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Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Advanced Compact Models for MOSFETsChristian Enz, Carlos Galup-Montoro,
Gennady Gildenblat, Chenming Hu, Ronald van Langevelde, Mitiko Miura-Mattausch,
Rafael Rios, Chih-Tang (Tom) SahJosef Watts (editor)
Colin McAndrew (presenter)
Slide 2Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Outline
Simulation NeedsApproaches to MOSFET Compact ModelingCharge-Based Models• ACM• EKV• BSIM5
Surface-Potential Based Models• Source-side only• HiSIM• MM11• SP
Slide 3Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
MOSFET Modeling Needs
Accurate representation of• standard DC and AC (gij and Cij) and S-parameter characteristics• NQS effects• noise (including induced correlated gate noise)• statistics
Over• bias• geometry (all layout configurations, including parasitics and substrate
connections, proximity effects, short- and narrow-channel effects)• temperature (potentially including self-heating)• device types (bulk, SOI, MG, LDMOS, …)
Key circuit metrics• “standard” FoMs: speed, leakage, fT, power, etc.• “RF” FoMs: phase noise/BER, linearity/IM3, NFmin, etc.
Slide 4Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
MOSFET Modeling Needs
but all of these need to be …
… based on a core model formulation
Slide 5Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Basic MOSFET Operation
2-dimensional problem
gatedrainsource
bulk(backgate)
y=0 y=L
x
Slide 6Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Basic MOSFET Operation
2-dimensional problemApproached by separating into 2 1-dimensional problems• vertical 1-D field electrostatics control conduction charge
gatedrainsource
bulk
+-+ + + + + + + + +
Slide 7Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Basic MOSFET Operation
2-dimensional problemApproached by separating into 2 1-dimensional problems• vertical 1-D field electrostatics control conduction charge
gatedrainsource
bulk
+-+ + + + + + + + +
1-d electrostatics
Slide 8Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Basic MOSFET Operation
2-dimensional problemApproached by separating into 2 1-dimensional problems• vertical 1-D field electrostatics control conduction charge
gatedrainsource
bulk
+-+ + + + + + + + +
1-d electrostatics ignore complexstuff here!
Slide 9Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Basic MOSFET Operation
2-dimensional problemApproached by separating into 2 1-dimensional problems• vertical 1-D field electrostatics control conduction charge• longitudinal 1-D field controls current flow
gatedrainsource
bulk
+-+ + + + + + + + +
+-
Slide 10Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
assume I is independent of y, integrate along channel
Pao-Sah Model – The “Golden” Reference
dxyxnWy
q
dxyxJWyIe ),(
),()(
∫
∫
∂∂
−=
=φ
µ
∫ ∫ ∂∂−=
db
sb
s
bulk
V
Vds dVd
xyxn
LWqI
ψ
ψψ
ψµ ),(
Slide 11Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Electrostatics:
Pao-Sah Model – The “Golden” Reference
∫ ∫−−
=db
sb
s
bulk
tFV
V
V
ds dVdE
eLWNqI
ψ
ψ
ϕϕψψ
ψµ
)(
)2(
( )( )( )ψϕ
ψϕ
ε ϕψϕϕ
ϕψ
−−+
+−=
+−
−
1
12 )2(
2
ttcbF
t
ee
eqNE
tV
t
s
Slide 12Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Charge-Sheet Model (CSM) Formulation
Inversion charge density Qi′ is basic variableLeads to implicit equation for the surface potential ψs• a function of gate bias and quasi-Fermi level splitting V
Current is then derived from
( ) ss
sids dVQLWI
sL
s
ψψ
ψµ ψ
ψ ∂∂
−= ∫0
)('
Slide 13Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
MOSFET Models
Historically the Pao-Sah and CSM formulations were considered too computationally burdensomeThe solution adopted was the threshold voltage based MOSFET model formulation• early models were piecewise formulations, with separate equations
used to model different regions of operation• later models used mathematical techniques to make the models
single-piece and a single set of model equations was applicable to all regions of operation
• not discussed: table models, tanh models
Advanced MOSFET models being developed today• charge based models• surface potential based models
Slide 14Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Other Issues
Complex doping profilesShort and narrow channel effectsAccurate mobility modelingPolysilicon depletionQuantum effectsVelocity saturation and drain saturation voltageOperation in accumulationParasiticsGate and substrate currentsDevice structure (SOI, MG, …)
Only core model formulation will be reviewed here
Slide 15Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Charge Based Models
Initial formulation in terms of charges by Maher and Mead, 1987Charge expression (for HFETs) and current formulation (for MOSFETs) from Shur’s group, 1990 & 1991EKV model July 1995ACM model November 1995Gummel 2001UCB group (genesis of BSIM5) 2003
Slide 16Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
ACM
ACM = “Advanced Compact MOSFET” modelDevelopment began in late 1980’sDriving need was for MOS varactors, then developed for MOSFETsPinch-off voltage and charge density
cbi
tnCitOXip dV
QdQnCQ
OX=
−−= '
1'''',
ϕϕ
cbpip
itnC
QQVV
OX
iip −=
+
−
'
'ln'
''ϕ
Slide 17Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
ACM
-6%
-5%
-4%
-3%
-2%
-1%
0%
0.0 0.5 1.0 1.5 2.0Vgb (V)
Erro
r
Charge-Sheet
UCCM
UCCM+
Slide 18Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
EKV – Introduction
Driven by needs of very low power analog designWeak and moderate inversion very important• conventional models unphysical in this region, depend only on the
numerical tricks used to make the models continuous
Symmetric formulationInitial emphasis was gm/Id, did use linearized inversion chargeLater moved to physical formulation, like Maher, that unifies weak to strong inversionConductance and capacitance coefficients follow simply from modeled charges
Slide 19Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
EKV – Foundations
Basic relation
Inversion charge linearization gives direct relation to surface potential
Direct link from charge based to surface potential based modelsDrain current given by
( ) ( )rf idd
issrf
spec
ds qqqqiiII
==
+−+=−= 22
)ln(2 sssbp qqVV +=−
OXitFps nCQmV )(2 '−−++= ϕϕψ
22 tOXspec LWCnI ϕµ=
Slide 20Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
108 107 106 105 104 103 102
ID [A]
0.8
g mϕ t
/ Id
[-]
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
L = 70 nm Vds = 1.5 V
measuredEKV
EKV – gm/Id Characteristics
Slide 21Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
BSIM5
Single set of equations used to calculate charges in all regions of operation• continuous and symmetric
Inversion charge density solution
Drain current
−−−−
−=+
1
lnlnnnnV
nVV
nq
nq
t
cbB
t
FBgbiiϕ
ϕϕ
−+
−= ds
dst
OXds qq
nqq
LWCI
2
222ϕ
µ
Slide 22Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
BSIM5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
1x10-10
1x10-9
1x10-8
1x10-7
1x10-6
Na=1x1016
1x10171x1018
Qin
Vgs [ V ]
Pao-Sah Charge-sheet BSIM5
Tox=20A
Slide 23Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Surface Potential Based Models
Origin is generally considered to be Brews (1978)HiSIM 1989 (DC), 1994 (AC)MISNAN in 1991DEC source-side model 1995MM11 1998SP 1998
Slide 24Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Source-Side Model
Developed for DEC’s Alpha chip designOnly requires solution for ψs at the source
qb is linearized w.r.t. source and drain end points• preserves source/drain symmetry
Drain saturation corrected to maintain correct behavior for small Vds
)( sFBgbOXg VVCq ψ−−=
)1( −+±= − tseq tsbϕψϕψγ
mmdsatdsdsdsx VVgVgV 1
00 ))(1( +=
Slide 25Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
Source-Side Model
1.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-031.E-021.E-011.E+00
-0.5 0.0 0.5 1.0
NumericalEq. (4)Eq. (5)Eq. (6)
Vgb (V)
q i /
Cox
(V)
V th
sbq ψ~
tsbq ϕψ +~
)1(~ −+ − tseq tsbϕψϕψ
Slide 26Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
HiSIM
Development began in late 1980’sIterative solution for ψs• accurate solution needed for conductance and capacitance
Physical handling of lateral doping profiles (halo)Consistent, simple formulation with a small number of physical parametersGCA plus lateral field gradient are maintained in “intrinsic” device• self-consistent solution maintained from pinch-off point to drain
Simulation time comparable with BSIM3v3
Slide 27Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
HiSIM
Slide 28Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
MM11
Development started in 1994, emphasis was analog and RF modeling• mobility model targeted distortion• accurate noise modeling• proper symmetry• of course, it works for digital too!
Model structure includes local (miniset, per geometry) and global (maxiset, over geometry) parameters• some parameters are common to both sets• simplifies parameter extraction and geometry modeling
Linearization is done around mid-point potential, 0.5(ψs0+ψsL)Original non-iterative ψs solution, iterative procedure used since MM1102
Slide 29Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
MM11
Slide 30Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
SP
Accurate non-iterative solution for ψs• extreme accuracy required for accurate modeling of conductance and
capacitance coefficients• modified form also applicable for overlap capacitance modeling
Symmetric linearization gave very compact, highly accurate modeling equations• substantially simpler than “classic” CSM expressions• linearization is about mid-point potential, 0.5(ψs0+ψsL)
Velocity saturation model used has no singularity at Vds=0 so symmetry is preservedMany bias and geometry dependent effects implemented via lateral gradient factorSpline-collocation-based NQS model
Slide 31Advanced Compact Models for MOSFETs, NanoTech/WCM 2005
SP
-1 0 1 2 3 40.0
0.3
0.6
0.9 Linearized CSM Original CSM
Cdg
Cbg
Csg
Cgg
N
orm
aliz
ed T
rans
capa
cita
nces
Vgs (V)