L30 01May03 1

Semiconductor Device Modeling and CharacterizationEE5342, Lecture 30Spring 2003

Professor Ronald L. Carterronc@uta.edu

http://www.uta.edu/ronc/

L30 01May03 2

Gummel-Poon Staticnpn Circuit Model

C

E

B

B’

ILC

ILEIBF

IBR ICC - IEC = {IS/QB}*

{exp(vBE/NFVt)-exp(vBC/NRVt)}

RC

RE

RBB

IntrinsicTransistor

L30 01May03 3

Gummel Poon npnModel Equations

IBF = IS expf(vBE/NFVt)/BF

ILE = ISE expf(vBE/NEVt)

IBR = IS expf(vBC/NRVt)/BR

ILC = ISC expf(vBC/NCVt)

ICC - IEC = IS(exp(vBE/NFVt - exp(vBC/NRVt)/QB

QB = { + + (BF IBF/IKF + BR IBR/IKR)1/2} (1 - vBC/VAF - vBE/VAR )-1

L30 01May03 4

VBIC Model Overview [5]

Self-heating effects included Improved Early effect modeling Quasi-saturation modeling Parasitic substrate transistor modeling Parasitic fixed (oxide) capacitance modeling An avalanche multiplication model included Base current is decoupled from collector current

L30 01May03 5

CAD Tools Support for VBIC

• Hspice [4]

Does not support PNP deviceDoes not scale with “Area” and “M” terms

• Spectre [5]

Support both NPN and PNP devicesscale with “Area” and “M” term

• HPADSNo temperature nodes (“dt” and “tl”), so

unable to simulate thermal coupling effects

L30 01May03 6

Temperature Designations for VBIC

25tnom27tnomParameters measurement temperature 27tref

25

0

Default

27

0

Default NameName

temptempAmbient temp.

dtemptriseTemperature rise of the device from ambient

Hspice [5]Spectre [4]Parameters Description

L30 01May03 7

Using VBIC in Spectre [5]

Name c b e [s] [dt] [tl] ModelName parameter=value ...

• Selft=1 and Rth>0 to enable Self-heating• 1 volt at the temperature nodes = 1 degree in

temperature• “tl” node represents the initial local

temperature of device which always corresponds to trise+temp

• “dt” node represents the rise above trise+temp caused by thermal dissipation, whose value equals V(dt)-V(tl)

• Device temperature=V(dt)-V(tl)+trise+temp

L30 01May03 8

Using VBIC in Cadence

• Need explicit external temperature nodes in the symbol to model inter-device thermal coupling by Connecting thermal network between “dt” nodes, or Adding VCVS between “tl” and “tlr” node

• Customized VBIC 6-terminal (5-pin) symbol

L30 01May03 9

Model Conversion

• Most BJTs are defined with SGP model • A conversion from SGP to VBIC is needed• Only approximate conversion is possible

• Some parameters are left unmapped such as Rth and Cth

• Two approaches are provided Manual conversion — done empirically and need

Local Ratio Evaluation [2]

Program conversion — “official” program sgp_2_vbic [3]

L30 01May03 10

Parameters Mapping by sgp_2_vbic

VBIC mapping VBIC mapping VBIC mappingRcx Rc Mc Mjc Xtf XtfRci 0 Cjcp Cjs Vtf VtfRbx Rbm Ps Vjs Itf ItfRbi Rb-Rbm Ms Mjs Tr TrRe Re Nei Nf Td Tf·Ptf/180Is Is Iben Ise Ea EgNf Nf Nen Ne Eaie EgNr Nr Ibei Is/Bf Eaic EgFc Fc Ibci Is/Br Eane EgCje Cje Nci Nr Eanc EgPe Vje Ibcn Isc Xis XtiMe Mje Ncn Nc Xii Xti-XtbCjc Cjc·Xcjc Ikf Ikf Xin Xti-XtbCjep Cjc(1-Xcjc) Ikr Ikr Kfn KfPc Vjc Tf Tf Afn Af

AFFbcAR

Fbe

AF

C

F

VVVV

V

I

gO

//1

/1

AFRbcAR

Rbe

AR

e

R

VVVV

V

I

go

//1

/1

1

11

1

/

/

ER

EF

eR

RbeR

beRbc

Fbe

cF

FbcF

bc

V

V

Ig

Cqq

qIg

Cq

o

o

Early Effect model is different Need Vbe, Vbc to solve the 3 equations below

L30 01May03 11

L30 01May03 12

HeterojunctionElectrostatics

Eo

EC,p

EV,p

EF,pEF,n

EC,n

EV,n

EC

EV

qp

qn

-xn xp0

L30 01May03 13

Poisson’s EquationEx

xxp-xn

p

A

p

px qNdxdE

n

D

n

nx qN

dxdE

n,bix VdxE

n,bix VdxE

0xE0xE

0x at eqn Continuity

xpxn

L30 01May03 14

Heterojunctionelectronics

d

2inonovn,vn,f

n,vn,fn,gnn

dcn,fc

n,fcnn,fon

npbi

pand

N/np , p/NlnkTEE

EEEqq

N/NlnkTEE

EEqEEq

V

xqNxqN ,neutrality Charge

L30 01May03 15

Heterojunctionelectronics (cont)

text. in 8.40 & 8.39 c.f.

, N/NlnkTEE

, EEEqq

. N/nn , n/NlnkTEE

, EEqEEq

avp,vp,f

p,vp,fp,gpp

a2ipopocp,fc

p,fcpp,fop

L30 01May03 16

Heterojunctionelectronics (cont)

form. eappropriat the is this then

E is barrier eappropriat the and

important, is injection hole Since

. /Nnp and , Np

, N

N

p

plnkTEqV

8.39 e.g.

v

d2inoapo

n,v

n,v

no

povbi

L30 01May03 17

Heterojunctiondepletion widths

p,apn,dnp,a

n,dbipnp

p,apn,dnn,d

p,abipnn

p,apn,dnp,an,d

2p,an,dbipn

pn

NNqN

NV2x

NNqN

NV2x

NNNqN

NNV2xxW

L30 01May03 18

Final Exam• Review a paper on “Device Parameter

Extraction”.• Paper to be reviewed will be posted

Monday, May 5, 2003 • Comment on Device Physics used.• Critique the extraction procedures

– Assumptions– Consistency of method w.r.t. assumptions

• One page solution due 11 AM, Thur., May 8

L30 01May03 19

References• Fujiang Lin, et al, “Extraction Of VBIC Model for SiGe HBTs

Made Easy by Going Through Gummel-Poon Model”, from http://eesof.tm.agilent.com/pdf/VBIC_Model_Extraction.pdf

• http://www.fht-esslingen.de/institute/iafgp/neu/VBIC/• Avanti Star-spice User Manual, 04, 2001. • Affirma Spectre Circuit Simulator Device Model Equations• Zweidinger, D.T.; Fox, R.M., et al, “Equivalent circuit

modeling of static substrate thermal coupling using VCVS representation”, Solid-State Circuits, IEEE Journal of , Volume: 2 Issue: 9 , Sept. 2002, Page(s): 1198 -1206