EE130 Lecture 25, Slide 1Spring 2007

Lecture #25

OUTLINE

• BJT: Deviations from the Ideal– Base-width modulation, Early voltage– Punch-through– Non-ideal effects at low |VEB|, high |VEB|

• Gummel plot

Reading: Chapter 11.2

Measured BJTCommon-Emitter

Output Characteristics:

EE130 Lecture 25, Slide 2Spring 2007

WNDn

LNDn

I

I

BEiE

EEBiB

LW

LW

NN

DD

n

ndcB

C

BEE

B

B

E

iB

iE

2

2

2

21

1

2

2

Base-Width Modulation

P+ N P

W

W(VBC)x

pB(x)

1/0 kTqV

BEBep

(VCB=0)

0

+ VEB

IE IC

Common-Emitter Configuration, Active Mode Operation

VEC

IC

EE130 Lecture 25, Slide 3Spring 2007

The base-width modulation effect is reduced if we

(a) increase the base width, W, or

(b) increase the base dopant concentration, NB, or

(c) decrease the collector dopant concentration, NC .

Which of the above is the most acceptable action?

EE130 Lecture 25, Slide 4Spring 2007

Output 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

Early Voltage, VA

VA

EE130 Lecture 25, Slide 5Spring 2007

Derivation of Formula for VA

00

g

IV

V

I

dV

dIg C

AA

C

EC

C Output conductance:

for fixed VEBBC

C

EC

CoBCEBEC dV

dI

dV

dIgVVV so

BC

nCC

BC

Co dV

dx

dW

dI

dV

dW

dW

dIg

where xnC is the width of the collector-junction depletion region on the base side

P+ N P

xnC

EE130 Lecture 25, Slide 6Spring 2007

W

Ie

NW

DqAn

dW

dI

eWN

DqAnI

CkTqV

B

BiC

kTqV

B

BiC

EB

EB

1

1

/2

2

/2

B

JC

BC

nC

BC

nCB

BC

nCB

BC

depCJC

qN

C

dV

dx

dV

dxqN

dV

xqNd

dV

dQC

)(

1)1( /)/sinh(

/cosh(

00/

)/sinh(1

0) kTqV

LW

LW

BLD

CLDkTqV

LWBLD

CCB

B

B

B

B

C

CEB

BB

B epnepqAI

JC

B

B

JCC

C

BC

nCC

CCA C

WqN

qNC

WI

I

dVdx

dWdI

I

g

IV

0

EE130 Lecture 25, Slide 7Spring 2007

BJT Breakdown Mechanisms• In the common-emitter configuration, for high output

voltage VCE, the output current IC will increase rapidly due to one of two mechanisms:– punch-through

– avalanche

EE130 Lecture 25, Slide 8Spring 2007

Punch-Through

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

As |VCB| increases, the potential barrier

to hole injection decreases and thereforeIC increases

EE130 Lecture 25, Slide 9Spring 2007

Avalanche Multiplication• Holes are injected into the base [0], then

collected by the B-C junction– Some holes in the B-C depletion region have

enough energy to generate EHP [1]

• The generated electrons are swept into the base [3], then injected into the emitter [4]– Each injected electron results in the injection of

IEp/IEn holes from the emitter into the base [0]

PNP BJT:

For each EHP created in the C-B depletion region by impact ionization,

(IEp/IEn)+1 > dc additional holes flow into the collector

i.e. carrier multiplication in C-B depletion region is internally amplified

mdc

CBCE

VV

/10

0 )1(

where VCB0 = reverse breakdown voltage of the C-B junction

62 m

EE130 Lecture 25, Slide 10Spring 2007

Non-Ideal Effects at Low VEB

• In the ideal transistor analysis, thermal R-G currents in the emitter and collector junctions were neglected.

• Under active-mode operation with small VEB, the thermal recombination current is likely to be a dominant component of the base current low emitter efficiency, hence lower gain

This limits the application of the BJT for amplification at low voltages.

GREnEp

Ep

III

I

EE130 Lecture 25, Slide 11Spring 2007

Non-Ideal Effects at High VEB

• Decrease in F at high IC is caused by:– high-level injection

– series resistance

– current crowding

1/2

kTqV

B

BiC

EBeWN

DqAnI

EE130 Lecture 25, Slide 12Spring 2007

dc

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

0.2 0.4 0.6 0.8 1.0 1.210-12

10-10

10-8

10-6

10-4

10-2

VBE

IB

IC

excess base current due to R-G in depletion region

high level injection in base

Gummel Plot and dc vs. IC

EE130 Lecture 25, Slide 13Spring 2007

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 number

EE130 Lecture 25, Slide 14Spring 2007

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 real BJTs, 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 Lecture 25, Slide 15Spring 2007

• High gain (dc >> 1)

One-sided emitter junction, so emitter efficiency 1• Emitter doped much more heavily than base (NE >> NB)

Narrow base, so base transport factor T 1• Quasi-neutral base width << minority-carrier diffusion length (W

<< LB)

• IC determined only by IB (IC function of VCE,VCB)

One-sided collector junction, so quasi-neutral base width W does not change drastically with changes in VCE (VCB)

• Based doped more heavily than collector (NB > NC)

(W = WB – xnEB – xnCB for PNP BJT)

Summary: BJT Performance Requirements

EE130 Lecture 25, Slide 16Spring 2007

Review: Modes of OperationCommon-emitter output characteristics

(IC vs. VCE)

Why?operation. mode active invertedfor lower is B

Cdc I

Iβ