MOS-AK 2009 EEE / NTU
X. ZHOU 1 © 2009
Xing Zhou
School of Electrical and Electronic Engineering &Institute for Sustainable Nanoelectronics,
Nanyang Technological University, Singapore
December 9, 2009
Email: [email protected]
Unification of MOS Compact Models with the Unified Regional Modeling Approach
Unification of MOS Compact Models with the Unification of MOS Compact Models with the Unified Regional Modeling ApproachUnified Regional Modeling Approach
MOSMOS--AK Workshop AK Workshop –– Johns Hopkins University, Baltimore, USAJohns Hopkins University, Baltimore, USA
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Presentation OutlinePresentation Outline
Motivation for MOS Model Unification
Unified Regional Modeling (URM) Approach
Xsim Model Results and Ultimate Goals
Model extendibility and modeling effortsSeamless physical scalability
Key challenges: symmetry and body contact, doping scaling (non-charge-sheet), contact effect (SB/DSS)Unique features: decoupled regional surface-potential solution, bulk/ground-reference and source/drain by label, ambipolar SB model, and subcircuit model for DSS
Bulk-MOS current and charge modelsFB-SOI and s-DG FinFETsSiNW and SB/DSS MOSFETsXsim: history, evolution, and future goals
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Sah–Pao (input)Voltage Equation
Pao–Sah (output)Current Equation φs-based
Qi-based
Vt-basedQb linearization
Qi linearization
Iterative / explicit
1966 1978 1985 1995 2005
Po
isso
n +
GC
A
Classical bulk-CMOS
Non-classical CMOS
ChargeSheetModel(Qsc=Qb+Qi)
~40 yrs
SOISOI
MGMG
Bulk Voltage/Current Equations, CSM
New Voltage/Current Equations
Partially-Depleted (PD)Fully-Depleted (FD), Ultra-Thin Body (UTB)
Non-Charge-Sheet
Symmetric/Asymmetric Double Gate (s-DG/a-DG)
no
ntr
ivia
ln
on
triv
ial
extension
Tri-gate, GAA, Heterostructure (strained-Si), …
MOSFET Compact Models: History and FutureMOSFET Compact Models: History and Future
Body Contact/Floating Body
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Need for an Extendable Core Model for Future GenerationNeed for an Extendable Core Model for Future Generation
Vt-based models
Time
’60 ’70 ’80 ’90 ’00 ’10
Qi-based models
φs-based models
Pao–Sah
Bulk PD-SOI FD-UTB/SOI DG/GAA/SB/DSS
ID
Ids
DGS
B
History has witnessed generations of MOS models
(B)
Sub
ID
DGS
Sub
DGS DG1S
G2
IDID
and efforts required from one generation to the next …
— Need for a core model extendable to future generations,and with less duplicating efforts
Do we want XXX-SOI-PD/FD ?-Bulk
-DG/GAA
• BSIM-SOI/MG• PSP-SOI-PD/DD• HiSIM-SOI• ULTRA-SOI• Xsim
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Vg
Vs Vd
Vb
(a)
PD-SOI
toxf
tSi
εoxf
εoxb toxb
φs
φb
φ0
Vg
Vs Vd
Vb
(b)
FD-UTB/SOI
Vg
Vs Vd
Vb
(c)
a-DG
Vg
Vs Vd
Vg
(d)
s-DG
Vg
Vs Vd
(e)
'Bulk-UTB'
Vg
Vs Vd
Vb
(f)
Bulk
Vb = Vg
toxb = toxftSi
half s-DGtSi
toxb → ∞ φ'0 = 0
φ0 ≠ 0
φ'b ≈ 0
φb = 0
φb ≠ 0 φ'b ≠ 0
φ'0 = 0
φs = φb
PD-SOI FD-UTB/SOI a-DG s-DG UTB Bulk
φ'b = 0
φb = 0
Seamless Transformation and Unification of Seamless Transformation and Unification of MOSFETsMOSFETs
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Common/Independent Symmetric/AsymmetricCommon/Independent Symmetric/Asymmetric--DG MOSFETDG MOSFET
Common/symmetric-DG [FinFET]• Vg1 = Vg2 = Vg: two gates with one bias• Cox1 = Cox2: s-DG (Xo = TSi/2)• Full-depletion: VFD = Vg(Xd=TSi/2)• Cox1 ≠ Cox2: ca-DG (Xo < TSi)
Independent/asymmetric-DG [SOI]• Vg1 ≠ Vg2: ia-DG, biased independently• Zero-field location may be outside body• Consider two “independent” gates; linked
through full-depletion condition: Xd1 + Xd2 = TSi
Unification of MOS• SOI ← ia-DG ↔ ca-DG ↔ s-DG → bulk
Zero-field potential: φo [φo'(Xo) = 0]
Vg
Vs Vd
Toxφ0 L
TSi
Kox
Xo
φs
φs2
φo (φo' = 0)
(φo' = 0)Kox2 Tox2
(Xo)
x
(φo' = 0)
Vg2
φs2
(Vb)
Since Poisson equation cannot be integrated twice when doping is considered, we do not solve combined solutions at the two Si/SiO2 interfaces; instead, we solve the two separately with zero-field as the other ‘boundary’.
→
SiNW
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Our Approach: Unified Regional Model (URM)Our Approach: Unified Regional Model (URM)
Start with s-DG with doped body (two unknowns, φs and φo)
Extend URMURM approach to φs solution ⎯ finding the “full-depletion voltage” VFD
( )
' φεφε
−= − = +
≡ −
gf soxs s
Si ox
gf g FB
VE
T
V V V0oE =
1 2s s sφ φ φ= = ( )( )
0sgn , 2 ,
sgn , , ,
φ
ϕ
φ φ φ ϒ ϒ ε ε
ϕ ϕ ϕ γ γ ϒ ϕ φ
− = − = =
− = − ≡ ≡ ≡
gf s s o Si ox ox ox ox
gf s s o th th th
V f q C C T
v f v v v V v
p
( ) ( ) ( ) ( ) ( ) ( )2, , ϕϕ ϕϕϕ
ϕ ϕ ϕϕϕ ϕϕ − + −− − ⎡ ⎤= − + − + − − −⎣ ⎦s or r s ocrF
s os o cv v
srv
of v e e e e e e e
Scale with Nch, TSi, Tox, Kox in all regions ⎯ φs readily applicable in bulk Ids(φs) Bulk model for short-channel/higher-order effects can be easily extended
Extending to a-DG ⎯ two ‘independent’ s-DG coupled by one VFD(Vg1,Vg2)
Without solving coupled solutions, which is impossible (rigorously) for doped bodyRecoverable to s-DG, FD/PD-SOI, undoped, bulk ⎯ unification of MOS models
0
φ= Fp thv
iep n
Highly-doped body: Charge-sheet approximation (CSA), similar to bulk
Undoped/(lowly-doped) body: Non-CSA (2nd integral of Poisson)
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L
Xo
y
TSi + Tox2
n+n+
VS
VG2
VD
VB
Ψ(x, y)
φs1(y)
φs2(y)
φo(y)
NA − ND
Ei = −qφs(y)
DG
Bulk
PN
SB
VdVs Vd,sat
VG1
−Tox1
0
x
TSi
Generic DG/SOIGeneric DG/SOI--MOSFET With/Without Body ContactMOSFET With/Without Body Contact
Symmetry
Body Contact
Body dopingBody thickness
S/D Contact
Carrier type
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Regional Regional φφss Solutions and FullSolutions and Full--Depletion VoltageDepletion Voltage
( )2
22
A os o o Si
Si
qN XX Tφ φ
ε− = =
( ) ( )1, 1, 2, 2,d FD g FD d FD g FD SiX V X V T+ = ( ),, 2g FDD id F SX V T=
22
2 4 gbfsub Vϒ ϒφ
⎛ ⎞= − + +⎜ ⎟⎜ ⎟
⎝ ⎠
gfdv depVφ ϒ φ= +
FD condition: s-DG:
{ }, ;subd eff fdp de ϑ φφ φ δ=
{ }, ;dds seff rv t φφφφ ϑ δ=
{ }2gbfs htr tV v Wφ = − L
Symbols: MediciLines: Model (Xsim)
Common Gate Voltage, Vg (V)
-2 -1 0 1 2
Sur
face
Pot
entia
l, φ s (
V)
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
φs
φacc
φs
φacc
φdep
φs
φacc
φdep
φvi
φs
φacc
φdep
φvi
φstr
φs
φacc
φdep
φvi
φstr
φdsφseff
φds
φstr
φvi
φdep
φacc
φs
Symbols: MediciLines: Model (Xsim)
Common Gate Voltage, Vg (V)
-2 -1 0 1 2
Sur
face
Pot
entia
l, φ s (
V)
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
VFB VFD Vt
φsφseffφdepφdv
φstr φacc
φds
a ceff dss cφ φ φ= + { }2gbra hcc tV v Wφ = + L
,
2
,
2 2
2 2 4 gf FA
SD
d D
id
Ff
XqNV
ϒφ ϒε
⎛ ⎞= = − + +⎜ ⎟⎜ ⎟
⎝ ⎠
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SurfaceSurface--Potential Derivatives and Regional ComponentsPotential Derivatives and Regional Components
Symbols: MediciLines: Model (Xsim)
Common Gate Voltage, Vg (V)
-2 -1 0 1 2
dφs/d
Vg
(V/V
)
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
φsφseffφdep
φdv
φacc
φstr
φds
Regional solutions scale with body doping (NA), body thickness (TSi), oxide thickness (Tox), and all terminal biases
Smooth higher-order derivatives
Regional charge model –key to physically-based parameter extraction
Foundation to unification of MOS compact models (bulk/SOI/DG/NW/SB/DSS)
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BodyBody--Doping Scaling: High to Zero (Doping Scaling: High to Zero (““UndopedUndoped””))
“Intrinsic”: NA – ND = ni (temp-dependent)Undoped = “pure” (ideal): NA = ND = 0
Nch = ni: not exactly symmetric
Nch = 0: exactly symmetric
Extrinsic: NA – ND > niHigh temperature
Vgb − VFB (V)-2 -1 0 1 2 3
d2 φ
s/dV
gb2
(V/V
2 )
-4
-2
0
2
4
Symbols: Newton−RaphsonLines: Model (Xsim)
Vgb − VFB (V)-2 -1 0 1 2 3
dφs/
dVgb
(V
/V)
0.0
0.5
1.0
(Vd = Vs = Vb = 0)
Nch (cm−3)
0
1010
1014
1017
1018
Seamless doping scaling
Key:has to be p0, not NA
10 exp sinh
2φ −⎡ ⎤⎛ ⎞−
= = ⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦
F thv A Di i
i
N Nnp e n
n
2ϒ ε= Si oxoq p C
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Inversion Charge and Effective DrainInversion Charge and Effective Drain––Source Voltage Source Voltage
Gate−Bulk Voltage, Vgb (V)
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Effe
ctiv
e V
ds,e
ff C
ompo
nent
s (V
)
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Effe
ctiv
e V
ds,e
ff C
ompo
nent
s (V
)
10-1410-1310-1210-1110-1010-910-810-710-610-510-410-310-210-1100101
Vds,effVdb,effVsb,eff
Vds = 1.2 V, Vsb = 0 V
Gate−Bulk Voltage, Vgb (V)
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Nor
mal
ized
Inve
rsio
n C
harg
e, Q
i/Cox
(V
)
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
qi =
Qi/C
ox =
γV
gt (
V)
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
RHS of Pao−SahLHS of Pao−Sah
( ) ( ) ( )φ ϒ φ= − − −i gb FB s sq y V V y y ( ) ( ) ( )( ) ( )2φ φϒ φ ϒ φ− −= + −s F cb thy V v
gt s th sV y y v e y( )
= =ii gt
ox
Q yq V
C
, , ,ds eff db eff sb effV V V= −
LHS RHS
Key to without requiring very accurate φs Key to symmetry without Vsb clipping
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UndopedUndoped--Body DG Body DG FinFETFinFET vs. GAA vs. GAA SiNWSiNW
FinFET (DG)
( )2
2c thV vi
Si
qnde
dxφφ
ε−= ( )1
c thV vi
Si
qnd dr e
r dr drφφ
ε−⎛ ⎞ =⎜ ⎟
⎝ ⎠
( ) ( )( )s c th o c thV v V vgf s i thV v e eφ φφ ϒ − −− = −
( ) ( ) 22
2gf c thV V vi
s c gf th
th
V y V v ev
ϒφ −⎧ ⎫⎪ ⎪⎡ ⎤ = − ⎨ ⎬⎣ ⎦⎪ ⎪⎩ ⎭L
( )( ) ( )
, 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
φ φϒϒ
ε
− −⎛ ⎞⎜ ⎟=⎜ ⎟⎝ ⎠
( ) ( )2 2, 2
φ φ+ −= s o c thV vigt c c
ox
RqnV V e
C
SiNW (GAA)
First integration
Second integration
Ignore the φo term
ε=ox o ox oxC K T ( )ln 1ε= +ox o ox oxC K R T R
Gate−Source Voltage, Vgs (V)
-0.5 0.0 0.5 1.0 1.5 2.0
No
rma
lize
d In
vers
ion
Ch
arg
e, V
gt (
V)
0.0
0.5
1.0
1.5
2.0
0.050.61.2
Vds (V)
Symbols: SiNWLines: FinFET
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Bulk/GroundBulk/Ground--Reference and Source/Drain by LabelReference and Source/Drain by Label
( )( ) ( )
,
,,
ds i b th ds eff
i b th i
s
s effb bd e b t
d
f hf
I q A v V
q A v q A v
I I
VV
β
β β
= + = −
= + − +(B)
Sub
Id
DGS
Ids
,, ,d effds ef sf effVVV = −
Is
S/D by label (layout)
Always Source Always Drain,, ,d effds ef b bf s effVVV = −
Effective drain–source voltage (Vds,eff)
S/D by convention (nMOS)
• Vd > Vs: Ids > 0 (D → S)• Vd < Vs: Ids < 0 (S → D)
• Vd > Vs: Ids > 0 (‘D’ → ‘S’)• Vd < Vs: Ids > 0 (‘D’ ↔ ‘S’)
FB: BC:
• By convention, nMOS Ids always flows from ‘D’ to ‘S’• Terminal swapping for –Vds: involving |Vds| in model
Key: Bulk/Ground-reference — auto switch to B/G-ref when body is biased or floatingIntrinsic Ids is an exact odd function of VdsPhysical modeling of asymmetric MOS (nontrivial with “terminal swapping” for negative Vds)
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GummelGummel Symmetry Test on Long/ShortSymmetry Test on Long/Short--Channel BulkChannel Bulk
Symbols: MediciLines: Model
Vx (V)
-1.0 -0.5 0.0 0.5 1.0
d2I d
s/dV
x2 (
μ S/V
μ m)
-40
-30
-20
-10
0
10
20
30
40
d2I d
s/dV
x2 (
mS
/Vμ m
)
-10
-5
0
5
10
tox = 2 nm
Nch = 6.8x10−17 cm−3
L = 10 μm
L = 90 nm
Vx
-0.15 0.00 0.15d
6 Id
s/d
Vx6
G. H. See, et al., T-ED, 55(2), p. 624, Feb. 2008.( )0 ,ds i b th ds effI q A v Vβ= +
0
0 ,1vo ds
dssd ds ds eff
g II
R I V=
+
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GummelGummel Symmetry Test on Symmetry Test on UndopedUndoped ss--DG Without BCDG Without BC
Symbol: MediciLine: Model
Vx (V)
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15
d2 I ds/
dVx2
(mS
/V-μ
m)
-0.10
-0.05
0.00
0.05
0.10L = 10 μm, Tox = 3 nm, TSi = 20 nm
Vx (mV)-60 -40 -20 0 20 40 60
d6 I ds/
dVx6
-20
-10
0
10
20Vg
Vg
Vg − Vx Vg + Vx
“Floating body” (without body contact): Key – “ground-referenced” model
Vx step size: 10 mV
-1.5
0.0
1.5
0
5
10
Vx (V)-0.2 0.0 0.2
-50
0
50
Vx (V)-0.2 0.0 0.2
0.0
1.5
Ids I'ds
I''ds I'''ds
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.
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Modeling Asymmetric MOSFETModeling Asymmetric MOSFET
Symbols: MediciLines: Model
Drain−Source/Source−Drain Voltage, VDS or VSD (V)
0.0 0.5 1.0 1.5 2.0
Dra
in C
urre
nt, |
I DS
| (m
A/μ
m )
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
VDS
VSD L = 90 nmtox = 2 nm
VDS or VSD (V)0.0 0.5 1.0 1.5 2.0
r out
(S
/μm
)
102
103
104
S D
G
B
G. H. See, et al., T-ED, 55(2), p. 624, Feb. 2008.
Xj,s = 80 nm, ND,s = 1019 cm−3; Xj,d = 30 nm, ND,d = 1018 cm−3
“Source” and “Drain” by label (rather than by MOS convention); i.e., VDS and VSD are different
Structural asymmetry (e.g., Xj, ND) can be captured by refitting physical parameters (e.g., vsat,s and vsat,d)
Models based on S/D terminal swapping for negative Vds at circuit level can never model asymmetric device easily (need to have two sets of symmetric model parameters)
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BulkBulk--Referenced Model: Transfer CharacteristicsReferenced Model: Transfer Characteristics
Symbols: MediciLines: Model (Xsim)
Gate−Bulk Voltage, Vgb (V)-0.5 0.0 0.5 1.0 1.5 2.0
Dra
in−S
ourc
e C
urre
nt, I
ds (
A/μ
m)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
Vb = 0
-0.5 0.0 0.5 1.0 1.5 2.0
Dra
in−S
ourc
e C
urre
nt, I
ds (
μA/ μ
m)
0
10
20
30
(Vds = 1.2 V)
Vs = 0.0, Vd = 1.2 V
Vs = 0.3, Vd = 1.5 VVs = 0.6, Vd = 1.8 V
L = 10 μm
Symbols: MediciLines: Model (Xsim)
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
Dra
in−S
ourc
e C
urre
nt,
I ds
(μA
/μm
)
0.0
0.5
1.0
1.5
2.0Vs = 0
Gate−Source Voltage, Vgs (V)-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
Dra
in−S
ourc
e C
urre
nt,
I ds
(A/μ
m)
10-16
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
Vb = 0
Vb = −0.4 V
Vb = −0.8 V
Vb = −1.2 V
(Vds = 0.05 V)
L = 10 μm
Saturation Ids–Vgb Linear Ids–Vgs
G. H. See, et al., T-ED, 55(2), p. 624, Feb. 2008.
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BulkBulk--Referenced Model: Output CharacteristicsReferenced Model: Output Characteristics
Long-Channel Ids–Vds L-Dependent Ids–Vds
G. H. See, et al., T-ED, 55(2), p. 624, Feb. 2008.
Vg = 1.2 V
Vs = Vb = 0
Vds0.0 0.5 1.0
g ds
(mS
/μm
)
0
5
10
Symbols: MediciLines: Model (Xsim)
Drain−Source Voltage, Vds (V)0.0 0.5 1.0
Dra
in−S
ourc
e C
urre
nt,
I ds
(mA
/μm
)
-1.0
-0.5
0.0
0.5
1.0
L = 10 μmL = 1L = 0.5L = 0.25L = 0.18L = 0.09
(A single smoothing δs)
Symbols: MediciLines: Model (Xsim)
Drain−Source Voltage, Vds (V)-0.5 0.0 0.5 1.0
Dra
in−S
ourc
e C
urre
nt,
I ds
( μA
/ μm
)
-15
-10
-5
0
5
10
15
Vgs = 0.4 V
Vgs = 0.8 V
Vgs = 1.2 V
L = 10 μm
Vds (V)
0.0 0.5 1.0
r out (
Ω/μ
m)
103
104
105
106
107
108
(Vbs = 0)
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BulkBulk--Referenced Model: ShortReferenced Model: Short--Channel CharacteristicsChannel Characteristics
Linear Ids/gm–Vgs Output Ids/gds–Vds
G. H. See, et al., T-ED, 55(2), p. 624, Feb. 2008.
Symbols: MediciLines: Model (Xsim)
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
Tra
nsco
nduc
tanc
e, g
m (
μS/μ
m)
0
50
100
150
200Vs = 0
Gate−Source Voltage, Vgs (V)-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
Dra
in−S
ourc
e C
urre
nt, I
ds (
A/μ
m)
10-1810-1710-1610-1510-1410-1310-1210-1110-1010-910-810-710-610-510-410-3
Vb = 0
Vb = −0.4 V
Vb = −0.8 V
Vb = −1.2 V
(Vds = 0.05 V)
L = 90 nm
Vs = Vb = 0
Gate−Source Voltage, Vgs (V)0.0 0.2 0.4 0.6 0.8 1.0 1.2
Dra
in−S
ourc
e C
urre
nt, I
ds (
mA
/μm
)
0.0
0.2
0.4
0.6
0.8
1.0
Dra
in C
ondu
ctan
ce, g
ds (
mS
/μm
)
0
2
4
6
8
10
12
Symbols: MediciLines: Model (Xsim)
L = 90 nm Vg = 0.4 V Vg = 0.8 V
Vg = 1.2 V
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Regional Charge Model Variation: Regional Charge Model Variation: TToxox, , NNchch, and , and NNgategate
Symbol: MediciLines: Model (Xsim)
Gate−Source Voltage, Vgs (V)
-2 -1 0 1 2
Gat
e C
apac
itanc
e, C
gg/W
L (μ
F/c
m2 )
0.0
0.5
1.0
1.5
2.0
2.5
(Vds = Vbs = 0)
Tox = 2 nm, Nch = 5x1017 cm−3
Tox = 1.5 nm
Tox = 2.0 nm
Tox = 2.5 nm
Nch = 1x1017 cm−3
Nch = 5x1017 cm−3
Nch = 1x1018 cm−3
Ngate = 1x1022 cm−3, κqm = 0
Symbols: MediciLines: Model (Xsim)
Gate−Source Voltage, Vgs (V)
-2 -1 0 1 2G
ate
Cap
acita
nce,
Cgg
/WL
(μF
/cm
2 )
0.0
0.5
1.0
1.5
2.0
5x1019
5x1020
1x1022
(Vds = Vbs = 0)
Ngate (cm−3)
Ngate = 5x1020 cm−3
Tox = 2 nm, Nch = 5x1017 cm−3, κqm = 0
Using URM surface-potential solutions, physical effects can be separated in the regional charge model for meaningful and decoupled parameter extraction.
PAE PDE
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LongLong--Channel (Normalized) Channel (Normalized) TranscapacitancesTranscapacitances
Gate−Source Voltage, Vgs (V)
-2 -1 0 1 2
Nor
mal
ized
Cap
acita
nce
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
d(C
gg/C
ox)/
dVgs
(1/
V)
-4
-2
0
2
4Symbols: MediciLines: Model (Xsim)
(Vds = 0.6 V, Vbs= 0)
CggCdgCsgCbg
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Gate Capacitance with Coupled PDE and QMEGate Capacitance with Coupled PDE and QME
Symbols: Medici Lines: Model (Xsim)
Gate−Source Voltage, Vgs (V)
-2 -1 0 1 2
Gat
e C
apac
itanc
e, C
gg/W
L (μ
F/c
m2 )
0.0
0.5
1.0
1.5
Vbs = 0
−0.6 V
−1.2 V
Vds = 0
0.6 V
1.2 V
κqm = 1, Ngate = 5x1019cm−3
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X. ZHOU 24 © 2009
ShortShort--Channel Channel CCgggg and and CCdgdg with Drainwith Drain--Bias VariationBias Variation
Symbols: MediciLines: Model (Xsim)
Gate−Bulk Voltage, Vgb (V)-2 -1 0 1 2
Nor
mal
ized
(C
gg,C
dg)/
Cox
(F
/F)
0.0
0.2
0.4
0.6
0.8
1.0
Leff = 90 nm
Tox = 2 nm
Nch = 5x1017 cm−3Cdg
Cgg
Vds = 0 V
Vds = 0.6 V
Vds = 1.2 V
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LengthLength--Dependent Dependent CCgggg with Bodywith Body--Bias Variation Bias Variation
Symbols: MediciLines: Model (Xsim)
Gate−Bulk Voltage, Vgb (V)
-3 -2 -1 0 1 2
Nor
mal
ized
Cgg
/Cox
(F
/F)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Vbs = 0
Vbs = −0.6 V
L = 0.09, 0.25, 0.5 μm
Vbs = −1.2 V
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ShortShort--Channel Channel TranscapacitanceTranscapacitance Symmetry/Reciprocity Symmetry/Reciprocity
Drain−Source Voltage, Vds (V)-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Nor
mal
ized
Cap
acita
nces
(F
/F)
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
Cgs
Cgd
Cdd
CbsCbd
Csd
Cds
CdgCsg
Css
CdbCsb
Leff = 90 nm
Tox = 2 nm
Nch = 5x1017 cm−3
Vgb = 1.2 V
Gate−Bulk Voltage, Vgb (V)
-2 -1 0 1 2
Nor
mal
ized
Cap
acita
nces
(F
/F)
-0.2
0.0
0.2
0.4
0.6
Cbd, Cbs
Csd, Cds
Cdd, Css
Cgd, Cgs
Leff = 90 nm
Tox = 2 nm
Nch = 5x1017 cm−3
Vds = 0
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FBFB--SOI: LongSOI: Long--Channel CharacteristicsChannel Characteristics
Transfer Ids–Vgs Output Ids–Vds
Symbols: MediciLines: Model (Xsim)
Gate−Source Voltage, Vgs (V)
-0.5 0.0 0.5 1.0 1.5 2.0
Dra
in C
urre
nt, l
og(I
ds)
(A/μ
m)
-17-16-15-14-13-12-11-10
-9-8-7-6-5-4-3
Dra
in C
urre
nt, I
ds (
mA
/ μm
)-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.050.61.2
Vds (V)
L = 1 μm, TSi = 10 nm, Tox = 1 nm, NA = 5x1017 cm−3
“Floating-body” SOI model comparison with Medici device.
Symbols: MediciLines: Model (Xsim)
Drain−Source Voltage, Vds (V)
-0.5 0.0 0.5 1.0 1.5 2.0
Dra
in C
urre
nt, I
ds (
mA
/μm
)
-0.05
0.00
0.050.30.60.91.2
Vgs (V)
L = 1 μm, TSi = 10 nm, Tox = 1 nm, NA = 5x1017 cm−3
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FBFB--SOI: ShortSOI: Short--Channel CharacteristicsChannel Characteristics
Transfer Ids–Vgs Output Ids–Vds
Symbols: MediciLines: Model (Xsim)
Gate−Source Voltage, Vgs (V)
-0.5 0.0 0.5 1.0 1.5 2.0
Dra
in C
urre
nt, l
og(I
ds)
(A/μ
m)
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
Dra
in C
urre
nt, I
ds (
mA
/ μm
)
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.050.61.2
Vds (V)
L = 0.1 μm, TSi = 10 nm, Tox = 1 nm, NA = 5x1017 cm−3
Symbols: MediciLines: Model (Xsim)
Drain−Source Voltage, Vds (V)
-0.5 0.0 0.5 1.0 1.5 2.0
Dra
in C
urre
nt, I
ds (
mA
/μm
)
-1.0
-0.5
0.0
0.5
1.0
1.5
0.30.60.91.2
Vgs (V)
L = 0.1 μm, TSi = 10 nm, Tox = 1 nm, NA = 5x1017 cm−3
“Floating-body” SOI model comparison with Medici device.
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X. ZHOU 29 © 2009
ss--DG: Evaluation in SurfaceDG: Evaluation in Surface--PotentialPotential--Based Based IIdsds((φφss) Model) Model
Symbols: MediciLines: Model (Xsim)
Common Gate Voltage, Vg (V)-0.5 0.0 0.5 1.0 1.5
Dra
in C
urre
nt, I
ds (
mA
/μm
)
0.0
0.2
0.4
0.6
0.8
1.0
Dra
in c
urre
nt,
log(
I ds)
(A
/μm
)-18-17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2
Ids
log(Ids)NA = 1018 cm−3
TSi = 50 nm
Tox = 3 nm
L = 1 μm
Vds = 0.05 VVds = 1.2 V
Symbols: MediciLines: Model (Xsim)
Common Gate Voltage, Vg (V)-0.5 0.0 0.5 1.0 1.5
Tra
nsco
nduc
tanc
e, g
ms
(mS
/μm
)
0
20
40
60
80
Tra
nsco
nduc
tanc
e, lo
g(g m
) (S
/μm
)
-18-17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2
g m0
(μS
/μm
)
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
gms
gm0
log(gm)
NA = 1018 cm−3
TSi = 50 nm
Tox = 3 nm
L = 1 μm
Vds = 0.05 VVds = 1.2 V
Linear/Saturation Current Transconductance
Doped symmetric-DG model (with depletion/volume-inversion) comparison with Medici device.
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X. ZHOU 30 © 2009
ss--DG/FinFETDG/FinFET: Short: Short--Channel Transfer CharacteristicsChannel Transfer Characteristics
Transfer Ids–Vgs Transfer gm–Vgs
Symbols: MeasurementLines: Model (Xsim)s-DG FinFET
Gate−Source Voltage, Vgs (V)
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Dra
in C
urre
nt,
I ds
(A/μ
m)
10-9
10-8
10-7
10-6
10-5
10-4
10-3
Dra
in C
urre
nt, I
ds (
mA
/ μm
)
0.00
0.05
0.10
0.15
0.20
0.25
0.050.61.2
L = 0.5 μm, TSi = 140 nm, Tox = 4 nm
Vds (V)
Symbols: MeasurementLines: Model (Xsim)s-DG FinFET
Gate−Source Voltage, Vgs (V)
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Tra
nsco
nduc
tanc
e, g
m (
S/μ
m)
10-9
10-8
10-7
10-6
10-5
10-4
Tra
nsco
nduc
tanc
e, g
m (
mS
/ μm
)
0.00
0.05
0.10
0.15
0.050.61.2
L = 0.5 μm, TSi = 140 nm, Tox = 4 nm
Vds (V)
Symmetric-DG FinFET model comparison with Measurement.
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X. ZHOU 31 © 2009
ss--DG/FinFETDG/FinFET: Short: Short--Channel Output CharacteristicsChannel Output Characteristics
Output Ids–Vds Output gds–Vds
Symbols: MeasurementLines: Model (Xsim)s-DG FinFET
Drain−Source Voltage, Vds (V)
-0.5 0.0 0.5 1.0 1.5 2.0
Dra
in C
urre
nt,
I ds
(mA
/μm
)
-0.10
-0.05
0.00
0.05
0.10
0.15
Vgs (V)
L = 0.5 μm, TSi = 140 nm, Tox = 4 nm
0.00.30.6
1.20.9
Symbols: MeasurementLines: Model (Xsim)s-DG FinFET
Drain−Source Voltage, Vds (V)
-0.5 0.0 0.5 1.0 1.5 2.0D
rain
Con
duct
ance
, g d
s (S
/μm
)
10-5
10-4
10-3
Vgs (V)
L = 0.5 μm, TSi = 140 nm, Tox = 4 nm
0.00.30.6
1.2
0.9
Symmetric-DG FinFET model comparison with Measurement.
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SiNWSiNW: Model Scalability with Radius and Gate Length: Model Scalability with Radius and Gate Length
Radius Variation Gate Length Variation
Si-nanowire model comparison with Medici device.
Symbols: MediciLines: Model (Xsim)
Gate−Source Voltage, Vgs (V)
-0.5 0.0 0.5 1.0 1.5 2.0
Dra
in C
urre
nt,
I ds
(μA
)
0.05
0.10
0.15
0.20
Dra
in C
urre
nt,
log(
I ds)
(A
)
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
4681012
Lg = 5 μm, Tox = 2 nm
R (nm)
Vds = 0.05 V
Symbols: MediciLines: Model (Xsim)
Gate−Source Voltage, Vgs (V)
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Dra
in C
urre
nt,
I ds
(A)
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
R = 10 nmTox = 2 nm
Vds = 1.2 V
Lg (nm)
2030456590130
180250500100020005000
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SiNWSiNW: Model Applied to Measured : Model Applied to Measured SiNWSiNW
Transfer Ids–Vgs Output Ids–Vds
Si-nanowire model comparison with Measurement.
Symbols: MeasurementLines: Model (Xsim)
Gate−Source Voltage, Vgs (V)
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
I ds
(A)
10-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
0.051.2
Vds (V)
L = 180 nm, R = 2 nm, Tox = 4 nm Symbols: MeasurementLines: Model (Xsim)
Drain−Source Voltage, Vds (V)
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
I ds
(μA
)
-10
-5
0
5
10 L = 180 nm, R = 2 nm, Tox = 4 nm
Vgs (V)
00.3
0.6
1.20.9
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SiNWSiNW: Model Applied to Measured : Model Applied to Measured SiNWSiNW
1st-order Transfer gm–Vgs 1st-order Output gds–Vds
Si-nanowire model comparison with Measurement.
Symbols: MeasurementLines: Model (Xsim)
Gate−Source Voltage, Vgs (V)
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
gm
(μS
)
0
2
4
6
8
10
12
0.051.2
Vds (V)
L = 180 nm, R = 2 nm, Tox = 4 nm Symbols: MeasurementLines: Model (Xsim)
Drain−Source Voltage, Vds (V)
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
g ds
(S)
10-8
10-7
10-6
10-5
10-4
L = 180 nm, R = 2 nm, Tox = 4 nm
Vgs (V)
00.30.6
1.20.9
MOS-AK 2009 EEE / NTU
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SiNWSiNW: Model Applied to Measured : Model Applied to Measured SiNWSiNW
2nd-order Transfer gm’–Vgs 2nd-order Output gds’–Vds
Si-nanowire model comparison with Measurement.
Symbols: MeasurementLines: Model (Xsim)
Gate−Source Voltage, Vgs (V)
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
gm
' (μS
/V)
0
5
10
15
20
25
30
0.051.2
Vds (V)
L = 180 nm, R = 2 nm, Tox = 4 nm Symbols: MeasurementLines: Model (Xsim)
Drain−Source Voltage, Vds (V)
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2g d
s' (
μS/V
)
-30
-20
-10
0
10
20L = 180 nm, R = 2 nm, Tox = 4 nm
Vgs (V)
00.30.6
1.20.9
MOS-AK 2009 EEE / NTU
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GAA GAA SiNWSiNW: : GummelGummel Symmetry Test (Measurement)Symmetry Test (Measurement)
Symbols: MeasurementLines: Model (Xsim)
I ds
(μA
)
-8
-6
-4
-2
0
2
4
6
8
0.40.60.81.01.2
L = 180 nm, R = 2 nm, Tox = 4 nm
Vg (V)
Vg
Vg/2 − Vx Vg/2 + Vx(ΔVx = 0.02 V)
dIds
/dV
x (μ
A/V
)
5
10
15
20
25
Vx (V)
-0.4 -0.2 0.0 0.2 0.4
d2I d
s/dV
x2 (μ A
/V2 )
-60
-40
-20
0
20
40
60
Vx (V)
-0.4 -0.2 0.0 0.2 0.4
d3 I ds/
dVx3 (
μ A/V
3 )
-0.6
-0.4
-0.2
0.0
0.2
0.4
(a) (b)
(d)(c)
MOS-AK 2009 EEE / NTU
X. ZHOU 37 © 2009
SchottkySchottky--Barrier MOSFET: Barrier MOSFET: AmbipolarAmbipolar CurrentCurrent
Symbols: MediciLines: Model (Xsim)
Gate−Source Voltage, Vgs (V)
-2 -1 0 1 2
Dra
in C
urre
nt, I
ds (
A/μ
m)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0.050.61.2
Vds (V)
ΦM,s/d = 4.6 eV
L = 65 nm, TSi = 20 nm, Tox = 3 nm
Hole tunneling Electron tunnelingElectron thermionicNo drift-diffusion!
VdVs
Vg
Vg
0L
TSi
x
y
Body Gate Oxide
Schottky Contact
S D
Tox
Gaussian box
Medici: two-carrierXsim: sum of two unipolar (Ids,n + Ids,p)
Ambipolar possible in undopedSB-MOS with mid-gap ΦM,s/d
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SBSB--MOS: Total Current = (Electron + Hole) CurrentsMOS: Total Current = (Electron + Hole) Currents
Symbols: MediciLines: Model (Xsim)
Drain−Source Voltage, Vds (V)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Dra
in C
urre
nt, I
ds (
A/μ
m)
10-18
10-17
10-16
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
00.30.60.91.2
Vgs (V)
L = 65 nm, TSi = 20 nm, Tox = 3 nm
ΦM,s/d = 4.6 eV
n + p
n
p
Ambipolar(In + Ip)current
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SBSB--MOS: Model Applied to Measured SBMOS: Model Applied to Measured SB--MOSMOS
Symbols: MeasurementLines: Model (Xsim)
Gate−Source Voltage, Vgs (V)
-4 -2 0 2 4
log(
I ds)
(A
/ μm
)
-15-14-13-12-11-10
-9-8-7-6-5-4-3
0.050.30.61.22.5
L = 200 nm, R = 12.5 nm, Tox = 28 nm
Vds (V)
(a)ΦM,s = 4.73 eV
ΦM,d = 4.77 eVSymbols: MeasurementLines: Model (Xsim)
Gate−Source Voltage, Vgs (V)
-4 -2 0 2 4
log(
I ds)
(A
/ μm
)
-15-14-13-12-11-10
-9-8-7-6-5-4-3
-0.05-0.3-0.6-1.2-2.5
Vds (V)
(b)
L = 200 nm, R = 12.5 nm, Tox = 28 nm
ΦM,s = 4.73 eV
ΦM,d = 4.77 eV
nMOS operation (+Vds) pMOS operation (−Vds)
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.
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DSSDSS--SiNWSiNW: : SubcircuitSubcircuit ModelModel
DSS-SiNW MOS subcircuit model comparison with Measurement.
G. J. Zhu, et al., SSDM, p. 402, Oct. 2009.
Symbols: TCAD (Medici)Lines: Model (Xsim)
Drain−Source Voltage, Vds (V)
0.0 0.5 1.0 1.5 2.0
Dra
in C
urr
ent,
I ds
(μA
)
0
10
20
30
40
0.5 1.0 1.5 2.0
g ds
Symbols: MesurementLines: Model (Xsim)
Gate−Source Voltage, −Vgs (V)
-0.5 0.0 0.5 1.0 1.5 2.0 2.5
Dra
in C
urre
nt, I
ds (
A)
-16-15-14-13-12-11-10-9-8-7-6-5-4-3
L = 100 nm, R = 10 nm Tox = 2nm
Vs VdVs'Leff
VgSB MOS
DSS MOS
S DVs Vd
Vg
Vg
y0
2R
Tox
r
0R
Lseg Lg
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:SBD (TT) + MOS (DD)
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XsimXsim: Basic Model Parameters: Basic Model 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]• Bulk charge sharing (BCS): channel (λc), gate (λp), overlap (λov)• Potential barrier lowering (PBL): accumulation (αacc), depletion/inversion (αds)• Extrinsic: lateral spread (σ), inversion/bulk charge factor (νi, νb)
DC parameters [19]• Mobility: vertical-field mobility (μ, μ2, μ3, ν)• Effective field: vertical (ζn, ζb), lateral (δL)• PBL: accumulation (αacc), depletion/inversion (αds), long-channel DIBL (αdibl)• BCL/lateral-doping: BCL (λ), halo-peak (κ), halo-spread (β), halo-centroid (lμ)• Series resistance: bias-dependent (υ), bias-independent (ρ)• Velocity saturation (vsat), velocity overshoot (ξ), effective D/S voltage (δs)
Smoothing parameters — internal model requirement
Total: 33 basic parameters DG/SiNWhas less parameters
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XsimXsim: History, Evolution, and Philosophy: History, Evolution, and Philosophy
20071997 2000 20021998 1999 2001 20052003 2004 2006 2008
K.Y.Lim
URM URM VVtt--based bulkbased bulkS.B.Chiah
Karthik
G.H.See
URM URM VVtt--based bulk with nonbased bulk with non--pinned pinned φφss
URM URM VVtt//φφss--based strainbased strain--Si/DGSi/DG
URMURM φφss--based bulk/DGbased bulk/DG
Nonuniform/halo doping, vertical/lateral-field mobility, bias-dep Rsd, DIBL, CLM/VS/VO
Idrift+Idiff, URM Qb/Qi, 2D-BCS/PBL, PDE/PAE/PIE, QME, W-dep
SiGe(x)/doping-dep φs, TSi/doping-dep s/a-DG
SC-Q, B/G-ref, S/D by labelKey
mo
del
ed e
ffec
tP
hil
oso
ph
y • URM: Unified Regional Modeling approach — single-piece physics-based regional solutions• New model/effect includes old ones as special cases — extendibility and backward compatibility• One/two-iteration parameter extraction — minimum data requirement and predictability• Selectable accuracy within one parameter set — consistent full/simple model for design/verification
MOS-AK 2009 EEE / NTU
X. ZHOU 43 © 2009
XsimXsim: Future and Ultimate Goal: Future and Ultimate Goal
20061997 2010 20122009 2011 20152013 2014 20162007 2008
S.H.Lin GAA/GAA/SiNWSiNW/Mismatch/Statistical/Mismatch/StatisticalC.Q.Wei SelfSelf--heating/heating/SiNWSiNW--NoiseNoise
G.J.Zhu SB/DSS/UTBSB/DSS/UTB--SOI/DG/SOI/DG/SiNWSiNWJ.B.Zhang SOI/DG/LDMOSSOI/DG/LDMOS
Vt-b
ased
bu
lk
Str
ain
ed-S
i
φ s-b
ased
bu
lk
iaia--DG DG – most difficult, yet complete, structure containing the rest
ss--DG DG – key to extending to other device structures/operations
Ultimate Goal Ultimate Goal —— Unification of MOS models, with seamless transitions across device types/operations
Why not Xsim-SOI/DG/NW?They’re all physically related and should be modeled in one core rather than one for each.
caca--DG DG – bridging (common-gate) s-DG and (independent-gate) a-DG
SOI SOI – PD/FD, Nch/TSi scaling, with/without body contact
M.K.Srikanth Variability/ReliabilityVariability/Reliability
MOS-AK 2009 EEE / NTU
X. ZHOU 44 © 2009
Current team members (PhD students)• Shihuan Lin• Chengqing Wei• Guojun Zhu• Junbin Zhang• Machavolu Srikanth
Previous team members (PhD/MEng students)• Dr Khee Yong Lim• Yuwen Wang• Dr Siau Ben Chiah
Sponsorships and collaborators• Semiconductor Research Corporation• Chartered Semiconductor Manufacturing
AcknowledgmentAcknowledgment
• Dr Zuhui Chen• Ramachandran Selvakumar• Yafei Yan• William Chandra
• Dr Karthik Chandrasekaran• Dr Guan Huei See• Guan Hui Lim
Our relevant publications: http://www.ntu.edu.sg/home/exzhou/Research/DOUST/pub.htm
• Institute for Sustainable Nanoelectronics (ISNE)
• Atomistix Asia Pacific Pte Ltd• Institute of Microelectronics
Research Staff:
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