Mextram 504 BJT model

F. Yuan

Advisor ： Prof. C. W. LiuGraduate Institute of Electronics Engineering and

Department of Electrical Engineering,

National Taiwan University, Taipei, Taiwan

Outline Charge modeling Collector current Base current series resistance, epilayer resistance Avalanche multiplication Extrinsic region AC small-signal model Noise and temperature effect

Depletion charge (Qte,Qtc)

Set Q=0 at V=0 Change function to

a smooth one to prevent the value become infinite at V=Vd

22

2

1

0

)1(

)1()1(

11

)1()1(

)1(11

)1(

)1(

)1(

)1(

12

12

12

12

12

12

E

E

E

EB

E

E

p

dE

EB

dE

EBp

E

dEjejete

p

dE

EB

E

dEjejetete

p

dE

EB

jeje

Ste

p

dE

EB

jejete

KV

VK

Kp

VCKXCQ

Vp

VCXCdVCQ

V

CXCC

V

CXCC

Base diffusion charge (QBE,QBC)

QBE+QBC=all diffusion charge in base

BB

W

pB WNdxpQB

0

0

Injected , so we caculate injected e- Define base charge at zero bias

pn

01

010'

'

0

2

1

2

1)0(

2

1

2

)0()(

BBBC

BBBB

B

W

BE

QqnQ

QqnWNN

n

Wn

dxxnQB

Assumed linear

Main current (IN)

ef

tC

er

tE

B

tcteB

B

BCBEtcteB

B

W

B

B

VVSN

VVEW

ieBnB

pC

V

V

V

V

Q

QQQq

Q

QQQQQ

Q

dxxp

q

qeeII

eeA

dxnD

p

qI

B

T

CB

T

EB

T

BC

T

BE

B

1

)(

1)(

)(

0

01

0

0

0

0

02

2212

q1=1 means no early effect

Total base charge (qB) Early effect (base width modulation)

Qte,Qtc

High level injection

QBE,QBC

Base current (IB1,IB2)

IB1 is ideal forward base current

IB2 is non-ideal forward base current

(2kT current at low bias) S means sidewall

2,)1(

)1(

)1()1(

12

11

1

12

2

1

11

LfVm

BfB

V

f

SB

S

V

f

SBB

meII

eI

XII

eI

XII

TLf

EB

T

EB

B

T

EB

SiGe HBT qB is modified by the bandgap difference of the

base region Only considered the linear graded Ge profile If there are a lot of defects in SiGe base, there is

neutral base recombination current (1kT current)

)1)(2()1)(1()1(

1

1

221212

11

1

1

ef

tCVVrec

Vrec

f

SBB

V

dE

V

dE

V

V

V

dE

V

V

IB

ef

tC

er

tE

V

VeeXeX

IXII

e

eeq

V

V

V

Vq

T

CB

T

EB

T

EB

T

g

T

g

ef

tC

T

g

er

tE

Diffusion charge (QE, Qepi) Emitter diffusion charge QE

Collector epilayer diffusion charge Qepi

11

0

1

00 112

m

ss

EEQ

m

sE

VmEE

Diffusion

I

I

Im

Q

dI

dQ

I

IQeQQ

dI

dQ

E

T

EB

)2(2

)1(

(min),

0

11

12

wepi

i

Cv

Tepiepi

VmS

m

k

SEE

EQk

ppW

x

R

VQ

eII

IQ

LetIIWhen

T

EB

E

Base capacitance Base current is injected from side, the

voltage on B1 and B2 may be different We must compensate the charge

)(5

12121

21

EBEtEBBBB

BB

CCCQ

VV

CVQ

Base resistance DC crowding effect

b

BBV

b

TBB

VB

B

Bvb

bBB

Re

R

VI

eI

q

RR

RRR

T

BB

BE

C

3)1(

3

221

21

21

B1

B2

RBvRBc

B

Collector resistance Buried layer to collector electrode resistance

is constant RCC

Epilayer resistance is a variable

Collector resistance When IC large, RC ： small to high to small

emsatepihc AvqNI

Collector resistance Kull, TED vol.32, no.6, p1103, 1985

2

141

2

1

2

141

2

1

1

1ln22

),(

12

22

1222

21

21

0

00

T

dCCB

T

dCCB

V

V

w

V

V

wwTC

CBCBCv

CCCCC

ep

ep

p

pppVE

fR

EI

.

1

0

0

.

0

0

constJ

xv

dx

d

J

Npn

constN

n

n

sat

n

nn

p

p

epi

epi

Collector resistance

hcCvCBdC

epi

ihcCvCBdC

epi

iCv

CBdCCC

w

ww

CvCC

T

epi

i

IRV

Wx

ISCRV

Wx

SCR

VI

pp

pppp

RI

V

W

x

12

12

12

21

21

)1(

)1(

2

12

2

0

00

Jeroen, SSC vol.36, no.9, p1390, 2001

Also considered the high current base push-out (Kirk effect)

Velocity saturation Final equation is

RF performance fT roll-off at high IC, IC1C2 is the key

When IC get large enough, base push-out occurs, increase and makes fT roll-off

Mextram model based on more physical parameters

ceBCBCBEC

FT

rrCCCqI

kT

f

21

F

Avalanche multiplication Weak avalanche effect Valid only for IC1C2 < Ihc Kloosterman, p172, BCTM 2000

)1(

0

)(

21

21

1)1()(

d

M

n

M

n

tC n

x

E

B

E

B

Mn

nCCavl

MM

WxE

B

nCCavl

eeEB

AII

xEx

ExE

dxeAII

Extrinsic region Base-SIC ： intrinsic Base-epilayer-buried layer ： extrinsic Base-(p-poly)-buried layer ： external

Reverse base current (Iex,IB3)

Iex is ideal reverse base current

IB3 is non-ideal reverse base current

(2kT current at low bias) Xext is partitioning factor

r

T

CB

r

T

CB

r

T

rL

T

CB

T

CB

T

EB

LCBV

Br

LCBV

Br

B

L

V

V

V

V

BrB

SCBBexkri

extex

VS

fBB

VeI

VeII

V

ee

eII

InIXI

eIXII

11

11

11

11

11

11

11

12

,

,

2,1

))(2

1(

1)1(

)1(1

)1(

2

3

22

3

11

Extrinsic region

External reverse base current, XIex

Extrinsic depletion charge, Qtex

External depletion charge, XQtex

Extrinsic diffusion charge, Qex

External diffusion charge, XQex

Parasitic PNP Base-Collector-Substrate ： parasitic PNP Only for it’s main current

smalliseI

bigise

I

I

I

I

eI

I

eII

CBV

ss

CBV

kS

S

ss

sub

V

kS

S

Vss

sub

T

CB

T

CB

T

CB

T

CB

11

11

11

11

11

11

,)1(

,

411

)1(2

2

Others Collector-Substrate depletion capacitance Reverse substrate current Constant B-E, B-C overlap capacitance

00

)1(1

BCBE

ts

VSSsf

CC

C

eII T

SC

Small-signal equivalent circuit

Small-signal equivalent circuit x ： VB2E1

y ： VB2C2

z ： VB2C1

z

Ig

y

Ig

x

Ig

z

Ig

y

Ig

x

Ig

z

Ig

y

Ig

x

Ig

z

Ig

y

Ig

x

Ig

BCz

BCy

BCx

BEz

BEy

BEx

CCzR

CCyR

CCxR

Nz

Ny

Nx

CvCvCv

,,,

,,,

,,,212121

dzggdyggdxggdzgdygdxg

III

III

II

zzRyyRxxRzyx

CCBCN

CCBCN

avlBC

CvCvCv ,,,,,,

21

21

Small-signal equivalent circuit x ： VB2E1

y ： VB2C2

z ： VB2C1 yyyR

zzRz

x

yyyR

xxRx

z

ggg

ggg

z

y

dz

dy

ggg

ggg

x

y

dx

dy

Cv

Cv

Cv

Cv

,,

,,

,,

,,

dz

dygg

dx

dygg

z

I

x

I

x

z

z

I

x

x

x

I

x

Ig

yRzRyRxR

x

CC

z

CC

vx

CC

vz

CC

v

CCm

CvCvCvCv

ECECEC

,,,,

2121

11

21

11

21

11

21

Small-signal equivalent circuit x ： VB2E1

y ： VB2C2

z ： VB2C1

dz

dygg

z

I

zx

I

v

Ig

dz

dy

dx

dygggggg

z

II

x

II

x

IIg

yRzR

x

CC

x

CC

xEC

CCout

yyzzxx

x

BCBE

z

BCBE

v

BCBE

CvCv

EC

,,

,,,,,,

2121

11

21

11

)(

Small-signal equivalent circuit x ： VB2E1

y ： VB2C2

z ： VB2C1

dz

dyCCCC

dx

dyCCCCC

dz

dygggg

z

II

v

IIg

yBCyBEzBCBC

yBCyBExBCxBEBE

yyzz

x

BCBE

xEC

BCBE

)(

)(

,,,

,,,,

,,,,

11

Small-signal equivalent circuit x ： VB2E1

y ： VB2C2

z ： VB2C1

Can get more precise parameters

Extrinsic added

BCexBCexBCyBCyBEzBCBC

BEyBCyBExBCSBExBEBE

bvBcTB

exexyyzz

m

yRzRm

yyzxzxS

XCCCdz

dyCCCC

Cdx

dyCCCCCC

rRr

Xggdz

dyggggg

g

g

dz

dy

dx

dyggg

dz

dy

dx

dygggggggg

CvCv

0,,,

0,,,,

,,,,

,,

,,,,,,

)(

)(

)(

)(

Hybrid-π model Let the equivalent circuit has only One

current source

'

''

'

'

'

'

g

g

gg

ggg

ggg

ggg

m

outout

mm

B2-E1-(C1-E1)=B2-C1

Cutoff frequency fT

CcexBCOBEOexBCexexBCex

zzBCzBEyyBCyBExxBCSBExBE

CC

i

ii

CC

i

i i

totT

CEVCC

T

TT

RXrCCXrXCrC

rCCrCCrCCC

I

vC

I

v

v

Q

constisVI

Q

f

CE

,,,,,,

0

2121

21

.

2

1

Cutoff frequency fT

Noise (for AC) Thermal noise

-- consider variable resistance Shot noise

Flicker noise (1/f noise)

-- non-ideal base current use KfN

kTRf

v4

2

DqIf

i2

2

1,2

bf

IK

f

ib

A

f

f

Temperature

Temperature rules are applied to various parameter

Self-Heating is considered

Comparison to GP fT-IC is more accurate

Mextram parameters are base on more physical way

Noise is considered more accurate because the variable resistance

Linear graded SiGe HBT model in Mextram 504

Weak avalanche breakdown

Still unconsidered B-E junction breakdown High injection current breakdown