel -calib a o
Ano he o he solu ions de eloped o ackle he compu a ional p oblem is a sel -calib a o .
All he nanode ice simula ions p esen ed in his hesis need o be calib a ed o some ex e nal
sou ce. Usually he sou ce is ei he expe imen al da a, when a ailable, o esul s om mo e
p ecise simula ions, like NEGF o Mon e Ca lo. In bo h cases, he calib a ion equi es he use
o guess he igh alues o he pa ame e s ha cha ac e ize ou d i -di usion simula o and
ha i he beha io o he de ice as close as possible. To ind hese pa ame e s, he o iginal
p ocedu e is o change hei alues, simula e he de ice, compa e he beha io and epea .
We de eloped a sel -calib a o ha uses he de ice speci ica ions and he desi ed beha io
o ob ain he alues o he pa ame e s ha closely ma ch ha desi ed beha io . This sel -
calib a o uses a gene ic algo i hm o decide he alues o he pa ame e s o each i e a ion,
and he GWM o manage he asks.
1.3.4 OpenCL implemen a ion
The simula o ha we a e using is implemen ed in C wi h MPI o ake accoun o he com-
munica ion be ween nodes. This implemen a ion is e y well es ed and op imized, so no
much ma gin o imp o emen is possible. New a chi ec u es like Gene al Pu pose G aphics
P ocessing Uni s (GPGPUs) o accele a o s, like he In el Xeon Phi, a e being used nowadays
o ob ain as e unning imes [49], e en i hey a e ailo ed o dense sys ems ins ead o he
spa se we a e wo king wi h. We ha e implemen ed he equi ed ope a ions o ans e he
engine o ou simula o om he MPI-enabled o a OpenCL implemen a ion, which can be
un in se e al di e en a chi ec u es wi hou changing he sou ce code. This is s ill a wo k in
p og ess, bu he p elimina y a icles al eady published in he opic a e lis ed in sec ion 1.5.
1.4. Ou line 13
1.4 Ou line
In he ollowing chap e s we p o ide he key a icles ha ep esen he main body o wo k
o his hesis. In all hese a icles, he au ho o he hesis has been he main con ibu o ,
o a coau ho ha highly con ibu ed o he pape . These a icles ha e been ei he published
in JCR jou nals o in high quali y in e na ional con e ences: IEEE T ansac ions on Elec on
De ices, Semiconduc o Science and Technology, In e na ional Con e ence on Simula ion
o Semiconduc o P ocesses and De ices (SISPAD), and IEEE In e na ional Con e ence on
Communica ion (CORE A). This selec ion o a icles has been made o del e in o he main
poin s men ioned in he in oduc ion, and o ha e a mo e comple e ep esen a ion o he wo k
ca ied ou doing his hesis, he ull e e ence lis in sec ion 1.5 should be conside ed. In ha
sec ion we lis a ull compendium o he jou nal publica ions and con e ence p esen a ions
ela ed o his hesis, which include jou nals like IEEE Elec on De ice Le e s and IEEE
In e ne Compu ing.
In chap e 2, we explain he Vo onoi me hod in oduced in sec ion 1.2.2, o model he
Me al Ga e G anula i y. We also analyze he e ec o changing he de ice body shape om
a comple e squa e o a ounded co ne shape. The i s measu es o MGG a iabili y we e
p esen ed o a 25 nm ga e leng h Silicon SOI FinFET de ice. This p esen a ion o he Vo onoi
me hod was well ecei ed by he scien i ic communi y and he indings o his a icle whe e
ci ed se e al imes. The Vo onoi me hod is being used oday by se e al esea che s o model
he MGG a iabili y.
Following a ecen ly published app oach o calcula e he MGG a iabili y ia he Rayleigh
dis ibu ion [39], in chap e 3, we compa e ou Vo onoi model wi h he Rayleigh app oach,
using he equi alen Gamma dis ibu ion ha a ises na u ally om he g ain a ea dis ibu ion
o a Vo onoi diag am. We also compa e bo h algo i hms wi h TEM images. We ound ha ou
app oach is way mo e sui able o ma ch he expe imen al esul s, and ha he Rayleigh dis i-
bu ion o e s a es he alue o he a iabili y. The analysis was done wi h expe imen al da a
o di e en ma e ials, p o ided by D . Kenji Ohmo i, om he Nano echnology Labo a o y
o Waseda Uni e si y, Tokyo [30].
Using bo h he Line Edge Roughness, explained in sec ion 1.2.1, and he Me al Ga e
G anula i y, we p esen in chap e 4 an analysis o he e ec o bo h hese a iabili y sou ces
in a 25 nm Silicon SOI FinFET de ice, he same de ice ha was used in chap e 2. This is he
i s a icle in which we p esen ou me hodology o gene a e LER p o iles, as an applica ion
o he same pe u ba ion pipeline. We ha e ound ha he MGG has a nega i e e ec in he
14 Chap e 1. In oduc ion
powe consump ion and he swi ching speed, dec easing he quali y o he de ice, as he g ain
size g ows. Simila ly o LER, we ha e ound ha bo h he co ela ion leng h and he ms
heigh ha e a nega i e e ec in he a iabili y o all igu es o me i , bu mo e p onounced
in he case o he ms heigh o he s udied pa ame e s. In gene al, his de ice shows mo e
sensi i i y o LER han o MGG.
In o de o expand he knowledge o bo h a iabili y sou ces and de ice ab ica ion, we
simula ed he same a iabili y sou ces as in chap e 4, bu o wo s a e-o - he-a de ices: a
Silicon SOI FinFET, and an InGaAs III-V-OI FinFET wi h a simila shape. In bo h cases,
we ha e also educed he size o he de ice om 25 nm o 10.7 and 10.4 nm, espec i ely.
We used da a om Mon e Ca lo simula ions o calib a e he simula o , because he e was
no expe imen al da a a ailable a he momen . The esul s o his compa ison a e shown
in chap e 5, whe e we ound ha in he sub- h eshold egion, he InGaAs de ice is mo e
esilien o MGG a iabili y han he Silicon de ice, specially o he sub h eshold swing,
and p oduces simila esul s o he LER a iabili y. Ne e heless, he esul s o on-cu en
p esen he opposi e end.
To ob ain he p e ious esul s, we ha e o un se e al housands o simula ions, o accoun
o he di e en de ices, a iabili y sou ces and pa ame e s. The p oposed Task Manage as
a Se ice in as uc u e was used o es i s alidi y in eal wo ld si ua ions. In chap e 6 we
p esen he Gene al Wo kload Manage , ou implemen a ion o he TMaaS compu ing model.
We ha e applied he GWM o di e en scena ios o show how i can handle wo kloads inde-
penden ly o he na u e o hem, and we also p esen how i can deal wi h h ee incompa ible
clus e s and a cloud p o ide in o de o deploy and manage he compu a ional asks.
Finally, in chap e 7, we p esen he conclusions o he hesis and o he a icles ep oduced
in he ollowing chap e s, along wi h he u u e wo k ha na u ally a ises om he a icles
w i en in his hesis.
1.5 Lis o publica ions
This is he lis o publica ions w i en by he au ho h oughou he de elopmen o he hesis.
A icles in pee e iewed jou nals:
•G. Indalecio, A.J. Ga cia-Lou ei o, N. Seoane, and K. Kalna, S udy o Me al-Ga e
Wo k-Func ion Va ia ion Using Vo onoi Cells: Compa ison o Rayleigh and Gamma
Dis ibu ions, IEEE T ansac ions on Elec on De ices, 63, pp. 2625-2628, 2016
1.5. Lis o publica ions 15
•G. Indalecio, F. Gomez-Folga , and A.J. Ga cia-Lou ei o, GWMEP: Task-Manage -
as-a-Se ice in Apache CloudS ack, IEEE In e ne Compu ing, 20, pp. 42-49, 2016
•G. Indalecio, N. Seoane, M. Aldegunde, K. Kalna, and A. J. Ga cia-Lou ei o, Va i-
abili y Cha ac e isa ion o Nanoscale Si and InGaAs Fin Field-E ec -T ansis o s a
Sub h eshold., Jou nal o Low Powe Elec onics, 11, pp. 256-263, 2015
•G. Indalecio, M. Aldegunde, N. Seoane, K.Kalna and A. J. Ga cia-Lou ei o, S a is ical
s udy o he in luence o LER and MGG in SOI MOSFET, Semiconduc o Science and
Technology, 29, 045005, 2014
•N. Seoane, M. Aldegunde, D. Nagy, M.A. Elmessa y, G. Indalecio, A.J. Ga cia-Lou ei o
and K. Kalna Simula ion s udy o scaled In0.53Ga0.47As and Si FinFETs o sub-16 nm
echnology nodes, Semiconduc o Science and Technology, 31, 075005, 2016
•N. Seoane, G. Indalecio, M. Aldegunde, D. Nagy, M.A. Elmessa y, A.J. Ga cia-Lou ei o,
K. Kalna, Compa ison o Fin-Edge Roughness and Me al G ain Wo k Func ion Va i-
abili y in InGaAs and Si FinFETs, IEEE T ansac ions on Elec on De ices, 63, pp.
1209-1215, 2016
•E. Co onado-Ba ien os, G. Indalecio and A. Ga cia-Lou ei o, S udy o basic ec o
ope a ions on In el Xeon Phi and NVIDIA Tesla using OpenCL, Annals o Mul ico e
and GPU P og amming, 2, 15, 2015
•N. Seoane, G. Indalecio, E. Comesana, M. Aldegunde, A. J. Ga cia-Lou ei o and K.
Kalna, Random Dopan , Line-Edge Roughness, and Ga e Wo k unc ion Va iabili y in a
Nano InGaAs FinFET, IEEE T ansac ions on Elec on De ices, 61, pp. 466-472, 2014
•N. Seoane, G. Indalecio, E. Comesa˜
na, A. J. Ga cia-Lou ei o, M. Aldegunde, and K.
Kalna, Th ee-Dimensional Simula ions o Random Dopan and Me al-Ga e Wo k unc-
ion Va iabili y in an In0.53Ga0.47As GAA MOSFET, IEEE Elec on De ice Le e s, 34,
pp. 205-207, 2013
A icles published in in e na ional con e ences:
•G. Indalecio, F. Gomez-Folga and A.J. Ga cia-Lou ei o, Gene al Wo kload Manage :
a Task Manage as a Se ice, IEEE In e na ional Con e ence on Communica ions, pp.
1859-1864, 2015
16 Chap e 1. In oduc ion
•G. Indalecio, N. Seoane, M. Aldegunde, K. Kalna and A. J. Ga cia-Lou ei o, Va iabili y
cha ac e isa ion o nanoscale Si and InGaAs FinFETs a sub h eshold, 5 h Eu opean
Wo kshop on CMOS Va iabili y, 2014
•G. Indalecio, N. Seoane, M. Aldegunde, K. Kalna, A. J. Ga cia-Lou ei o, Scaling o
Me al Ga e Wo k unc ion Va iabili y in nanome e SOI-FinFETs, 15 h In e na ional
Con e ence on Ul ima e In eg a ion on Silicon, pp. 105-108, 2014
•G. Indalecio, M. Aldegunde, A.J. Ga cia-Lou ei o, S a ic Mul ipole Me hod Applied
o Bounda y Condi ions o Semiconduc o De ice Simula ions The 2012 In e na ional
Con e ence on High Pe o mance Compu ing & Simula ion, pp. 654-659, 2012
•G. Indalecio, A.J. Ga cia-Lou ei o, M. Aldegunde, and K. Kalna, 3D Simula ion S udy
o Wo k-Func ion Va iabili y in a 25 nm Me al-Ga e FinFET wi h Cu ed Geome y
using Vo onoi G ains, 2012 In e na ional Con e ence on Simula ion o Semiconduc o
P ocesses and De ices, pp. 149-152, 2012
•M.A. Elmessa y, D. Nagy, M. Aldegunde, N. Seoane, G. Indalecio, J. Lindbe g, W.
De me , D. Pe i, A.J. Ga cia-Lou ei o and K. Kalna, Scaling/LER S udy o Si GAA
Nanowi e FET using 3D Fini e Elemen Mon e Ca lo Simula ions, In e na ional EU-
ROSOI Wo kshop and In e na ional Con e ence on Ul ima e In eg a ion on Silicon, pp.
52-55, 2016
•F. Gomez-Folga , G. Indalecio, N. Seoane, A. J. Ga cia-Lou ei o, and T. F. Pena, S udy
o Poin - o-Poin Communica ion La ency o MPI Implemen a ions in Cloud, The 22nd
In e na ional Con e ence on Pa allel and Dis ibu ed P ocessing Techniques and Appli-
ca ions, ACCEPTED, 2016
•F. Gomez-Folga , G. Indalecio, A.J. Ga cia-Lou ei o and T.F. Pena, A Flexible Clus e
Sys em o he Managemen o Vi ual Clus e s in he Cloud, IEEE 17 h In e na ional
Con e ence on High Pe o mance Compu ing and Communica ions, pp. 1693-1698,
2015
•M. Fo es, E. Comesa˜
na, G. Indalecio, J. Rod iguez, P. O e o, A. Ga cia-Lou ei o, M.
Ve e , Design and Mon e Ca lo Simula ion o a LED-based Op ic Couple , 17 h In e -
na ional Con e ence on Compu e Modelling and Simula ion, pp. 577-581, 2015
1.5. Lis o publica ions 17
•A. Abdika imo , G. Indalecio, E. Comesa˜
na, N. Seoane, K. Kalna, A.J. Ga cia-Lou ei o,
A.E. A amu a o , In luence o de ice geome y on elec ical cha ac e is ics o a 10.7
nm SOI-FinFET, 17 h In e na ional Wo kshop on Compu a ional Elec onics, pp. 247-
248, 2014
•N. Seoane, G. Indalecio and A.J. Ga c´
ıa-Lou ei o, K. Kalna, Impac o c oss-sec ion
o 10.4 nm ga e leng h In0.53Ga0.47As FinFETs on me al g ain a iabili y, 2016 In-
e na ional Con e ence on Simula ion o Semiconduc o P ocesses and De ices, AC-
CEPTED, 2016
•N. Seoane, G. Indalecio, E. Comesa˜
na, M. Aldegunde, A. J. Ga cia-Lou ei o and K.
Kalna, WN and TiN me al ga e wo k unc ion a iabili y in a 10.4 nm ga e leng h In-
GaAs FinFET, 17 h In e na ional Wo kshop on Compu a ional Elec onics, pp. 239-
240, 2014
•N. Seoane, A. Ga cia–Lou ei o, E. Comesa˜
na, R. Valin, G. Indalecio, M. Aldegunde
and K. Kalna, 3D simula ions o andom dopan induced h eshold ol age a iabili y
in in e sion–mode In0.53Ga0.47As GAA MOSFETs, 2012 In e na ional Con e ence on
Simula ion o Semiconduc o P ocesses and De ices, pp. 392-395, 2012
A icles published in na ional con e ences:
•G. Indalecio, F. Gomez-Folga and A. J. Ga cia-Lou ei o, Compa ison o s a e-o - he-
a dis ibu ed compu ing amewo ks wi h he GWM, 10 h Spanish Con e ence on
Elec on De ices, 2015
•G. Indalecio, M. Aldegunde, K. Kalna, A. Ga cia-Lou ei o, S udy o s a is ical a i-
abili y in nanoscale ansis o s in oduced by LER, RDF and MGG, 2013 Spanish Con-
e ence on Elec on De ices, pp. 95-98, 2013
•E. Co onado-Ba ien os, G. Indalecio and A.J Ga cia-Lou ei o, Implemen a ion and
pe o mance analysis o he AXPY, DOT, and SpMV unc ions on In el Xeon Phi and
NVIDIA Tesla using OpenCL, Segundas Jo nadas de P og amacion Pa alela Mul ico e
y GPU, 2015
•E. Co onado-Ba ien os, A. Ga cia-Lou ei o, G. Indalecio N. Seoane, Implemen a ion
o nume ical me hods o nanoscaled semiconduc o de ice simula ion using OpenCL,
10 h Spanish Con e ence on Elec on De ices, 2015
18 Chap e 1. In oduc ion
•F. Gomez-Folga , G. Indalecio, E. Comesana, A. J. Ga cia-Lou ei o, T. F. Pena, A ool
o deploy nanode ice simula ions on Cloud, 10 h Spanish Con e ence on Elec on De-
ices, 2015
CHAPTER 2
3D SIMULATION STUDY OF
WORK-FUNCTION VARIABILITY IN A 25
NM METAL-GATE FINFET WITH CURVED
GEOMETRY USING VORONOI GRAINS
Following is a ep oduc ion o an a icle o which he au ho o his hesis is a main con-
ibu o . This is a e ba im ep oduc ion, and he o iginal can be ound online a he URL
h p://in4.iue. uwien.ac.a /pd s/sispad2012/8-3.pd , o wi h he ol-
lowing in o ma ion:
In e na ional Con e ence on Simula ion o Semiconduc o P ocesses and
De ices, 2012, pp. 149-152
G. Indalecio, A.J. Ga c´
ıa-Lou ei o, M. Aldegunde and K.Kalna
CHAPTER 6
GENERAL WORKLOAD MANAGER:ATASK
MANAGER AS A SERVICE
Following is a ep oduc ion o an a icle o which he au ho o his hesis is a main con ibu o .
This is a e ba im ep oduc ion, and he o iginal can be ound online a he ollowing URL
h p://dx.doi.o g/10.1109/ICCW.2015.7247451, o wi h his in o ma ion:
IEEE In e na ional Con e ence on Communica ions - Wo kshop on Cloud
Compu ing Sys ems, Ne wo ks, and Applica ions, pp. 1859-1864, 2015
G. Indalecio, F. G´
omez-Folga and A.J. Ga c´
ıa-Lou ei o
CHAPTER 7
CONCLUSION
The au ho s a ed his hesis wi h he objec i e o ad ancing he exis ing knowledge o semi-
conduc o de ices in he nanoscale egime. In o de o do ha , he analysis o a iabili y
sou ces was selec ed as an in e es ing combina ion ha in ol es se e al abili ies. On he one
hand, i equi es knowledge o he physical mechanisms ha a ec he semiconduc o s be-
ha io , and also o he manu ac u ing p ocess, because o i s impac on he a iabili y o be
s udied. On he o he hand, i equi es powe ul ools o be able o simula e housands o
de ices o unde s and he e ec o small changes on he de ice cha ac e is ics.
As a s a ing poin we de eloped a pipeline based in a pe u ba ion model ha allows o
modi y he simula ion o accoun o di e en a iabili y sou ces, wi hou many changes in he
simula o code. Using his pipeline, we ha e implemen ed wo a iabili y sou ces: he Me al
Ga e G anula i y (MGG) and he Line Edge Roughness (LER). These a iabili y sou ces ha e
been applied o se e al de ices: Silicon and InGaAs FinFETs and ga e-all-a ound Nanowi es.
These ools a e cu en ly being used by o he au ho s in he Uni e si ies o San iago de Com-
pos ela and in Swansea Uni e si y, o u he s udy he e ec o ha a iabili y sou ces.
The simula o ha was used and modi ied is a d i -di usion 3D simula o . I uses densi y
g adien co ec ions o accoun o he quan um e ec s ha a ise when sh inking he de ice
unde ce ain sizes. The de ice is modeled wi h a e ahed al mesh, because he simula o uses
ini e elemen s o disc e ize he p oblem. Se e al meshes whe e gene a ed o his simula o ,
wi h di e en shape, size o densi y, o manage he associa ed con e gence p oblems ha can
happen i he densi y is oo low and o explo e di e en a chi ec u es.
The Me al Ga e G anula i y was s udied using ou own app oach which is based on he
30 Chap e 7. Conclusion
ma hema ical s uc u e o he Vo onoi diag am. To implemen he Line Edge Roughness, we
ha e de eloped a in e se Fou ie ans o m o a spec a. To ob ain comp ehensi e da a o he
e ec o his a iabili y sou ces in semiconduc o de ices, we need o change he pa ame e s
ha de ine he sou ces o a iabili y, and also use di e en de ices. We deployed se e al hou-
sands o simula ions in se e al compu ing esou ces hanks o he Gene al Wo kload Manage ,
which was also de eloped du ing all he pe iod o his hesis.
The ollowing bulle lis summa izes some o he indings p esen ed in he p e ious chap-
e s ha we e achie ed h oughou his hesis:
•We ha e de eloped a pipeline based in a pe u ba ion model, ha allows o implemen
se e al a iabili y sou ces in ou semiconduc o de ice simula o s. This pipeline in-
oduces he a iabili y sou ce as a pe u ba ion, wi hou many changes in he o iginal
sou ce o he simula o . This is cu en ly being used by se e al scien is s om wo
di e en esea ch ins i u ions.
•One o he mos impo an applica ions o his pipeline, he Vo onoi app oach o he
Me al Ga e G anula i y a iabili y, was p esen ed and alida ed agains expe imen al
da a. These alues ha e been p o ided by D . Kenji Ohmo i [30], and consis ed on
TEM images o di e en ma e ials: TiN and Ru. In bo h cases, ou Vo onoi app oach
gene a es a g ain dis ibu ion ha i s p ope ly he expe imen al g ain dis ibu ion, wi h
p- alues o 0.17 and 0.42, o TiN and Ru, espec i ely. We ha e also checked wi h he
same expe imen al da a an op ion de eloped by ano he au ho s: he Rayleigh app oach,
and concluded ha is no adequa e o accoun o he g ain dis ibu ion o MGG sim-
ula ions. The same i o he same expe imen al da a esul ed in p- alues o 3 ×10−14
and 0.0029 o TiN and Ru. We ha e also demons a ed ha he a iabili y calcula ed
wi h Rayleigh o e es ima es he eal a iabili y by 11.9% and 7.14% o TiN and TaN
ma e ials, which ou app oach does no .
•Using he p esen ed pipeline, we ha e analyzed he impac o he MGG and LER
sou ces o a iabili y in he pe o mance o se e al s a e-o - he-a semiconduc o de-
ices. This is a key poin o unde s and he p ocess o de ice ab ica ion and how i
has an impac on he de ice cha ac e is ics. We ha e simula ed 10.7 and 10.4 nm ga e
leng h Silicon and InGaAs de ices modeled acco ding o he ITRS p edic ions. Those
simula ions we e calib a ed using he da a om a mo e p ecise bu slowe simula o ,
based on 3-D Non-Equilib ium G een’s Func ions, because no expe imen al da a was
31
a ailable a he momen . F om his compa ison we ha e ound ha he InGaAs de ice
is mo e esilien o he a iabili y sou ces in he sub h eshold egime. The beha io o
he on-cu en a iabili y is he opposi e, ha ing mo e sensi i i y in he InGaAs de ice.
•Independen ly o he de ice, o he MGG we ha e ound and cha ac e ized a depen-
dency o he a iabili y on h eshold ol age, o cu en and sub h eshold swing wi h
he in e se o he oo squa e o he g ain size. Also, we ha e ound ha he de ice
powe consump ion and swi ching speed diminish when he g ain size i la ge. This
means ha no only a a ia ion o he pa ame e s is o be expec ed, bu also a ne educ-
ion o he quali y o he de ice.
•Rega ding he LER, we ha e ound ha he e ec o he co ela ion leng h is smalle
han he e ec o he oo mean squa e o he heigh , o he pa ame e s ha a e usually
s udied. This esul is ound o be applicable o bo h Silicon and InGaAs FinFETs. We
ha e also s udied he impac o co ela ed e sus unco ela ed LER, and we ha e con-
cluded ha he unco ela ed LER has mo e impac on he a iabili y because i changes
he de ice wid h along he cu en low di ec ion.
•In o de o u he unde s and he e ec o he a iabili y sou ces, we ha e implemen ed
and p esen ed a Fluc ua ion Sensi i i y Map (FSM) o s udy he MGG a iabili y. The
FSM shows us ha we can de ec he posi ion in he de ice whe e he oxide is wide ,
because i educes he sensi i i y o he de ice o he g ain o ien a ion. Also, we ha e
ound ha a educ ion o he wid h o he de ice body nea he op o he Fin has a
simila e ec o a oxide bu e : i educes he sensi i i y.
•Finally, ega ding he in as uc u e o manage asks, he GWM, we ha e es ed i us-
ing he e ogeneous wo k loads, compu ing esou ces incompa ible be ween hemsel es,
di e en queuing engines o he asks, and cloud in as uc u es. We ha e also bench-
ma ked he sys em wi h a 16 nodes cloud machine, and ound ha he GWM is capable
o keeping a mean usage o 14.98 nodes du ing he simula ions, le e aging he a ailable
esou ces. Almos all he simula ions o his wo k ha e been ca ied wi h his ool, and
he esul s a e posi i e.
32 Chap e 7. Conclusion
7.1 Fu u e wo k
We p esen he e a comp ehensi e lis o u u e asks ha can be ca ied in o de o con inue
he wo k s a ed in his hesis.
•The MGG a iabili y can be u he imp o ed by aking in o conside a ion he e ec
o he ga e- i s and ga e-las echniques. Doing his, we could gene a e Vo onoi g ains
ha ep esen he ga e in he wo possible implan a ion echniques and compa e hem
di ec ly.
•The LER a iabili y sou ce can be applied in di e en lines o he de ice. We ha e
only used he mos impo an , he FER, which is applied in he body o he de ice in
he di ec ion o he cu en low. Applying his a iabili y along he ga e, ans e se o
he de ice, may p o e use ul.
•The FSM can be applied o ano he a iabili y sou ce o he han MGG, and also o
mo e de ices geome y in o de o imp o e ou knowledge o he sensi i i y o he
de ice.
•GWM is being expanded igh now o implemen new mechanisms, like dependency
be ween asks ha allows he use o de ine no only a ask bu a pipeline o da a be ween
asks. This would allow complex in e ac ions o be ca ied on au oma ically.
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Lis o Tables
