1

EE130/230A Discussion 15

Peng Zheng

Early Voltage, VAOutput resistance:

C

A

EC

C

I

V

V

Ir

1

0

A large VA (i.e. a large ro ) is desirable

IB3

IC

VEC0

IB2

IB1

VA

JC

B

B

JCC

C

BC

nCC

CCA C

WqN

qN

C

W

I

I

dV

dx

dW

dI

I

g

IV

0

Punch-Through

E-B and E-B depletion regions in the base touch W = 0

As |VCB| increases, the potential barrier to hole injection decreases and hence IC increases

EE130/230A Fall 2013 Lecture 27, Slide 3 R. F. Pierret, Semiconductor Device Fundamentals, Figs. 11.7-11.8

Gummel Plot and bdc vs. IC

bdc

From top to bottom:VBC = 2V, 1V, 0V

bdc

EE130/230A Fall 2013 Lecture 27, Slide 4 C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figures 8-8 & 8-9

Gummel NumbersFor a uniformly doped base with negligible band-gap narrowing, the base Gummel number is

B

BB D

WNG

(total integrated “dose” (#/cm2) of majority carriers in the base, divided by DB)

E

BWW

NN

DD

nGG

EE

B

B

E

Bi

Ein

1

1

1

1

2

2Emitter efficiency

11 /2

/2

kTqV

B

ikTqV

B

BiC

EBEB eG

qAne

WN

DqAnI

GE is the emitter Gummel numberEE130/230A Fall 2013 Lecture 27, Slide 5

dxxD

xN

n

nG

B

BW

Bi

iB )(

)(0 2

2

B

E

LW

LW

NN

DD

n

dc G

G

BEE

B

B

E

Bi

Ein

2

21

2

2

1Notice that

In practice, NB and NE are not uniform, i.e. they are functions of x

The more general formulas for the Gummel numbers are

dxxD

xN

n

nG

E

EW

Ei

iE )(

)(0 2

2

EE130/230A Fall 2013 Lecture 27, Slide 6

Charge Control Model

B

BB

B Qi

dt

dQ

Wx

BB tptxp 1),0(),(

WB

BB

tpqAWdxtxpqAQ

0 2

),0(),(

A PNP BJT biased in the forward-active mode has excessminority-carrier charge QB stored in the quasi-neutral base:

In steady state,B

BB

B Qi

dt

dQ

0

EE130/230A Fall 2013 Lecture 27, Slide 7

Base Transit Time, tt

2

),0( tpqAWQ B

B

Bt D

W

2

2

• time required for minority carriers to diffuse across the base • sets the switching speed limit of the transistor

t

BBBC

BB

Wx

BBC

Q

W

QDi

W

tpqAD

x

txpqADi

2

2

),0(),(

EE130/230A Fall 2013 Lecture 27, Slide 8

Small-Signal Model

Transconductance:

vber gmvbe

C

E

B

E

C

+

Common-emitter configuration,forward-active mode:

kTqVFFC

BEeII /0

qkT

IeI

dV

d

dV

dIg CkTqV

FFBEBE

Cm

BE

//

0

“hybrid pi” BJT small signal model:

EE130/230A Fall 2013 Lecture 28, Slide 9

R. F. Pierret, Semiconductor Device Fundamentals, Fig.12.1(a)

Small-Signal Model (cont.)

, mFBE

CFBED

C

FF

gdV

IdC

I

Q

BE

F

dV

dQC BED,

BEdep

s

W

AC

,BEJ,

m

dc

dc

m

BE

C

dcBE

B

gr

g

dV

dI

dV

dI

r

11

BEDBEDBEJ CCCC ,,,

where QF is the magnitude of minority-carrier charge stored in the base and emitter regions

forward transit time

EE130/230A Fall 2013 Lecture 28, Slide 10

Summary: BJT Small Signal Model

vber gmvbe

C

E

B

E

C

+

Hybrid pi model for the common-emitter configuration, forward-active mode:

m

dc

gr

mFBEJ gCC ,

qkT

Ig C

m /

EE130/230A Fall 2013 Lecture 28, Slide 11

12

Thanks very much for your continuous support throughout the semester.

Good luck to the final exam!