L27 23Apr021 Semiconductor Device Modeling and Characterization EE5342, Lecture 27 -Sp 2002 Professor Ronald L. Carter

L27 23Apr02 1

Semiconductor Device Modeling and CharacterizationEE5342, Lecture 27 -Sp 2002

Professor Ronald L. [email protected]

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

L27 23Apr02 2

Ebers-Moll Model(No G-R curr)

-JEAE

= IE

JCAC = IC

E

B

C

RIRFIF

(Fig. 9.30 Semiconductor Physics & Devices, by Neamen, Irwin, Chicago, 1997, * throughout)

L27 23Apr02 3

Source of Ebers-Moll Equations (E)

SFFB0BRR

E

ESB0BE0EES

B0BnE

E0EpE

nEpEE

/exp /sinhnqD

/exp

/tanhnqD

/tanhpqD

/sinh/exp

/tanh/expnqDJ

1exp/tanhpqDJ

/JJJ

IVVf

AJLxL

AVVf

AJAI

LxLLxLJ

LxVVf

LxVVf

L

VV

LxL

AI

tBEBBBtBC

BBBEEE

BB

tBC

BB

tBE

B

t

BE

EEE

EE

L27 23Apr02 4

Source of Ebers-Moll Equations (C)

StBCBBBtBE

C

CS

BBBCCC

BB

tBE

BB

tBC

B

t

BC

CCC

CC

IVVf

AJLxL

AVVf

AJAI

LxLLxLJ

LxVVf

LxVVf

L

VV

LxL

AI

/exp /sinhnqD

/exp

/tanhnqD

/tanhpqD

/sinh/exp

/tanh/expnqDJ

1exp/tanhpqDJ-

/JJJ

RRB0BFF

B0BC0CCS

B0BnC

C0CpC

nCpCC

L27 23Apr02 5

Common emitter current gain,

lim. , V2VexpDn2

xxn , xDNxDN

L2x

lim. , V2VexpDn2

xxn , L2x

xDNxDN

limited. or limited is BJT a Usually,V2VexpDn2

xxnL2x

xDNxDN

1 so , 1 ; III with ,II

TtBE

0BBOBBEi

EBEBEB

2B

2B

tBE

0BBOBBEi

2B

2B

EBEBEB

T

1

tBE

0BBOBBEi

2B

2B

EBEBEB

00

0CBEBC

0

L27 23Apr02 6

Charge componentsin the BJT

From Getreau, Modeling the Bipolar Transistor,Tektronix, Inc.

L27 23Apr02 7

Gummel-Poon Staticnpn Circuit Model

C

E

BB’

ILC

ILE IBFIBR ICC - IEC =

IS(exp(vBE/NFVt) -exp(vBC/NRVt)/QB

RC

RE

RBB

IntrinsicTransistor

L27 23Apr02 8

Recombination/GenCurrents (FA)

CBCB

BCeff,

1gen

BCeff,BCbiC

BCgen

BCiGC

1rec

BEt

BErec

iBERE

NNNNN and

rate, ionrecombinat the is and DR CB

the is qNVV2W where ,2

WqnJ

.rate ionrecombinat the is and DR

EB the is W where ,V2Vexp2

nqWJ

L27 23Apr02 9

Gummel Poon npnModel Equations

IBF = IS expf(vBE/NFVt)/BFILE = ISE expf(vBE/NEVt)

IBR = IS expf(vBC/NRVt)/BRILC = 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

L27 23Apr02 10

+

-+

-

VAF ParameterExtraction (fEarly)

iCiB

vCEvBE

0.2 < vCE < 5.00.7 < vBE < 0.9

Forward Active Operation

iC = ICC =(IS/QB)exp(vBE/NFVt),

where ICE = 0, andQB

-1 =

(1-vBC/VAF-vBE/VAR )* {IKF terms}-1,

so since vBC = vBE - vCE,VAF = iC/[iC/vBC]vBE

L27 23Apr02 11

iE = - IEC =(IS/QB)exp(vBC/NRVt),

where ICC = 0, andQB

-1 =

(1-vBC/VAF-vBE/VAR ) {IKR terms}-1,

so since vBE = vBC - vEC,VAR = iE/[iE/vBE]vBC

VAR ParameterExtraction (rEarly)

+

-+

-

iEiB

vECvBC

0.2 < vEC < 5.00.7 < vBC < 0.9

Reverse Active Operation

L27 23Apr02 12

BJT CharacterizationForward GummelvBCx= 0 = vBC + iBRB - iCRC

vBEx = vBE +iBRB +(iB+iC)RE

iB = IBF + ILE = ISexp(vBE/NFVt)/BF

+ ISEexpf(vBE/NEVt)iC = FIBF/QB =

ISexp(vBE/NFVt) (1-vBC/VAF-vBE/VAR )

{IKF terms}-1

+

-

iC RC

iB

RE

RB

vBEx

vBC

vBE

++

-

-

L27 23Apr02 13

Definitions ofNeff and ISeff• In a region where iC or iB is approxi-

mately a single exponential term, theniC or iB ~ ISeffexp (vBEext /(NFeffVt)

whereNeff = {dvBEext/d[ln(i)]}/Vt,

and ISeff = exp[ln(i) - vBEext/(NeffVt)]

L27 23Apr02 14

Region a - IKFIS, RB, RE, NF, VAR

Region b - IS, NF, VAR, RB, RE

Region c - IS/BF, NF, RB, RE

Region d - IS/BF, NFRegion e - ISE, NE

Forward GummelData Sensitivities

1.E-121.E-101.E-081.E-061.E-041.E-02

0.1 0.3 0.5 0.7 0.9iC(A),iB(A) vs. vBE(V)

iC

vBCx = 0

iB

a

b

c

d

e

L27 23Apr02 15

Simple extractionof IS, ISE from data

1.E-16

1.E-14

1.E-12

1.E-10

0.1 0.3 0.5 0.7 0.9

Data set used • IS = 10f• ISE = 10E-14Flat ISeff for iC data =

9.99E-15 for 0.230 < vD < 0.255

Max ISeff value for iB data is 8.94E-14 for vD = 0.180ISeff vs. vBEext

iB data

iC data

L27 23Apr02 16

Simple extraction of NF, NE from fg data

Data set used NF=1NE=2

Flat Neff region from iC data = 1.00 for 0.195 < vD < 0.390

Max Neff value from iB data is 1.881 for 0.180 < vD < 0.181

0.91.11.31.51.71.92.1

0.1 0.3 0.5 0.7 0.9NEeff vs. vBEext

iB data

iC data

L27 23Apr02 17

0

25

50

75

100

1.E-10 1.E-06 1.E-02

Simple extractionof BF from data

• Data set used BF = 100

• Extraction gives max iC/iB = 92 for 0.50 V < vD < 0.51 V 2.42A < iD < 3.53A

• Minimum value of Neff =1 for slightly lower vD and iD

iC/iB vs. iC

L27 23Apr02 18

BJT CharacterizationReverse Gummel

+

-

iE

RC

iB

RE

RB

vBCxvBC

vBE

++

-

-

vBEx= 0 = vBE + iBRB - iERE

vBCx = vBC +iBRB +(iB+iE)RC

iB = IBR + ILC = (IS/BR)expf(vBC/NRVt)

+ ISCexpf(vBC/NCVt)iE = RIBR/QB =

ISexpf(vBC/NRVt)(1-vBC/VAF-vBE/VAR )

{IKR terms}-1

L27 23Apr02 19

1.E-10

1.E-08

1.E-06

1.E-04

1.E-02

0.1 0.3 0.5 0.7 0.9

Sample rg data forparameter extraction

• IS=10f• Nr=1• Br=2• Isc=10p • Nc=2• Ikr=.1m• Vaf=100• Rc=5• Rb=100

iE, iB vs. vBCext

iB data

iE data

L27 23Apr02 20

0.0

0.5

1.0

1.5

2.0

1.E-10 1.E-06 1.E-02

Simple extractionof BR from data

• Data set used Br = 2

• Extraction gives max iE/iB = 1.7 for 0.48 V < vBC < 0.55V 1.13A < iE < 14.4A

• Minimum value of Neff =1 for same range

iE/iB vs. iE

L27 23Apr02 21

1.E-16

1.E-14

1.E-12

1.E-10

0.2 0.4 0.6

Simple extractionof IS, ISC from data

Data set used • IS = 10fA• ISC = 10pAMin ISeff for iE data =

9.96E-15 for vBC = 0.200

Max ISeff value for iB data is 8.44E-12 for vBC = 0.200ISeff vs. vBCext

iB data

iE data

L27 23Apr02 22

0.91.11.31.51.71.92.1

0.1 0.3 0.5 0.7 0.9

Simple extraction of NR, NC from rg data

Data set used Nr = 1Nc = 2

Flat Neff region from iE data = 1.00 for 0.195 < vBC < 0.375

Max Neff value from iB data is 1.914 for 0.195 < vBC < 0.205NEeff vs. vBCext

iB data

iE data

L27 23Apr02 23

Fully biased n-MOScapacitor

0y

L

VG

Vsub=VB

EOx,x> 0

Acceptors

Depl Reg

e- e- e- e- e- e- n+

n+

VS VD

p-substrate

Channel if VG > VT

L27 23Apr02 24

Flat band with oxidecharge (approx. scale)

Ev

Al SiO2 p-Si

EF

m

Ec,Ox

Eg,ox~8eV EFp

Ec

Ev

EFi

'Ox

'ssmsOxmsFB

OxOxc

Ox

'ssx

ssm

ss

CQVV

xV

dxdE

q1QE

surface gate the onis Q'Q' charge

a cond FB at thenbound, Ox/Si the at

is Q' charge a If

q(fp-ox)

q(Vox)

q(m-ox)

q(VFB) VFB= VG-VB, when Si bands

are flat

Ex

+<--Vox-->-

L27 23Apr02 25

Flat-band parametersfor p-channel (n-subst)

0nNlnVq2

EnNNlnV

qE gate, Si-poly p a For

den chg Ox/Si the is 'Q ,x'C

change) (no 'C'QV :substraten

idt

g2i

dvtms

gsms

ssOxOx

Ox

OxssmsFB

L27 23Apr02 26

Fully biased n-channel VT calc

0V ,qN

VV22x

,xNqQ' ,0NnlnV

VV'C'Q2VVV

VV :substratep

aCBp

d,max

d,maxad,maxaitp

FBOx,maxd

pFBCT

Tthreshold at ,G

L27 23Apr02 27

Fully biased n-channel VT calc

0V ,qNVV22x

,xNqQ' ,0NnlnV

VV'C'Q2VVV

VV :substratep

a

sBpmaxd,

maxd,amaxd,a

itp

FBOx

max,dpFBsT

Tthreshold at ,G

L27 23Apr02 28

Q’d,max and xd,max forbiased MOS capacitor

Fig 8.11**

x d,m

ax (m

icron

s)

|Q’ d,

max

|/q (c

m-2

)

L27 23Apr02 29

2Emax.damax,d

Eamax,dmax,d

21

EE

Emax.d

E

Ep

21

a

pmaxd,

cm/coul936.8XqNQ102.5Nx m31.1x

144196.1264.021485.87.112x

mV2641045.1144ln02586.0

qN022x

L27 23Apr02 30

Fully biased p-channel VT calc

0V ,qNVV22x

,xNqQ' ,0nNlnV

VV'C'Q2VVV

VV :substraten

dBCn

d,max

d,maxdd,maxidtn

FBOx,maxd

nFBCT

Tthreshold at ,G

L27 23Apr02 31

I-V relation for n-MOS (ohmic reg)

2TGSOxn

sat,D

sat,DSDS

Lys,sat,DS

sat,DSTGDS

2DSDSTG

OxnD

VVLW

2'CI

VV for const iscurr. channel that assume

0n' ,V Atphysical.-non is result

,VVVVfor Note .VVVV2L

W2'CI

ID

VDSVDS,sa

t

ID,sat

ohmic non-physical

saturated

L27 23Apr02 32

Universal draincharacteristic

9ID1

ID

4ID1

ID1VGS=VT+1V

VGS=VT+2V

VGS=VT+3V

2DS

Oxnsat,D VLW

2'CI

VDS

2Oxn1D V1LW

2'CI

saturated, VDS>VGS-VTohmic

L27 23Apr02 33

Characterizing then-ch MOSFET

VD

IDDSG B

2TGSOxn

sat,D

TGSDSTGSDS

VVLW

2'CI

so , VVV0V , VV

VGSVT

DI

LW

2'CslopeOxn

L27 23Apr02 34

Substrate bias effect on VT (body-effect)

pSBpOx

aSiSBT

SBTTa

SBpmaxd,

Ox

maxd,apFBST

T

2V2'CNq20VV

VVV so , qNV22x

where , 'CxNq2VVV

Source to relative be ncalculatio V Letting

L27 23Apr02 35

Body effect dataFig 9.9**

L27 23Apr02 36

EqQ,CQV

0.097V

cm/F 986cm/coul98.36- - C

Qcm/nf 86

7401485.89.3

tCcm740m940t

ssox

ssms FB

2E

E

ox

max,d

2E

Eoxox

ox

EEox

L27 23Apr02 37

V186.09E86E19E6.1

CQ-

-0.817V 10E45.1

14E419E8.2ln02586.0

'ox

'ss

2ms

2

iactssms n

NNlnVXX

L27 23Apr02 38

Values for ms

with silicon gate

idt

g

dCt

dCtSi

gSims

iat

g2i

aCt

2i

aCtSiSims

nNlnVq2

ENNlnV :Note

NNlnVq

E :Si-n to poly p

nNlnVq2

EnNNlnV :Note

nNNlnV :Si-p to poly n

L27 23Apr02 39

SPICE mosfet model levels• Level 1 is the Schichman-Hodges

model• Level 2 is a geometry-based,

analytical model• Level 3 is a semi-empirical, short-

channel model• Level 4 is the BSIM1 model• Level 5 is the BSIM2 model, etc.

L27 23Apr02 40

Level 1 Static Const.For Device EquationsVfb = -TPG*EG/2 -Vt*ln(NSUB/ni) -

q*NSS*TOX/eOxVTO = as given, or

= Vfb + PHI + GAMMA*sqrt(PHI)KP = as given, or = UO*eOx/TOXCAPS are spice pars., technological

constants are lower case

L27 23Apr02 41

Level 1 Static Const.For Device Equations = KP*[W/(L-2*LD)] = 2*K, K not spiceGAMMA = as given, or = TOX*sqrt(2*eSi*q*NSUB)/eOx2*phiP = PHI = as given, or = 2*Vt*ln(NSUB/ni)ISD = as given, or = JS*ADISS = as given, or = JS*AS

L27 23Apr02 42

Level 1 Static Device Equationsvgs < VTH, ids = 0VTH < vds + VTH < vgs, id = KP*[W/(L-2*LD)]*[vgs-VTH-vds/2] *vds*(1 + LAMBDA*vds)VTH < vgs < vds + VTH, id = KP*[W/(L-2*LD)]*(vgs - VTH)^2 *(1 + LAMBDA*vds)

L27 23Apr02 43

Level 2 StaticDevice EquationsAccounts for variation of channel

potential for 0 < y < LFor vds < vds,sat = vgs - Vfb - PHI + 2*[1-sqrt(1+2(vgs-Vfb-vbs)/2]id,ohmic = [/(1-LAMBDA*vds)] *[vgs - Vfb - PHI - vds/2]*vds -2[vds+PHI-vbs)1.5-(PHI-vbs)1.5]/3

L27 23Apr02 44

Level 2 StaticDevice Eqs. (cont.)For vds > vds,sat

id = id,sat/(1-LAMBDA*vds)

where id,sat = id,ohmic(vds,sat)

L27 23Apr02 45

Level 2 StaticDevice Eqs. (cont.)Mobility variationKP’ = KP*[(esi/eox)*UCRIT*TOX /(vgs-VTH-UTRA*vds)]UEXP

This replaces KP in all other formulae.

L27 23Apr02 46

References• CARM = Circuit Analysis Reference Manual,

MicroSim Corporation, Irvine, CA, 1995.• M&A = Semiconductor Device Modeling with SPICE,

2nd ed., by Paolo Antognetti and Giuseppe Massobrio, McGraw-Hill, New York, 1993.

• M&K = Device Electronics for Integrated Circuits, 2nd ed., by Richard S. Muller and Theodore I. Kamins, John Wiley and Sons, New York, 1986.

• Semiconductor Physics and Devices, by Donald A. Neamen, Irwin, Chicago, 1997