UC Berkeley EE241 Andrei Vladimirescu
MOSFET Modeling in SPICE
Andrei Vladimirescu
UC Berkeley EE241 Andrei Vladimirescu
MOSFET Device
Mname nd ng ns nb Modname <<L=>L> <<W=>W>+ <AD=AD> <AS=AS> <PD=PD> <PS=PS>+ <NRD=NRD> <NRS=NRS>
<OFF><IC=vgs0,vds0,vbs0>
UC Berkeley EE241 Andrei Vladimirescu
MOS Level=1 DC
l Parameters: VTO, KP, GAMMA, PHI, LAMBDA
IDS =
0 for VGS ≤VTH
KP2
WLe ff
VGS − VTH( )2 1 + LAM BDA ⋅VDS( ) for 0 < VGS − VTH ≤VDS (3.29 )
KP2
WLe ff
VDS 2 VGS − VTH( )− VDS( )1+ LAM BDA ⋅VDS( ) for 0 < VDS < VGS − VTH
VTH = VTO + GAM M A PH I − VBS − PH I( )
UC Berkeley EE241 Andrei Vladimirescu
MOS1 IDS Characteristics
UC Berkeley EE241 Andrei Vladimirescu
Large-Signal Model
UC Berkeley EE241 Andrei Vladimirescu
Dynamic Model
l Gate-Oxide Charges: TOX, CGSO, CGDO, CGBO
ê If TOX specified CGS, CGD and CGB represent Qch=f(V) below G- CGSO, CGDO and CGBO model just overlap of G over diff/bulk
l D and S Junction: CBD, CBS, P, MJ
Cox = εoxε0
TOXCGDO = CGSO = 1
2 CoxLCGBO = CoxW
CBD = CBD1 − VBD PB( )M J
CBS = CBS1 − VBS PB( )M J
LEVEL=1 w/o TOX
UC Berkeley EE241 Andrei Vladimirescu
Sidewall Junction Capacitance
UC Berkeley EE241 Andrei Vladimirescu
Dynamic CG-V Model
UC Berkeley EE241 Andrei Vladimirescu
Small-Signal Model
gds = 1rds
= dIDS
dVDS
gm = dIDS
dVGS
gm bs = dIDS
dVBS
UC Berkeley EE241 Andrei Vladimirescu
.MODEL Parameters MOS1
l .MODEL Modname NMOS/PMOS <VTO=VTO...>
UC Berkeley EE241 Andrei Vladimirescu
Second-Order Effects in MOS3
l Bulk-Charge Contributionl Small-Size Effectsl Subthreshold Conductionl Limited Carrier Velocity Saturation
UC Berkeley EE241 Andrei Vladimirescu
MOS Level=3 DC
IDS = β VGS − VTH − 1 + FB
2VDS
VDS
β = µ e ffCox
WLe ff
µ s = UO1 + TH ETA VGS − VTH( )
µ e ff = µ s
1 + µ s
VM AX ⋅Le ff
VDS
VTH = VFB + PH I − σVDS + γFS PH I − VBS + FN PH I − VBS( )
σ = ETA8.15⋅10 − 22
CoxLe ff3
UC Berkeley EE241 Andrei Vladimirescu
MOS3 Saturation
l Velocity Saturation: VMAX, KAPPA
VDSAT = VGS − VTH
1 + FB
+VMAX ⋅Le ff
µs
− VGS − VTH
1 + FB
2
+VMAX ⋅Le ff
µ s
2
∆L= X d
EPX d
2
2
+ KAPPA VDS − VDSAT( )− EPXd
2
EP = IDSAT
GDSATLe ff
UC Berkeley EE241 Andrei Vladimirescu
MOS3 Subthreshold
l NFS
VON = VTH + nk Tq
n = 1 + Cfs
Cox
+ Cd
Cox
Cfs = q ⋅NFS
Cd = ∂QB
∂VBS
= − γSd
dVBS
PH I − VBS − ∂γS
∂VBS
PH I − VBS + DELTA πεsi
4CoxW
Cox
UC Berkeley EE241 Andrei Vladimirescu
MOS3 SubVT Characteristics
UC Berkeley EE241 Andrei Vladimirescu
Temperature Model
UC Berkeley EE241 Andrei Vladimirescu
Noise Model
l Resistive Channel and Flicker: TOX, KF, AF
ids2 = 8k Tgm
3∆f + KF⋅IDS
AF
fCoxLe ff2 ∆f
UC Berkeley EE241 Andrei Vladimirescu
Advanced MOSFET Modelsfor ICs
Andrei Vladimirescu
UC Berkeley EE241 Andrei Vladimirescu
Physical Effects in Level 2,3
l Short and Narrow-channel effectsl Mobility reduction due to electrical fieldl Bulk-charge effectl Channel-length modulationl Subthreshold Conductionl Carrier velocity saturationl Parasitic Drain and Source resistance
UC Berkeley EE241 Andrei Vladimirescu
Physical Effects Needed
l Non-uniform channel dopingl Drain-induced barrier loweringl Substrate-current-induced body effectl Temperature effectsl Poly-gate depletion effectl Velocity overshoot
UC Berkeley EE241 Andrei Vladimirescu
Model Requirements
l Analytical» Continuity of IDS=f(VDS,VGS,VBS) and its first derivatives» Parameter/Formulation choice for accuracy, scalability
l Simulation» Computationally efficient (time and #iterations)» Solid convergence» Robust (no singularities)» Charge representation for transient
UC Berkeley EE241 Andrei Vladimirescu
BSIM Models
l Based on Bell Labs CSIM (1981)l BSIM1 (1984) - L>1µ, Tox>150Al BSIM2 (1990) - BSIM for deep-submicronl BSIM3 (1993)
UC Berkeley EE241 Andrei Vladimirescu
BSIM References
l ___, BSIM3v3 Manual (Final Version), Univ. of California, Berkeley, 1995.l S.Liu and L.W.Nagel, Small-Signal MOSFET Models for Analog Circuit Design,
IEEE JSSC, Vol. SC-17, no. 6, pp. 983-998, Dec. 1982.l B.J.Sheu, D.L. Scharfetter and H.C. Poon, Compact Short-Channel IGFET
Model (CSIM), ERL Memo M84/20, Univ. of California, Berkeley, Mar. 1984.l B.J.Sheu, D.L.Scharfetter and P.K.Ko, SPICE2 Implementation of BSIM, ERL
Memo M85/42, Univ. of California, Berkeley, May 1985.l M.C.Jeng, Design and modeling of Deep-Submicron MOSFETs, ERL Memo
M90/90, Univ. of California, Berkeley, Oct 1990.l BTA Technology, Inc., BSIMPro and Presentations on MOSFET Modeling,
Santa Clara, California.
UC Berkeley EE241 Andrei Vladimirescu
Parameter Philosophy
l For each process parameter P there is» length correction PL» width correction PW
l Three Model Parameters for each Effect» P0, PL, PW, e.g., VFB, LVFB, WVFB
P= P0 + PL
Li − DL+ PW
W i − DW
UC Berkeley EE241 Andrei Vladimirescu
BSIM3(v3)
l Single I-V formulation for IDS, Rout» from subthreshold to strong inversion» from saturation to linear
l W dependence of QB and Rds
l Improved scalability» ∆L and ∆W dependency on L and W
l Improved Capacitance model for small-sizel Non-quasi static relaxation model
UC Berkeley EE241 Andrei Vladimirescu
Deep Subµ MOSCharacteristic
UC Berkeley EE241 Andrei Vladimirescu
BSIM3 VTH
l Vertical and Lateral Nonuniform Doping» K1, K2
VTH = VTide al + K1 φs − VBS − φs( )+ K 2VBS + K 1 1 + NLX
Le ff
φs
UC Berkeley EE241 Andrei Vladimirescu
BSIM3 VTH (Cont’d)
l Short, Narrow Channel
VTH = VTide al + ∆VTdoping + (K 3 + K 3BVBS ) tox
W e ff + W 0
φs
− DVTOW e − DVT1w W e ff Le ff 2ltw + 2e − DVT1w W e ffLe ff ltw( )VBI − φs( )−− DVTO e − DVT1Le ff 2lt + 2e − DVT1w Le ff lt( )VBI − φs( )−− e − D sub Le ff 2lt0 + 2e − D sub Le ff lt0( )η0 + ηBVBS( )VDS
UC Berkeley EE241 Andrei Vladimirescu
BSIM3 VTH = f(L)
UC Berkeley EE241 Andrei Vladimirescu
BSIM3 Poly-Gate Effect
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BSIM3 Poly-Gate Effect on IDS
UC Berkeley EE241 Andrei Vladimirescu
BSIM3 Mobility
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BSIM3 IDS
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BSIM3 Unified IDS
UC Berkeley EE241 Andrei Vladimirescu
Vdseff Function
UC Berkeley EE241 Andrei Vladimirescu
BSIM3 NQS
l QS model ignores finite time for channel charge build-upl Elmore equivalent of channel charge retains lowest freq pole
UC Berkeley EE241 Andrei Vladimirescu
BSIM3 Characteristics
UC Berkeley EE241 Andrei Vladimirescu
BSIM3 Summary
l Continuous Model for wide range of W and Ll Major physical mechanisms of subm devicesl New narrow-width modell Introduction of Non-Quasi-Static behaviourl Superior scaling and statistical modelingl Charge conservingl Computationally efficient
UC Berkeley EE241 Andrei Vladimirescu
MOS Modeling Trends
l Single-formulation Models» BSIM3, MOS9, EKV, ...
l Standard Models (Public Domain)l Good fit for large- and small-signal characteristics
(function and derivatives)l Scalability with device dimensionsl Support for statistics