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IEEE EDS DL IEEE EDS DL –– Tokyo Institute of Technology, JapanTokyo Institute of Technology, Japan
IEEE-EDS / DL EEE / NTU
U ifi ti f MOS C t M d l ith thU ifi ti f MOS C t M d l ith thU ifi ti f MOS C t M d l ith thU ifi ti f MOS C t M d l ith thUnification of MOS Compact Models with the Unification of MOS Compact Models with the Unified Regional Modeling ApproachUnified Regional Modeling Approach
Unification of MOS Compact Models with the Unification of MOS Compact Models with the Unified Regional Modeling ApproachUnified Regional Modeling Approach
Xi ZhXing Zhou
School of Electrical and Electronic EngineeringNanyang Technological University, Singapore
August 26, 2011
Email: [email protected]
X. ZHOU 1 © 2011
OutlineOutline
IEEE-EDS / DL EEE / NTU
OutlineOutline
Motivation for MOS Model Unification
Unified Regional Modeling (URM) Approachg g ( ) pp Surface potential of generic MOSFET for bulk/SOI/DG/GAA Body doping and thickness scaling Model symmetry and asymmetric MOS modeling
Model Extension to SB/DSS Modeling
Model symmetry and asymmetric MOS modeling
Shottky-barrier (SB) MOS with ambipolar transport Dopant-segregated Shottky (DSS) MOS with subcircuit approach
Xsim Model Summary
X. ZHOU 2 © 2011
CMOS Technology Generations and Scaling LimitsCMOS Technology Generations and Scaling Limits
IEEE-EDS / DL EEE / NTU
CMOS Technology Generations and Scaling LimitsCMOS Technology Generations and Scaling Limits
Today
Technology?Technology?ec o ogyec o ogy
Physics?Physics?
Statistics?Statistics?
Economics?Economics?(Yield)(Yield)
X. ZHOU 3 © 2011
Models and Modeling GroupsModels and Modeling Groups
IEEE-EDS / DL EEE / NTU
Models and Modeling GroupsModels and Modeling Groups
NGSOI/MG ModelNGSOI/MG Model
BSIMBSIM EKVEKV HiSIMHiSIM ULTRAULTRA--SOISOIACMACMUFDG/UFSOIUFDG/UFSOI
XsimXsim Technology-dependent predictive model DG/SOI/GaN SiNW/CNT PCMOS
ISNEISNE
Low Eng/GaN
X. ZHOU 4 © 2011
XsimXsim Technology-dependent predictive model DG/SOI/GaN SiNW/CNT PCMOS Low Eng/GaN
MOSFET Compact Models: History and FutureMOSFET Compact Models: History and Future
IEEE-EDS / DL EEE / NTU
1966 1978 1985 1995 2005
MOSFET Compact Models: History and FutureMOSFET Compact Models: History and Future
V basedQb linearization
1966 1978 1985 1995 2005
CA
Classical bulk-CMOS ~40 yrs
Sah–Pao (input)Voltage Equation
Pao–Sah (output)C t E ti
Qi-based
Vt-basedQi linearization
Iterative / explicitsso
n +
GC
ChargeSheetModel(Q =Q +Q )Current Equation s-based
Iterative / explicit
Po
is (Qsc=Qb+Qi)
Non-classical CMOS ntr
ivia
ln
triv
ial
Non-classical CMOS
SOISOIBulk Voltage/Current Equations, CSM
Partially-Depleted (PD)Fully-Depleted (FD), Ultra-Thin Body (UTB)
Non Charge Sheet
no
no
MGMG New Voltage/Current Equations
Non-Charge-Sheet
Symmetric/Asymmetric Double Gate (s-DG/a-DG)
Tri-gate, GAA, Schottky-barrier, DSS, TFET, …Body Contact/Floating Body
X. ZHOU 5 © 2011
Tri gate, GAA, Schottky barrier, DSS, TFET, …Body Contact/Floating Body
Need for an Extendable Core Model for Future GenerationNeed for an Extendable Core Model for Future Generation
IEEE-EDS / DL EEE / NTU
Need for an Extendable Core Model for Future GenerationNeed for an Extendable Core Model for Future Generation
Time
Vt-based models
’60 ’70 ’80 ’90 ’00 ’10
Q b d d l
Pao–Sah One model for each structure is
Qi-based models
s-based models
History has witnessed generations of MOS models
and efforts required from one generation to the next …
— Need for a core model extendable to future generations, MG/FinFET is just
duplicating efforts
IDGS
IDGS DGS DG1S
II
g ,and with less duplicating efforts
MG/FinFET is just a special case
ID
Ids (B)
ID IDID
B lk PD SOI FD UTB/SOI DG/GAA/SB/DSS
B Sub Sub
G2
X. ZHOU 6 © 2011
Bulk PD-SOI FD-UTB/SOI DG/GAA/SB/DSS
New Challenges in SOI/MG/GAA MOSFET ModelingNew Challenges in SOI/MG/GAA MOSFET Modeling
IEEE-EDS / DL EEE / NTU
New Challenges in SOI/MG/GAA MOSFET ModelingNew Challenges in SOI/MG/GAA MOSFET Modeling
SymmetrySeparate S/D modeling
y
VSVD
VdVs Vd sat
VG1
Tox1
0Carrier type
Separate S/D modeling with G(B)-ref for complete symmetry, as well as for asymmetric device
L
y
n+n+ s1(y)
DGPN
VdVs Vd,sat0
Core model (s) applicable to both unipolar (PN) and
Xo(x, y)o(y)
Ei = qs(y)
PN
S/D Contact
‘ambipolar’ (SB)
s2(y)NA ND
Bulk
SB“Thick-body” effect due to 2D field in S/D
TSi + Tox2
V
VB
s2(y)NA ND
x
TSi
Body Contact
Body dopingBody thickness
TSi/NSi full scaling from Lightly-doped can be
X. ZHOU 7 © 2011
VG2x
thin/doped to thick/pure body “intrinsic” at high temp
Generic DoubleGeneric Double--Gate MOSFET with Any Body DopingGate MOSFET with Any Body Doping
IEEE-EDS / DL EEE / NTU
Generic DoubleGeneric Double Gate MOSFET with Any Body DopingGate MOSFET with Any Body Doping
VG1V VLLrx2 NA (cm3) 02 2dm Si FX qp VS VD
NNg1g1
LLgg
Tox1
00
y1
RR
r
p1p1
1017
1014
Bulk
FinFET/SiNW(unintentional doped)(ox1)
(< 60 m)
0dm Si F qp
s1s1
o1o1
nn++
00 R R nn++
XXo1o1(V(Vg1g1))1010
( p )(intrinsic @ 200 C)
Intrinsic doping(27 C)
0o1o1
00 o1o1 = = o2o2 = = VVrr = 0 = 0 (at (at VVgigi==VVFBiFBi, V, Vss==VVdd=0)=0)
Xdm (m)0.1 1 10010
(NA = ND = 0: undoped = “pure” Si)
03 60
TTSiSiNNsdsd 2200
o2o2XXo2o2(V(Vg2g2))
y2
Bulk: TSi >> Xdm, with BC: o = Vb = VB
SOI: T > X without BC: ‘floating’
0 0DA N nN p
TTSiSi
Tox2
s2s200
NNg2g2
y2
p2p2
(ox2)
SOI: TSi > Xdm, without BC: o floating
DG/GAA: TSi/R << Xdm: ‘volume inversion’
( : ‘virtual electrode’)2
X. ZHOU 8 © 2011
x1 VG2
(o: virtual electrode )
DGDG FinFETsFinFETs / GAA/ GAA SiNWsSiNWs
IEEE-EDS / DL EEE / NTU
DG DG FinFETsFinFETs / GAA / GAA SiNWsSiNWs
G VG Vg = VFB~Vt In undoped ‘long’/thick body
DS
G G
VS VD
y0Tox
+ +
L
V Vd + V ( )
Vg
Nsd
g
0
Lg
s
FB In undoped long /thick-body DG/GAA, potential reference (Vr) is at one point: o at Vgr = VFB
and Vd = 0n+ n+
TSiNA ND
Xo [Eo = 0]
VsVdFn = F + Vc(y) Nsd
Xo
TSi
Xj = TSi
R
0 GAA:TSi = 2R
s
oo = VrFp = F + Vr
and Vds = 0
“Volume inversion” for VFB<Vgr<Vt: o follows Vg
x
Tox
Vg
TSi
G VG Vg
o follows Vg
“Strong inversion” for Vgr>Vt
In ‘short’/thick-body DG/GAAx
x
Vbi,s + Vs
Vbi,d + Vd
G
g In short /thick-body DG/GAA, source/drain (S/D) region 2D fields extend to the channel, causing VFB to be TSi dependent
S Ds(0)
s(L)
Go = Vr
causing VFB to be TSi dependent
‘Thin-body’ DG/GAA have ‘long’-channel behaviors
X. ZHOU 9 © 2011
yL0
o channel behaviors
The Generic SOI/DG/GAA MOSFETThe Generic SOI/DG/GAA MOSFET
IEEE-EDS / DL EEE / NTU
The Generic SOI/DG/GAA MOSFETThe Generic SOI/DG/GAA MOSFET
Vg1 Common/symmetric-DG [GAA]g
Vs Vd
Tox1 y0 LKox1s1
o(Xo)
Xj Vc
NA NDVr
y [ ] Vg1 = Vg2 = Vg: two gates with one bias Cox1 = Cox2: s-DG (Xo = TSi/2; [R]) Full-depletion: VFD = V (Xd=TSi/2)
V
Tox2x
TSiKox2
s2
oo
Vc
A Dr Full-depletion: VFD = Vg(Xd=TSi/2) Cox1 Cox2: ca-DG (Xo < TSi)
Independent/asymmetric-DGVg2
Zero-field potential: o [o'(Xo) = 0]
Independent/asymmetric DG Vg1 Vg2: ia-DG, biased independently Zero-field location may be outside body Consider two “independent” gates; linked
Imref-split: Vcr = Fn – Fp = Vc – Vr
Vr = Vb (BC: body-contacted)V = V = min(V V ) (“FB”: w/o BC)
Consider two independent gates; linked through full-depletion condition: Xd1 + Xd2 = TSi
Vr = Vmin = min(Vs, Vd) ( FB : w/o BC)
Bulk: special case of s-DG SOI: special case of ia-DG
GAA Unification of MOS
SOI ia-DG ca-DG s-DG bulk
X. ZHOU 10 © 2011
SOI ia-DG ca-DG s-DG bulk
The PoissonThe Poisson––Boltzmann Equation and SolutionBoltzmann Equation and Solution
IEEE-EDS / DL EEE / NTU
2
2D A
DA
q p n N Ndn
qNNp
2 2d d GCA:
The PoissonThe Poisson Boltzmann Equation and SolutionBoltzmann Equation and Solution
Charge neutrality:
20 02
2
,1 FF thc cb hb tth
Si Si Si
cbSi Si
D
V v
A
VvV v
ndx
qp qpG V
NN
eee
p
2 2dy dx
GCA:
Fn thvin n e
Charge neutrality:
0 0
F th Fn th
A D
v vi
p n N N
n e e
Fp thv
ip n e
0, , 0,y y E y E y
B.C.’s: o dmX X
0F cb th
b
V viV
n n n e
10 exp sinh
2F th
b
v A Di iV
i
N Np p n e n
n
2 2
0s s sEsE qpd
E dE d G V d
2
2x x x
x
dE dE dEd dE
dx dx d dx d
x
dE
dx
Fp F bV
0, , 0,
, 0, , 0
s x s
o b x o
y y E y E y
X y V E X y
1 2
s
F V G V d
Fn F cV
020 0 0
,2
sx x cb
Si
qpE dE d G V d
dx
22 20 02 21 1 ,F th th tsscb hv v v
s th th s ssV
cs b
qp qpE e v e v e F V
0
, ,s s cb cbF V G V d thv kT q
02 Siq p
C
S Sii
2, sgn 1 12
sbF c sss s cb s ss
vth
EF v v e e e
qp
s s th
F F th
v
v
oxC
X. ZHOU 11 © 2011
02 Siqp cb cb thv V v
The Complete (“SahThe Complete (“Sah––Pao”) Voltage EquationPao”) Voltage Equation
IEEE-EDS / DL EEE / NTU
E E Q C TGauss law: E QE Q
The Complete ( SahThe Complete ( Sah Pao ) Voltage EquationPao ) Voltage Equation
Si s ox ox oxE E Q
gb MS ox sV V ox ox oxE V T
ox ox oxC T
02 Si oxq p C FB MS ox oxV Q C
Gauss law:
Potentialbalance:
Si s scE Q ox ox gE Q
ox gb MS s ox ox gb FB sox ox ox oxox ox oxs
Si Si Si Si
C V Q C V VV T QE QE
Poisson
sgn
2 2sgn exp exp 1 exp 1 exps
ss
gb FB s s
F Fs
cb cbth th s
V V f
v vv v v
V
v
V
p AN n DN
th th th thv v v v
g oxoxQQ C
oxsc CQ
ox os xdi C QQ CQ
strb acox ou xc s bC CQ Q QQ
= +
Ward–Dutton partition
Unified Regional Model (URM)Charge balance
b oxigQ Q Q Q smoothing
one-piece
Charge sheet model (CSM)
X. ZHOU 12 © 2011
Unified Regional Model (URM)Charge balance Charge-sheet model (CSM)
The SurfaceThe Surface--Potential SolutionsPotential Solutions –– Piecewise RegionalPiecewise Regional
IEEE-EDS / DL EEE / NTU
The SurfaceThe Surface Potential Solutions Potential Solutions Piecewise RegionalPiecewise Regional
Accumulationths vh bv e V V
sgngb FB s sV V f
2
, Accumulation
,Depletion
,Strong inversionF th tb hsc
th gb FB
FB gb t
v vth gb t
V
s
v e V V
V V V
v e e V V
, gth gb t
Piecewise regional solutions
V V
2
2
2 ,Only holes,
,Only acceptors,2 4
gb FB th cc gb FB
s gb FB FB gb tdd A
cc V V v W V V
V V V V
p
V N
L exp22
gb FBcc
thth
V VW
vv
2 4
2 ,Only electrons,gb FB th ss gb tss V V v V nW V
L
2exp
22gb FB F
sst
c
hth
bV VW
vv
V
WL is the Lambert W function, which is the solution of the equation: exp 0X aX B
where and 21exp , thvB
W a
22, ,
2gb FB F cbss F cb
ss ss
V V VVX B
v v
, ,
2gb FBcc
cc cc
V VX B
v v
X. ZHOU 13 © 2011
a a 2 th th
v v2 th thv v
The SurfaceThe Surface--Potential SolutionsPotential Solutions –– Unified RegionalUnified Regional
IEEE-EDS / DL EEE / NTU
The SurfaceThe Surface Potential Solutions Potential Solutions Unified RegionalUnified Regional
Smoothing and transition functions ;f x g
2; 0.5 4f x x x
2; 0.5 4r x x x
satx
, ;eff satx x
x
;x
Unified regional solutions
;r
2, ; 0.5 4eff sat sat sat sat satx x x x x x x x
x
;r x
Unified regional solutions
2
2
2gb FB gbr
gbr th ccV V Vacc cc V v W
L ;r gbgbr FB aV VV
gbar FBgb gbVVV V
2
2 4
2
gb FB gbf
gb FB gbf
sub dds gbfV V V
gbs f th ssV V Vtr ss
V
V v W
L
;gbf f gb FB fV V V
• Turn f to satisfy charge neutrality s(VFB) = 0;• Tune for smoothness at V = V
;f gbgba FB aV VV
Single-piece unified solutions
;d ff b a ceff dss c b
• Tune a for smoothness at Vgb = VFB.
X. ZHOU 14 © 2011
, ;suds seff rb t a ceff dss c accsa sub
The Surface Potential: Unified Regional Modeling (URM)The Surface Potential: Unified Regional Modeling (URM)
IEEE-EDS / DL EEE / NTU
The Surface Potential: Unified Regional Modeling (URM)The Surface Potential: Unified Regional Modeling (URM)
g FBdv depV V , ;dds seff rv t a ceff dss c Single
piece
Symbols: MediciLines: Model (Xsim)
V) 1.0
1.2
g p a ceff dss c
V (y) dependentSmoothing
2gbfs ttr h ssV v W L(volume inversion)
piece
tial, s (
V
0 6
0.8
s
acc
dep , ;bd ff fd d ,d g FD Sis X Vd Tf
Vcb(y) dependentSmoothing
TSi and NA
ce P
oten
t
0.4
0.6 dv
str
, ;subd eff fdp de
22
V
Adding(‘ tit hi ’
s at Vgb = VFB is not solved exactly but two pieces are
(e.g., FD-SOI) dependent
Sur
fac
0.0
0.2 2 4 gbfsub V
(‘stitching’,not ‘glueing’)
exactly, but two pieces are “stitched” (rather than “glued”) to form a single-piece (seff) seamlessly “Glued”/iterative
Gate Voltage V (V)
-2 -1 0 1 2-0.2
VFB VFD Vt
2V v W L
seamlessly. Glued /iterative solution requires retaining all the terms in the voltage equation.
X. ZHOU 15 © 2011
Gate Voltage, Vg (V) 2gbra tcc h ccV v W L equa o
SurfaceSurface--Potential Derivatives and Regional ComponentsPotential Derivatives and Regional Components
IEEE-EDS / DL EEE / NTU
SurfaceSurface Potential Derivatives and Regional ComponentsPotential Derivatives and Regional Components
S b l M di i1.2
R i l l ti lSymbols: MediciLines: Model (Xsim)
0 8
1.0sseffd
Regional solutions scale with body doping (NA), body thickness (TSi), o ide thickness (T ) and
dVg
(V/V
)
0 4
0.6
0.8 depdv
acc
str
ds
oxide thickness (Tox), and all terminal biases
Smooth higher-order d i ti
d s/d
0.2
0.4 derivatives
Regional charge model –key to physically-based
i
-2 -1 0 1 2-0.2
0.0 parameter extraction
Foundation to unification of MOS compact models
Common Gate Voltage, Vg (V)(bulk/SOI/DG/NW/SB/DSS)
X. Zhou, et al., (invited review article), J. Comput. Electron., Mar. 2011.
X. ZHOU 16 © 2011
http://www.springerlink.com/content/x8t0742r3m051650/
DopingDoping--DependentDependent ss: “Depletion” vs. Volume Inversion: “Depletion” vs. Volume Inversion
IEEE-EDS / DL EEE / NTU
DopingDoping Dependent Dependent ss: Depletion vs. Volume Inversion: Depletion vs. Volume Inversion
“Depletion” (N = 1014)Symbols: MediciLines: Model (Xsim)
V)
1.0
NA (cm3)
s-DG (Vg1 = Vg2 = Vg)Depletion (NA = 1014)
Slope 1
21 1
2 4sd
dV V
ntia
l, s (
V
0.5
1 2
0
1014
1016
1018
Volume inversion(undoped NA = 0, or
2 4g grfdV V
ace
Pot
en
0.0
Vgs
(V
/V)
0.6
0.8
1.0
1.210beyond full-depletion)Slope = 1
“Low-doping depletion”
Sur
fa
-0.5
2 1 0 1 2
ds/
dV
0.0
0.2
0.4
0.6
Tox = 3 nm
T = 50 nm
Low-doping depletion and “zero-doping volume inversion” have similar behaviors but different
Common Gate Voltage,Vgs (V)-2 -1 0 1 2
-1.0Vgs (V)
-2 -1 0 1 2TSi = 50 nmphysics
Full-doping scaling (zero to high) is only possible to b d l d b th URM
X. ZHOU 17 © 2011
be modeled by the URM
Paradigm Shift: B/GParadigm Shift: B/G--reference and Source/Drain by Labelreference and Source/Drain by Label
IEEE-EDS / DL EEE / NTU
Paradigm Shift: B/GParadigm Shift: B/G reference and Source/Drain by Labelreference and Source/Drain by Label
S/D by convention (nMOS) S/D by convention (nMOS)
• Vd > Vs: Ids > 0 (‘D’ ‘S’)• Vd < Vs: Ids > 0 (‘D’ ‘S’)
• By convention, nMOS Ids always flows from ‘D’ to ‘S’• Terminal swapping for –Vds: involving |Vds| in model
,, ,d effds ef sf effVVV
S/D by label (layout)
Always Source Always Drain,, ,d effds ef b bf s effVVV
Effective drain–source voltage (Vds,eff)
FB: BC:
,ds i b th ds eff sdI q A v V
A A
I I
VV
Id
DGS
Is
,,i b th i s effb bd e b tf hfq A v q A v VV (B)
Ids
Key: Bulk/Ground-reference — auto switch to B/G f h b d t t i bi d fl tiSub
• Vd > Vs: Ids > 0 (D S)• Vd < Vs: Ids < 0 (S D)
B/G-ref when body-contact is biased or floating Intrinsic Ids is an exact odd function of Vds
Physical modeling of asymmetric MOS (nontrivial with “terminal swapping” for negative V )
X. ZHOU 18 © 2011
d s ds ( ) with terminal swapping for negative Vds)
Modeling Asymmetric Source/Drain MOSFETModeling Asymmetric Source/Drain MOSFET
IEEE-EDS / DL EEE / NTU
Modeling Asymmetric Source/Drain MOSFETModeling Asymmetric Source/Drain MOSFET
Symbols: Medici0.8 “Source” and “Drain” by
Symbols: MediciLines: Model
mA
/m
)
0.4
0.6VDS
VSD L = 90 nmt 2
104
ylabel (rather than by MOS convention); i.e., VDS and VSD are different
ent,
|I DS
| (m
0.2
0.4 tox = 2 nmt
(S/
m)
103
10
G Structural asymmetry (e.g., Xj, ND) can be captured by refitting
rain
Cur
re
-0.2
0.0
0 0 0 5 1 0 1 5 2 0
r ou
102
S D
B
p y gphysical parameters (e.g., vsat,s and vsat,d)
M d l b d S/D
0.0 0.5 1.0 1.5 2.0
Dr
-0.4 VDS or VSD (V)0.0 0.5 1.0 1.5 2.0 Models based on S/D
terminal swapping for negative Vds at circuit level can never model
DrainSource/SourceDrain Voltage, VDS or VSD (V)
Xj,s = 80 nm, ND,s = 1019 cm3; Xj,d = 30 nm, ND,d = 1018 cm3
level can never model asymmetric device easily (need to have two sets of symmetric model
t )
X. ZHOU 19 © 2011
G. H. See, et al., T-ED, 55(2), p. 624, Feb. 2008. parameters)
Gummel Symmetry Test on Undoped sGummel Symmetry Test on Undoped s--DG Without BCDG Without BC
IEEE-EDS / DL EEE / NTU
Gummel Symmetry Test on Undoped sGummel Symmetry Test on Undoped s DG Without BCDG Without BC
“Floating body” (without body contact): Key – “ground-referenced” model
Symbol: MediciLine: Model
0.10L = 10 m, Tox = 3 nm, TSi = 20 nm
Floating body (without body contact): Key ground referenced model
1.5 10Ids I'ds
Line: Model
/V-
m)
0.05
Vg
Vg Vx Vg + Vx0.0 5
dVx2
(mS
/
0.00
dVx6
0
10
20Vg
-1.5 0
501.5
I''ds I'''ds
d2 I ds/
d
-0.05
-60 -40 -20 0 20 40 60
d6 I ds/
d
-20
-10
0
0
0.0
V (V)
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15-0.10
Vx (mV)Vx step size: 10 mV
Vx (V)-0.2 0.0 0.2
-50
Vx (V)-0.2 0.0 0.2
V V V
X. ZHOU 20 © 2011
Vx (V)Identical curves with any Vg , , ,ds eff d eff s effV V V G. J. Zhu, et al., T-ED, 55(9), p. 2526, 2008.
HarmonicHarmonic--Balance SimulationBalance Simulation
IEEE-EDS / DL EEE / NTU
HarmonicHarmonic Balance SimulationBalance Simulation
ln 2 ln s th d thV nv V nvnv e e SIC S t i I f C ti
-110SIC (n=1)Without SIC
ln 2 ln s th d tho thnv e e SIC: Symmetric Imref Correction
-130
-120
Without SIC
1st
I ds
(dB
)
-140
130
2nd
V
-150 3rd Vrf
Vg
~
V f (dB)
-30 -28 -26 -24 -22 -20
-160
X. ZHOU 21 © 2011
Vrf (dB)
UndopedUndoped--Body DG FinFET vs. GAA SiNWBody DG FinFET vs. GAA SiNW
IEEE-EDS / DL EEE / NTU
UndopedUndoped Body DG FinFET vs. GAA SiNW Body DG FinFET vs. GAA SiNW
FinFET (DG) SiNW (GAA)DGS
2
2c thV vi
Si
qnde
dx
1
c thV vi
Si
qnd dr e
r dr dr
V) 2.0G
s c th o c thV v V vgf s i thV v e e
First integration
n C
ha
rge,
Vgt
(V
1.0
1.5
0Symbols: SiNWLines: FinFET
G
22 gf c thV V viV y V v e
L
Ignore the o term
aliz
ed In
vers
ion
0.0
0.5 0.050.61.2
Vds (V)
22
s c gf th
th
V y V v ev
L
Second integration ox o ox oxC K T ln 1 ox o ox oxC K R T R
GateSource Voltage, Vgs (V)
-0.5 0.0 0.5 1.0 1.5 2.0
Nor
m
( ) ( )
, sin4
s c c o c c
th th
V V V V
v vi ox Sigt c c i th th
Si th
C TV V v e v e
v
2 2, 2
s o c thV vigt c c
ox
RqnV V e
C
X. ZHOU 22 © 2011
Si th
ss--DG/FinFET: ShortDG/FinFET: Short--Channel Transfer CharacteristicsChannel Transfer Characteristics
IEEE-EDS / DL EEE / NTU
ss DG/FinFET: ShortDG/FinFET: Short Channel Transfer CharacteristicsChannel Transfer Characteristics
Transfer Ids–Vgs Transfer gm–Vgs
Symbols: Measurement10-3 0.25
L = 0 5 m T = 140 nm T = 4 nm Symbols: Measurement0.15
L = 0 5 m TS = 140 nm T = 4 nmSymbols: MeasurementLines: Model (Xsim)s-DG FinFET
s (A
/m
)
10-5
10-4
(mA
/ m
)
0 15
0.20
L = 0.5 m, TSi = 140 nm, Tox = 4 nm Symbols: MeasurementLines: Model (Xsim)s-DG FinFET
, gm
(S
/m
)
10-5
10-4
g m (
mS
/m
)
0.10
L = 0.5 m, TSi = 140 nm, Tox = 4 nm
in C
urre
nt, I
d
10-7
10-6
n C
urre
nt,
I ds
0.10
0.15
0.05
Vds (V)
cond
ucta
nce
10-7
10-6
cond
ucta
nce,
0.050.050 6
Vds (V)
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Dra
10-9
10-8 Dra
in0.00
0.050.61.2
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0T
rans
c
10-9
10-8
Tra
nsc
0.00
0.61.2
GateSource Voltage, Vgs (V) GateSource Voltage, Vgs (V)
Symmetric-DG FinFET model comparison with Measurement
X. ZHOU 23 © 2011
Symmetric-DG FinFET model comparison with Measurement.
ss--DG/FinFET: ShortDG/FinFET: Short--Channel Output CharacteristicsChannel Output Characteristics
IEEE-EDS / DL EEE / NTU
ss DG/FinFET: ShortDG/FinFET: Short Channel Output CharacteristicsChannel Output Characteristics
Output Ids–Vds Output gds–Vds
Symbols: Measurement L = 0.5 m, TSi = 140 nm, Tox = 4 nm Symbols: Measurement)
10-3
L = 0.5 m, TSi = 140 nm, Tox = 4 nmLines: Model (Xsim)s-DG FinFET
s (m
A/
m)
0.10
0.15
Vgs (V)
0.00.3
Lines: Model (Xsim)s-DG FinFET
e, g
ds (
S/
m)
n C
urre
nt,
I d
0.00
0.050.6
1.20.9
Con
duct
ance 10-4
Vgs (V)
0.00 3
-0 5 0 0 0 5 1 0 1 5 2 0
Dra
in
-0.10
-0.05
-0 5 0 0 0 5 1 0 1 5 2 0
Dra
in C
10-5
0.30.6
1.2
0.9
DrainSource Voltage, Vds (V)
-0.5 0.0 0.5 1.0 1.5 2.0
DrainSource Voltage, Vds (V)
-0.5 0.0 0.5 1.0 1.5 2.0
Symmetric-DG FinFET model comparison with Measurement
X. ZHOU 24 © 2011
Symmetric-DG FinFET model comparison with Measurement.
GAA: Model Comparison with MeasurementGAA: Model Comparison with Measurement
IEEE-EDS / DL EEE / NTU
GAA: Model Comparison with Measurement GAA: Model Comparison with Measurement
Symbols: MeasurementLines: Model (Xsim)
10-6
10-5
8
10
1.0
1.2
Vds (V)
GAA SiNW Symbols: MeasurementLines: Model (Xsim)
10
GAA SiNW
(A
)
10-8
10-7
10-6
A)6
8
0.6
0.80.051.2
Vds (V)
A)
5
log(
I ds)
10-10
10-9
I ds,
sat (
2
4,li
n (
A)
0 2
0.4 I ds
(
5
0
Vgs (V)
00 3
10-13
10-12
10-11
0
2
I ds,
0 2
0.0
0.2
L = 180 nm, R = 2 nm, Tox = 4 nm -10
-5
L = 180 nm, R = 2 nm, Tox = 4 nm
0.3
0.6
1.20.9
Vgs (V)
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.210-13 -0.2
Vds (V)
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2-10
X. ZHOU 25 © 2011
GAA: Model Comparison with Measurement (1GAA: Model Comparison with Measurement (1stst Derivative)Derivative)
IEEE-EDS / DL EEE / NTU
GAA: Model Comparison with Measurement (1GAA: Model Comparison with Measurement (1 Derivative) Derivative)
Symbols: MeasurementLines: Model (Xsim)
6
10-5
10
121.5
Vds (V)
GAA SiNW Symbols: MeasurementLines: Model (Xsim)
80
100
(S)
10-5
10-4
GAA SiNW
) (S
)
10 8
10-7
10-6
(S
)
6
81.00.051.2
ds ( )
S) 60
-0.4 0.0 0.4 0.8 1.2
log(
g ds)
10-7
10-6
log(
g m)
10-10
10-9
10-8
g m,s
at (
4
6
in ( S
)
0.5
g ds
(
20
40Vds (V)
Vgs (V)
00 3
10-12
10-11
10-10
0
2
g m,l
0.0L = 180 nm, R = 2 nm, Tox = 4 nm 0
20
L = 180 nm, R = 2 nm, Tox = 4 nm
0.30.6
1.20.9
Vgs (V)
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.210 12
Vds (V)
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
X. ZHOU 26 © 2011
GAA: Model Comparison with Measurement (2GAA: Model Comparison with Measurement (2ndnd Derivative)Derivative)
IEEE-EDS / DL EEE / NTU
GAA: Model Comparison with Measurement (2GAA: Model Comparison with Measurement (2 Derivative) Derivative)
Symbols: MeasurementLines: Model (Xsim)
30
0.051 2
Vds (V)
GAA SiNW
Symbols: MeasurementLines: Model (Xsim)
10
20 Vgs (V)
00.30 6
GAA SiNW
S/V
)
201.2
S/V
) 0
0.6
1.20.9
gm
' (
10
g ds'
(
-20
-10
0
L = 180 nm, R = 2 nm, Tox = 4 nm -30 L = 180 nm, R = 2 nm, Tox = 4 nm
Vgs (V)
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
Vds (V)
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
X. ZHOU 27 © 2011
GAA: MeasuredGAA: Measured GummelGummel Symmetry TestSymmetry Test
IEEE-EDS / DL EEE / NTU
GAA: Measured GAA: Measured GummelGummel Symmetry Test Symmetry Test
Symbols: Measurement8L = 180 nm R = 5 nm T = 4 nmV (V)
Vx
(A
/V)
15
20
25y
Lines: Model (Xsim)
(A
)
0
2
4
60.40.60.81.01.2
L = 180 nm, R = 5 nm, Tox = 4 nmVg (V)
dIds
/dV
5
10
(b)
I ds
8
-6
-4
-2
0Vg
Vg/2 Vx Vg/2 + Vx(Vx = 0.02 V)(a)
/V2 )
40
60
-8( )
/V3 )
0.2
0.4
2 I ds/
dVx2 (
A/
40
-20
0
20
3 I ds/
dVx3 (
A/
-0 4
-0.2
0.0
V (V)
-0.4 -0.2 0.0 0.2 0.4
d2
-60
-40
(c)
V (V)
-0.4 -0.2 0.0 0.2 0.4
d3
-0.6
0.4
(d)
X. ZHOU 28 © 2011
Vx (V) Vx (V)
SchottkySchottky--Barrier MOSFET: Ambipolar CurrentBarrier MOSFET: Ambipolar Current
IEEE-EDS / DL EEE / NTU
SchottkySchottky Barrier MOSFET: Ambipolar CurrentBarrier MOSFET: Ambipolar Current
Symbols: Medici10-2
L = 65 nm T = 20 nm T = 3 nm Symbols: MediciV) 2
L = 1 m, R = 10 nm, Tox = 3 nmSymbols: MediciLines: Model (Xsim)
s (A
/m
)
10-7
10-6
10-5
10-4
10-3 L = 65 nm, TSi = 20 nm, Tox = 3 nm Symbols: MediciLines: Model (Xsim)
oten
tial, s
(V
0
1
0 0
Vs, Vd
L 1 m, R 10 nm, Tox 3 nm
n C
urre
nt,
I d
10-11
10-10
10-9
10-8
10
V (V) 2 1 0 1 2
Sur
face
Po
-2
-1
0, 0 0, 1 1, 0 0, 0.50.5, 0
2 1 0 1 2
Dra
in
10-15
10-14
10-13
10-12
0.050.61.2
Vds (V)
M,s/d = 4.6 eV
ElectronVg
T
Flatband-Shifted GateSource Voltage, Vgs VFB (V)
-2 -1 0 1 2
GateSource Voltage, Vgs (V)
-2 -1 0 1 2
Hole tunneling
Electrontunneling
Electron thermionic
VdVsTSiS D
Tox
No drift-diffusion! Vg
0L
y
Body Gate Oxide
Gaussian box
Medici: two-carrier Xsim: sum of two
unipolar (I + I )Ambipolar possible in undoped SB MOS with mid gap
X. ZHOU 29 © 2011
xy
Schottky Contactunipolar (Ids,n + Ids,p)SB-MOS with mid-gap M,s/d
SBSB--MOS: Total Current = (Electron + Hole) CurrentsMOS: Total Current = (Electron + Hole) Currents
IEEE-EDS / DL EEE / NTU
SBSB MOS: Total Current (Electron Hole) CurrentsMOS: Total Current (Electron Hole) Currents
10 5
10-4
n
A/
m)
10-8
10-7
10-6
10-5 n
Symbols: MediciLines: Model (Xsim)nt
, Ids
(A
10-11
10-10
10-9
10-8
n + p
Ambipolar(In + Ip)current
Lines: Model (Xsim)
n C
urre
n
10-14
10-13
10-12
10
00.3
Vgs (V)M,s/d = 4.6 eV
n + p
Dra
i
10-17
10-16
10-15
100.60.91.2
L = 65 nm T = 20 nm T = 3 nm
p
Drain Source Voltage V (V)
0.0 0.5 1.0 1.5 2.0 2.5 3.010-18
10 L = 65 nm, TSi = 20 nm, Tox = 3 nm
X. ZHOU 30 © 2011
DrainSource Voltage, Vds (V)
SBSB--MOS: Model Applied to Measured SBMOS: Model Applied to Measured SB--MOSMOS
IEEE-EDS / DL EEE / NTU
SBSB MOS: Model Applied to Measured SBMOS: Model Applied to Measured SB MOSMOS
nMOS operation (+Vds) pMOS operation ( Vds)
-4-3
L = 200 nm, R = 12.5 nm, Tox = 28 nm -4-3
L = 200 nm, R = 12.5 nm, Tox = 28 nm
nMOS operation (+Vds) pMOS operation (Vds)
s) (
A/
m)
10-9-8-7-6-5
Vds (V) ) (A
/ m
)
-9-8-7-6-54
Vds (V)
Symbols: MeasurementLines: Model (Xsim)
log(
I ds
15-14-13-12-11-10 0.05
0.30.61.22.5 (a)
M,s = 4.73 eV
M,d = 4.77 eVSymbols: MeasurementLines: Model (Xsim)
log(
I ds
15-14-13-12-11-10 -0.05
-0.3-0.6-1.2-2.5
ds ( )
(b)M,s = 4.73 eV
M,d = 4.77 eV
GateSource Voltage, Vgs (V)
-4 -2 0 2 4-15 Lines: Model (Xsim)
GateSource Voltage, Vgs (V)
-4 -2 0 2 4-15
( )M,d
SB-MOS model comparison with Measurement.(Same model and same device with different bias)
G J Zhu et al T ED 56(5) p 1100 May 2009
X. ZHOU 31 © 2011
G. J. Zhu, et al., T-ED, 56(5), p. 1100, May 2009.
DSSDSS--SiNW: Subcircuit ModelSiNW: Subcircuit Model
IEEE-EDS / DL EEE / NTU
DSSDSS SiNW: Subcircuit ModelSiNW: Subcircuit Model
Vg
Tox
r
Dopant-Segregated Schottky (DSS) SiNW:
S DVs Vd2R
Tox
0R
Dopant Segregated Schottky (DSS) SiNW:
• Thermionic/tunneling (TT) + drift-diffusion (DD)• The unique convex curvature in Ids–Vds can
only be modeled by a subcircuit model:
Symbols: TCAD (Medici)Lines: Model (Xsim)
40Symbols: MesurementLines: Model (Xsim)5
-4-3
L = 100 nm, R = 10 nm Tox = 2nm
Vg
y0 Lseg Lg
only be modeled by a subcircuit model:SBD (TT) + MOS (DD)
Lines: Model (Xsim)
urr
ent,
I ds
(A
)
20
30
0.5 1.0 1.5 2.0
g ds
Lines: Model (Xsim)
Cur
rent
, Ids
(A
)
11-10-9-8-7-6-5
VgSB MOS
0 0 0 5 1 0 1 5 2 0
Dra
in C
u
0
10
0 5 0 0 0 5 1 0 1 5 2 0 2 5
Dra
in C
-16-15-14-13-12-11
Vs VdVs'Leff
gS OS
DSS MOS
DSS-SiNW MOS subcircuit model comparison with Measurement.
DrainSource Voltage, Vds (V)
0.0 0.5 1.0 1.5 2.0
GateSource Voltage, Vgs (V)
-0.5 0.0 0.5 1.0 1.5 2.0 2.5
X. ZHOU 32 © 2011
G. J. Zhu, et al., SSDM, p. 402, Oct. 2009; T-ED, 57(4), p. 772, Apr. 2010.
DSSDSS--SiNWSiNW:: SubcircuitSubcircuit Model for Two Measured DevicesModel for Two Measured Devices
IEEE-EDS / DL EEE / NTU
DSSDSS SiNWSiNW: : SubcircuitSubcircuit Model for Two Measured DevicesModel for Two Measured Devices
(a) Device 1
A) 12 Lg = 40 nm, R = 10 nm Tox = 4 nmVgs (V) (c)
25Symbols: MesurementLi M d l (X i )
Lg = 40 nm, R = 10 nm Tox = 4 nm
rren
t, I d
s (
A
6
8
100.60.81.01.21.41.6
g
e, g
ds (S
)
15
20
Lines: Model (Xsim)g
Vgs = 1 V
Dra
in C
ur
0
2
4
1.61.82
Con
duct
anc
10
15
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
(b) Device 2
s (
A)
10
12
14
0.60 8
Symbols: MesurementLines: Model (Xsim)
Vgs (V)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Dra
in C
0
5Device 1Device 2
n C
urre
nt,
I ds
4
6
8
10 0.81.01.21.41.61.82 0
DrainSource Voltage, Vds (V)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
DSS-SiNW MOS subcircuit modeli ith t d d i
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Dra
in
0
22.0 comparison with two measured devices:
Device 1: normal concave curvatureDevice 2: unique convex curvature
X. ZHOU 33 © 2011
DrainSource Voltage, Vds (V) G. J. Zhu, et al., T-ED, 57(4), p. 772, Apr. 2010.
XsimXsim: Basic Bulk: Basic Bulk--MOS Model ParametersMOS Model Parameters
IEEE-EDS / DL EEE / NTU
XsimXsim: Basic Bulk: Basic Bulk MOS Model ParametersMOS Model Parameters
Physical parameters [6] Total: 33 basic parameters Physical parameters [6] Oxide thickness (Tox), S/D junction depth (Xj) Doping: channel (Nch), gate (Ngate), S/D (Nsd), overlap (Nov)
AC/Poly/QM parameters [8]
Total: 33 basic parameters
(less for DG/GAA)
AC/Poly/QM parameters [8] Bulk charge sharing (BCS): channel (c), gate (p), overlap (ov) Potential barrier lowering (PBL): accumulation (acc), depletion/inversion (ds)
E t i i l t l d ( ) i i /b lk h f t ( ) Extrinsic: lateral spread (), inversion/bulk charge factor (i, b) DC parameters [19]
Mobility: vertical-field mobility (, 2, 3, ) Effective field: vertical (n, b), lateral (L) PBL: accumulation (acc), depletion/inversion (ds), long-channel DIBL (dibl) BCL/lateral-doping: BCL (), halo-peak (), halo-spread (), halo-centroid (l) Series resistance: bias-dependent (), bias-independent () Velocity saturation (vsat), velocity overshoot (), effective D/S voltage (s)
Smoothing parameters — internal model requirement
X. ZHOU 34 © 2011
g p q