Advanced Compact Models for MOSFETs - NSTI · Advanced Compact Models for MOSFETs, NanoTech/WCM 2005 Advanced Compact Models for MOSFETs Christian Enz, Carlos Galup-Montoro, Gennady

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


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.


MOSFET Modeling Needs

but all of these need to be …

… based on a core model formulation


Basic MOSFET Operation

2-dimensional problem

gatedrainsource

bulk(backgate)

y=0 y=L

x



2-dimensional problemApproached by separating into 2 1-dimensional problems• vertical 1-D field electrostatics control conduction charge

gatedrainsource

bulk

+-+ + + + + + + + +




gatedrainsource

bulk

+-+ + + + + + + + +

1-d electrostatics




gatedrainsource

bulk

+-+ + + + + + + + +

1-d electrostatics ignore complexstuff here!



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

+-+ + + + + + + + +

+-


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 ),(


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


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

)('


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


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


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


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

QQ

OX

iip −=

+

−

'

'ln'

''ϕ


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+


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


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=


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


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


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


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


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( +=


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


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


HiSIM


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


MM11


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


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)

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Advanced Compact Models for MOSFETs - NSTI · Advanced Compact Models for MOSFETs, NanoTech/WCM 2005 Advanced Compact Models for MOSFETs Christian Enz, Carlos Galup-Montoro, Gennady