Impac o in insic pa ame e luc ua ions on he
pe o mance o In0.75Ga0.25As implan ee MOSFETs
N. Seoane1, A. Ga cia–Lou ei o1, M. Aldegunde1, K. Kalna2
and A. Aseno 2
1Dep . o Elec onics & Compu e Science, Uni . o San iago de Compos ela,15782
San iago de Compos ela, Spain
2Dep . o Elec onics & Elec ical Enginee ing, Uni . o Glasgow, Glasgow G12
8LT, Sco land, Uni ed Kingdom
E-mail: [email p o ec ed]s
Abs ac . We in es iga e he le el o s a is ical a iabili y in implan ee (IF)
MOSFETs, which a e one o he mos p omising candida es III–V channels
implemen a ion. We epo esul s o he h eshold ol age (VT) luc ua ions in
agg essi ely scaled IF III–V MOSFETs induced by andom disc e e dopan s in he
δ–doping plane ob ained using 3D d i –di usion (D–D) de ice simula ions. The D–
D simula o is me iculously calib a ed agains esul s ob ained om ensemble Mon e
Ca lo de ice simula ions. The simula ed 30, 20 and 15 nm ga e leng h In0.75Ga0.25As
channel IF ansis o s exhibi h eshold ol age s anda d de ia ions o 42, 58 and
61 mV, espec i ely, a a d ain ol age o 0.1 V. A a d ain ol age o 0.8 V, he
h eshold ol age s anda d de ia ions inc ease o 55, 71 and 81 mV, espec i ely.
While he s anda d de ia ions o VTin he 30 and 20 nm IF MOSFETs a e close
o hose obse ed in bulk Si MOSFETs wi h equi alen ga e leng hs, he h eshold
ol age s anda d de ia ion in he 15 nm ga e leng h IF MOSFET is lowe .
PACS numbe s: 81.05.Ea, 85.30.De
Submi ed o: Semicond. Sci. Technol.
Impac o in insic pa ame e luc ua ions on he pe o mance o IF MOSFETs 2
1. In oduc ion
Wi h he scaling o he CMOS echnology owa ds he 22 nm gene a ion, silicon
channel con en ional and no el MOSFET a chi ec u es ace di icul ies o mee he
pe o mance equi emen s [1]. The e o e, in ensi e esea ch is unde way o eplace
he Si channel wi h o he high mobili y semiconduc o which can deli e signi ican
pe o mance imp o emen . MOSFETs wi h Ge channels [2] o p–channel applica ions
o compound semiconduc o s [3] o n–channel applica ions a e now a widely accep ed
op ion o o e coming he pe o mance limi a ions inhe en o he low mobili y o Si
[4]. Recen de elopmen s such as he demons a ion o a high–κga e dielec ic s ack
o GaAs wi h an unpinned in e ace [5], and sui able epi axial laye s uc u es ha e
subs an ially imp o ed he p ospec o he in oduc ion o III–V MOSFETs o high
pe o mance low powe CMOS applica ions. III–V n–channel MOSFETs in combina ion
wi h high pe o mance p–channel Ge ansis o s a e becoming se ious candida es o co–
in eg a ion in dual channel CMOS pla o ms [1], which may ha e unique ad an ages in
ega d o RF, swi ching and powe con ol unc ions.
Wi h he scaling o silicon MOSFETs o nanome e dimensions, he in insic
pa ame e a ia ion in oduced mainly by disc e eness o cha ge and ma e has become
a majo bo leneck o scaling and in eg a ion [6]. One o he majo sou ces o s a is ical
a iabili y a e he andom disc e e dopan s in he ac i e egion o he ansis o s. The IF
MOSFETs may ha e supe io obus ness agains dopan s induced a iabili y as dopan s
a e sepa a ed om he mobile elec ons in he channel. Howe e , he p oximi y o he
δ–doping plane may s ill signi ican ly a ec he elec on popula ion and anspo in
he channel. The e o e, he analysis o he po en ial in insic a ia ions is i al o he
p ope assessmen o he scaling po en ial o III–V IF MOSFETs.
In his wo k, we s udy he h eshold ol age a iabili y due o he p esence o
andom disc e e dopan s in he δ–doping laye o IF In0.75Ga0.25As MOSFETs. The
de ices, scaled o ga e leng hs o 30, 20 and 15 nm, ha e been simula ed using a 3D
pa allel d i –di usion (D–D) de ice simula o desc ibed in de ails elsewhe e [7]. The
pa allelisa ion o he code has been ca ied ou using he s anda d message passing
in e ace (MPI) [8].
In sec ion 2 we in oduce he basic ea u es o ou 3D D–D de ice simula o and
he adop ed simula ion me hodology. The de ice s uc u e and he calib a ion o he
d i –di usion simula o agains Mon e Ca lo simula ion da a a e p esen ed in sec ion 3.
The simula ed a iabili y in he h eshold ol age is p esen ed in sec ion 4. Finally, he
las sec ion summa ises he main conclusions o his wo k.
2. Simula ion me hodology
Figu e 1 shows he low cha o he 3D pa allel ini e elemen simula o o IF
he e os uc u e MOSFETs illus a ing he compu a ional p ocedu e used o sol e he
d i –di usion anspo model equa ions. In his model, he Poisson and he con inui y
Impac o in insic pa ame e luc ua ions on he pe o mance o IF MOSFETs 3
equa ion o elec ons a e sol ed consis en ly wi h mixed Di ichle and Neumann
bounda y condi ions. The disc e isa ion o he Poisson equa ions has been ca ied ou
using he Ri z–Gale kin app oxima ion wi h linea ini e elemen basis unc ions [9].
On he o he hand, he disc e isa ion o he con inui y equa ions equi es a special
app oach. In pa icula , he Scha e e –Gummel disc e isa ion scheme has been used
in his wo k [9].
The non–linea Poisson equa ion and he cu en con inui y equa ion o elec ons
a e decoupled using Gummel i e a ions and linea ised using he New on–Raphson
me hod. The linea sys ems a e hen sol ed in pa allel using domain decomposi ion
me hods [10]. To sol e he local linea sys ems wi hin each subdomain we ha e
used K ylo subspace sol e s, such as he FGMRES and he BiCGSTAB me hods,
p econdi ioned by Incomple e LU ac o isa ions dependen on bo h a nume ical
h eshold and a ce ain le el o ill–in (s anda d ILUT p econdi ione ). Mo e de ails
abou he simula o can be ound in [7].
Quan um co ec ions like he densi y g adien me hod [11] ha e no been included
in o he D–D app oach a his s age, al hough a such simula ed dimensions he use
o quan um co ec ions would be desi able. The quan um co ec ions would a ec he
desc ip ion o he indi idual dopan s in he δ–doping laye and he shape o ca ie
densi y in he channel. Elec os a ically he dopan s induce a deep Coulomb well
esul ing in an a i icially high ca ie densi y in he a ac i e po en ial case. The
quan um co ec ions like densi y g adien me hod would es ic he high ca ie densi y
by app oxima ing he quan um con inemen e ec s. This a i icial high ca ie densi y
c ea ed by he Coulomb po en ial o a poin –like cha ge is educed in ou case by he
use o a cloud–in–cell assigmen wich sp eads he cha ge o e he e ahed al elemen
[12]. Besides, only he ails o he Coulomb po en ial o he disc e e dopan s in he
δ–doping laye a ec he po en ial dis ibu ion in he channel and he a i icial ca ie
apping in his case is less p onounced. The e o e, ou classical simula ions, which a e
compu a ionally less expensi e, s ill p o ide use ul quali a i e esul s.
3. De ice s uc u e and calib a ion
The de ices analysed he e a e In0.75Ga0.25As enhancemen mode MOSFETs wi h
implan ee sou ce/d ain egions [13]. The MOSFET s uc u e is g own on an InP
subs a e and consis s o a 49 nm In0.52Ga0.48As bu e laye and a Si δ–doping laye wi h
3×1012 cm−2. The In0.75Ga0.25As channel laye is sandwiched be ween In0.53Ga0.47As
embed laye s. The high mobili y channel o ms a quan um well wi h ene gy ba ie s
compa able o he supply ol ages a and beyond he 22 nm node. In his way,
he ca ie s a e well con ined o he channel, p o iding ul a– hin body like scaling
pe o mance. Finally, an amo phous Ga2O3/GdGaO dielec ic s ack is used o sepa a e
a me al ga e as shown in igu e 2. The de ices ha e been scaled, in bo h e ical and
ho izon al dimensions in espec o ga e leng hs o 30, 20 and 15 nm. All dimensions
used in he scaling p ocess a e collec ed in able 1.
Impac o in insic pa ame e luc ua ions on he pe o mance o IF MOSFETs 4
The 3D D–D simula o is me iculously calib a ed agains ID–VGcha ac e is ics
ob ained om MC simula ion esul s [14] a d ain biases o 0.1 and 0.8 V as shown in
igu e 3 o ga e leng hs o 30, 20 and 15 nm, espec i ely. The wo k unc ion o he
me al ga e was ixed o 4.0 eV. In he calib a ion, we ha e used a high ield mobili y
model [15]. In he calib a ion p ocess, he low ield mobili y and he sa u a ion eloci y
a e adjus ed o ma ch accu a ely he MC simula ion da a. The calib a ion p ocess
yields a low ield mobili y o 5000 cm2/Vs and a sa u a ion eloci y o 4 ×107cm/s
in he channel o he 30 nm ga e leng h implan ee In0.75Ga0.25As MOSFET, and o
4000 cm2/Vs and 108cm/s o he 20 nm ga e leng h and, inally, o 5000 cm2/Vs and
6.5×107cm/s o he 15 nm ga e leng h.
Figu e 3 also show he da a ob ained om he D–D simula ions on a loga i hmic
scale in he inse s in o de o illus a e he sub h eshold slope. Table 2 collec s he
sub h eshold slope a low and high d ain ol ages o he h ee scaled de ices. The
sub h eshold slope wo sen only sligh ly when he IF ansis o is scaled om 30 o
20 nm ga e leng h, bu i de e io a es by 17% when scaled o he 15 nm ga e leng h.
The sub h eshold slopes a e simila o hose measu ed in Si hin–body ansis o s [16].
Finally, we would like o s ess he limi a ions o ou simula ion model. The D–D
app oach does no p ope ly ep esen he non–equilib ium ca ie dynamics and ballis ic
anspo e ec s in sub–50 nm IF MOSFETs. Howe e , when accu a ely calib a ed
agains he esul s om ensemble Mon e Ca lo de ice simula ions [14] he D–D
app oach gi es a good indica ion o he expec ed in insic ma e ial pa ame e s a ia ions
associa ed wi h de ice elec os a ics like he h eshold ol age luc ua ions [17].
4. Th eshold ol age a iabili y
To in es iga e he h eshold ol age a ia ions in he IF MOSFETs in oduced by he
andom disc e e dopan s in he δ–doped laye , a andom dis ibu ion o dopan s is
gene a ed om he con inuous doping p o ile. The andom placemen o he dopan s in
he δ–doped laye is pe o med on an a omis ic g id de ined by he posi ions o he In,
Al and As a oms, as can be seen in igu e 4. The cha ge associa ed wi h his dis ibu ion
is hen mapped o he de ice simula ion mesh using a cloud–in–cell algo i hm [12]. Fo
e e y dopan , i s cha ge is spli among he ou nodes o he e ahed on enclosing i .
The ac ion o he cha ge assigned o he pa icula node is a ba ycen ic coo dina e
o he cha ge posi ion wi h espec o ha node. In his way, he poin –like cha ge is
smoo hed on he nea es neighbou mesh nodes. Figu e 5 depic s elec on densi y and
conduc ion band p o ile ac oss he he e os uc u e a he posi ion o a andom dopan
in he del a–doped laye . The ionised impu i y a ec s he conduc ion band, p oducing
a po en ial well which esul s in a e y sha p peak o he elec on densi y. The in luence
o his e ec in a h ee–dimensional simula ion can be seen in igu e 6 which shows an
example o he elec on densi y a loga i hmic scale inside he channel and he δ–doping
laye . The posi ion o he dopan s in luences he cha ge dis ibu ion in he channel
al hough he e is a physical sepa a ion be ween hem. The ails o Coulomb po en ial
Impac o in insic pa ame e luc ua ions on he pe o mance o IF MOSFETs 5
associa ed wi h he ionised dono s p oduce a lowe ing o he conduc ion band le el and
an inc ease in he elec on densi y in he channel. The ail o Coulomb po en ial abo e
he disc e e dopan s c ea es islands o nega i e cha ge esul ing in di e en a ou ed
pa hs o he elec ons and consequen ly di e en I–V cha ac e is ics.
We ha e gene a ed s a is ical samples o 100 mic oscopically di e en ansis o s
wi h di e en andom posi ions o dopan s in he δ–doping laye o analyse he impac o
andom disc e e dopan s induced luc ua ions on he h eshold ol age. We ha e used
a cons an cu en c i e ion o ex ac he h eshold ol age. A low d ain bias, he
elec os a ic beha iou below he channel is e y simila o he scaled de ices because
he dimensions o he channel and he laye s below a e kep cons an du ing he scaling
and he same cons an cu en c i e ion has been used (ID= 10 nA·W/L). Howe e ,
wi h an inc easing he d ain bias o 0.8 V he elec os a ic beha iou o each scaled
ansis o becomes a e y di e en . The e o e, a he high d ain bias, we ha e used a
di e en cons an cu en c i e ion o each one o he h ee scaled de ices (ID= 100
nA·W/L, ID= 50 nA·W/L and ID= 300 nA·W/L o he 30, 20 and 15 nm ga e
leng h de ices, espec i ely). The c i e ion has been chosen conside ing he esul s om
simula ions wi h a con inuous doping p o ile whe e ID–VGcha ac e is ics on a log scale
exhibi s a linea beha iou in he sub– h eshold egion. The dis ibu ions o h eshold
ol age a d ain biases o 0.1 V and 0.8 V a e p esen ed in igu es 7 and 8 espec i ely,
o each ga e leng h de ice. The s a is ical mean o he h eshold ol age ob ained
om he sample o de ices wi h di e en dopan dis ibu ions in he δ–doping laye is
always la ge ha he nominal alue om he con inuous simula ions, a bo h low and
high d ain biases. This beha iou is opposi e o he gene al ends o a e age h eshold
ol age lowe ing obse ed in sub–100 nm ga e leng h bulk Si MOSFETs simula ed wi h
andom disc e e dopan s in he channel egion only [18]. This is no o ally su p ising
because he luc ua ions in hese wo de ice a chi ec u es a e coming om wo di e en
sou ces: accep o s in he channel in he bulk Si MOSFET and dono s in he δ–doping in
he IF MOSFET. The disc e e dopan s om he δ–doping laye induce he localisa ion
o elec ons in o Coulomb wells. This localisa ion, on a e age, educes he cu en low
along he channel when compa ed o he con inuous δ–doping simula ions and he ga e
has o lowe , on a e age, he po en ial ba ie much mo e. The a e age h eshold ol age
inc ease a a low d ain ol age is mo e p onounced when he de ices a e scaled down
o 15 nm. Howe e , his beha iou is no seen a high d ain ol age, when he a e age
inc ease is mos impo an o he 20 nm ga e leng h de ice.
Figu e 9 shows he conduc ion band p o ile and elec on densi y in a plane om
sou ce o d ain along he middle o he channel o he 15 nm ga e leng h de ice, a
VD=0.1 V and VG=0.5 V. The e ec o he posi ion and numbe o andom dopan s
on he channel is shown o h ee di e en andom dopan con igu a ions and compa ed
o a de ice wi h con inuous doping (smoo h). The con igu a ion ha p oduces a
highes cu en has a la ge numbe o dopan s, 29, compa ed o he nominal alue
o 21. In his case, he po en ial ba ie is lowe han in he o he cases and he he
elec on densi y is highe , which leads o a highe d ain cu en . The o he wo andom

Impac o in insic pa ame e luc ua ions on he pe o mance o IF MOSFETs 6
dopan con igu a ions ha e 18 and 16 dopan s p o iding cu en s o 20 A/m and 10
A/m espec i ely (since we simula e de ices wi h pa icula wid h and no ansla ion
symme y i is no app op ia e o p o ide cu en densi y bu he exac simula ed
cu en ). The e ec o he posi ion o he dopan s is also no iceable in he igu e.
Fo ins ance, o he lowes cu en de ice, he po en ial ba ie below he ga e is lowe
on one side o he channel, which a ou s he cu en low he e. Howe e , o he de ice
wi h a cu en o 20 A/m he po en ial ba ie below he ga e is highe in he middle o
he de ice, so he cu en low will be h ough he la e al egions o he de ice.
Table 3 shows he s anda d de ia ion o he h eshold ol ages ob ained om his
a iabili y s udy as a unc ion o he ansis o ga e leng h and he applied d ain ol age.
The s anda d de ia ion alues o scaled bulk Si MOSFETs a e p o ided in he same
igu e o compa ison [17]. The impac o luc ua ions becomes mo e p onounced wi h
he applied d ain bias since he s anda d de ia ion inc eases. The s anda d de ia ion o
he h eshold ol age also inc eases wi h educing ga e leng h, ollowing app oxima ely
an ae ial dependence o he andom dopan induced h eshold ol age a ia ion which
magni ude is p opo ional o he i s o de o 1
√W L . Resul s show ha he s anda d
de ia ion o In0.75Ga0.25As IF MOSFET is close o ha o bulk silicon MOSFETs wi h
compa able ga e leng h as can be seen in able 3. The magni ude o he h eshold
ol age luc ua ions indica es ha he andom dopan induced a iabili y om he δ–
doping laye in IF MOSFETs has a simila impac on hei scaling and in eg a ion as
in he same ga e leng h implan ed Si ansis o s [17].
5. Conclusion
In his wo k, a calib a ed pa allel ini e elemen 3D D–D de ice simula o [7] has been
adop ed o he simula ion o IF III–V MOSFETs. The simula o has been me iculously
calib a ed agains ID–VGcha ac e is ics a low and high d ain ol ages ob ained om
comp ehensi e Mon e Ca lo de ice simula ions [14]. The simula o has been used
o in es iga e he in luence o andom disc e e dopan s in he δ–doping laye on he
h eshold ol age in 30 nm, 20 nm and 15 nm ga e leng h IF In0.75Ga0.25As MOSFETs.
The sub h eshold slopes o he IF MOSFETs in he ange o 100 mV/dec, ex ac ed
om he d i –di usion simula ions, a e compa able wi h hose obse ed in no el Si
hin–body ansis o s [16]. The sub h eshold slope sligh ly inc eases when he de ice is
scaled om 30 nm o 20 nm ga e leng h. When he IF ansis o is scaled in espec o
a ga e leng h o 15 nm, he sub h eshold slope de e io a es by 17%.
Resul s show ha he impac o luc ua ions becomes mo e p onounced wi h he
inc ease in he applied d ain bias and wi h he educ ion o he ga e leng h. The
magni ude o he h eshold ol age s anda d de ia ion is simila o ha obse ed in
equi alen bulk Si MOSFETs. The e o e, he in insic pa ame e induced a ia ions in
he h eshold ol age may p esen a simila p oblem o in eg a ion and ci cui design
using IF MOSFETs as o he equi alen ga e leng h Si MOSFETs.
Impac o in insic pa ame e luc ua ions on he pe o mance o IF MOSFETs 7
Acknowledgemen s
This wo k was suppo ed by Spanish Go e nmen (TIN2007–67537–C03–01) and by
Xun a de Galicia (DXIDI07TIC01CT and INCITE08PXIB206094PR). NS and MA
hank Xun a de Galicia and Minis e io de Educaci´on y Ciencia de Espa˜na o hei
awa ded ellowships (A. Al a i˜no and FPU espec i ely). NS also hanks Xun a de
Galicia o p o iding inancial suppo o he posi ion as a isi ing esea che a he
Uni e si y o Glasgow. KK would like o acknowledge he UK EPSRC suppo h ough
g an (EP/D070236/1).
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Impac o in insic pa ame e luc ua ions on he pe o mance o IF MOSFETs 9
Lis o Tables
Table 1. Dimensions conside ed o he scaling o IF In0.75Ga0.25As MOSFETs.
Ga e leng h [nm]
Thickness o [nm] 30 20 15
Sou ce- o-ga e sepa a ion 30 20 15
Ga e- o-d ain sepa a ion 30 20 15
High-κdielec ic 3 2 1.5
In0.52Al0.48As op space 2 1 1
In0.53Ga0.47As op embed 1 0.5 0.5
In0.75Ga0.25As channel 5 5 5
In0.53Ga0.47As bo om embed 1 1 1
In0.52Al0.48As bo om space 2 2 2
δ-doping 3 ×1012cm−2
In0.52Al0.48As bu e 49 49 49
Table 2. The sub h eshold slope a low (VD= 0.1 V) and high (VD= 0.8 V) d ain
ol ages o he IF In0.75Ga0.25As MOSFETs scaled in espec o indica ed ga e leng hs.
Ga e leng h Sub h eshold slope [mV/dec]
[nm] VD= 0.1 V VD= 0.8 V
30 87.5 94.7
20 88.1 106.2
15 105.6 131.7
Table 3. S anda d de ia ion o he h eshold ol age as a unc ion o he ga e leng h
and he d ain ol age o scaled In 0.75Ga0.25As IF MOSFETs compa ed wi h he
s anda d de ia ion obse ed in scaled bulk Si MOSFETs.
In0.75Ga0.25As IF MOSFETs Bulk Si MOSFETs [17]
VDGa e leng h [nm] Ga e leng h [nm]
[V] 30 20 15 35 25 18 13
S anda d de ia ion, σVT[mV]
0.1 42 58 61 33 46 61 100
0.8 55 71 81 – – – –
Impac o in insic pa ame e luc ua ions on he pe o mance o IF MOSFETs 16
(a) (b)
Figu e 9. Conduc ion band p o ile (a) and elec on densi y (b) in a plane om sou ce
o d ain along he middle o he channel o he 15 nm ga e leng h IF MOSFET de ice.
Fou si ua ions a e ep esen ed: a de ice wi h con inuous doping (smoo h) and h ee
de ices wi h di e en andom dopan con igu a ions. The ob ained d ain cu en o
each case is also indica ed. The sou ce and d ain egions a e on he igh and le ,
espec i ely.