Lecture 25

Lecture 25

OUTLINE

The BJT (cont’d) • Ideal transistor analysis• Narrow base and narrow emitter• Ebers-Moll model• Base-width modulation

Reading: Pierret 11.1-11.2; Hu 8.2-8.6

Notation (PNP BJT)

NE NAE

DE DN

E n

LE LN

nE0 np0 = ni2/NE

NB NDB

DB DP

B p

LB LP

pB0 pn0 ni

2/NB

NC NAC

DC DN

C n

LC LN

nC0 np0 ni2/NC

EE130/230M Spring 2013 Lecture 25, Slide 2

“Game Plan” for I-V Derivation• Solve the minority-carrier diffusion equation in each quasi-neutral

region to obtain excess minority-carrier profiles– different set of boundary conditions for each region

• Find minority-carrier diffusion currents at depletion region edges

• Add hole & electron components together terminal currents

0""

xdx

ndEEn

EqADI0

xdx

pdBEp

BqADI

Wxdxpd

BCpBqADI

0''

xdx

ndCCn

CqADI


Emitter Region Analysis• Diffusion equation:

• General solution:

• Boundary conditions:

• Solution:

E

EE n

dx

ndED

2

2

"0

EE LxLxE eAeAxn /"

2/"

1)"(

)1()0"(

0)"(/

0

kTqV

EE

E

EBenxn

xn

EEB LxkTqVEE eenxn /"/

0 )1()"(

)1( /00""

kTqVEL

D

xdxnd

EEnEB

E

EE enqAqADI


Collector Region Analysis

CC LxLxC eAeAxn /'

2/'

1)'(

CCB LxkTqVCC eenxn /'/

0 )1()'(

C

CC n

dx

ndCD

2

2

'0

)1()0'(

0)'(/

0

kTqV

CC

C

CBenxn

xn

• Diffusion equation:



• Solution:

)1( /00''

kTqVCL

D

xdxnd

CCnCB

C

CC enqAqADI


Base Region Analysis

BB LxLxB eAeAxp /

2/

1)(

B

BB p

dx

ndBD

2

2

0

)1()(

)1()0(/

0

/0

kTqV

BB

kTqVBB

CB

EB

epWp

epp

BLWBLW

BLxBLxCB

BLWBLW

BLxWBLxWEB

eeeekTqV

B

eeeekTqV

BB

ep

epxp

//

//

//

/)(/)(

)1(

)1()(/

0

/0

• Diffusion equation:



• Solution:


Since

we can write

as

2sinh ee

BLWBLW

BLxBLxCB

BLWBLW

BLxWBLxWEB

eeeekTqV

B

eeeekTqV

BB

ep

epxp

//

//

//

/)(/)(

)1(

)1()(

/0

/0

B

BCB

B

BEB

LW

Lx

kTqVB

LW

LxW

kTqVBB

ep

epxp

sinh

sinh)1(

sinh

sinh)1()(

/0

/0


1)1( /)/sinh(

1/)/sinh(

/cosh(

0

0

)

kTqVLW

kTqVLW

LW

BLD

xdxpd

BEp

CB

B

EB

B

B

B

B

B

eepqA

qADI

1)1( /)/sinh(

/cosh(/)/sinh(

10

)

kTqVLW

LWkTqVLWBL

D

Wxdxpd

BCp

CB

B

BEB

BB

B

B

eepqA

qADI

cosh22

sinh

eeee

d

d

d

d

B

BCB

B

BEB

LW

Lx

kTqVB

LW

LxW

kTqVBB epepxp

sinh

sinh)1(

sinh

sinh)1()( /

0/

0


BJT Terminal Currents• We know:

• Therefore:

1)1( /)/sinh(

1/)/sinh(

/cosh(

0) kTqV

LWkTqV

LW

LW

BLD

EpCB

B

EB

B

B

B

B eepqAI

)1( /0 kTqVEL

DEn

EB

E

E enqAI

1)1( /)/sinh(

/cosh(/)/sinh(

10

) kTqVLW

LWkTqVLWBL

DCp

CB

B

BEB

BB

B eepqAI

)1( /0 kTqV

CLD

CnCB

C

C enqAI

1)1( /)/sinh(

10

/)/sinh(

/cosh(

00) kTqV

LWBLDkTqV

LW

LW

BLD

ELD

ECB

BB

BEB

B

B

B

B

E

E epepnqAI

1)1( /)/sinh(

/cosh(

00/

)/sinh(1

0) kTqV

LW

LW

BLD

CLDkTqV

LWBLD

CCB

B

B

B

B

C

CEB

BB

B epnepqAI


BJT with Narrow Base• In practice, we make W << LB to achieve high current gain.

Then, since

we have:

1for 1cosh

1for sinh

2

2

WxkTqV

B

WxkTqV

BB

CB

EB

ep

epxp

)1(

1)1()(/

0

/0


BJT Performance Parameters

221

221

221

2

2

2

2

2

2

1

1

1

1

1

1

1

BEE

B

B

E

Bi

Ei

BEE

B

B

E

Bi

Ei

B

EE

B

B

E

Bi

Ei

LW

LW

NN

DD

n

dc

LW

LW

NN

DD

n

dc

LWT

LW

NN

DD

n

n

n

n

Assumptions: • emitter junction forward

biased, collector junction reverse biased

• W << LB


BJT with Narrow Emitter

221

221

221

2

2

2

2

2

2

1

1

1

1

1

1

1

BEE

B

B

E

Bi

Ei

BEE

B

B

E

Bi

Ei

B

EE

B

B

E

Bi

Ei

LW

LW

NN

DD

n

dc

LW

LW

NN

DD

n

dc

LWT

LW

NN

DD

n

n

n

n

Replace with WE’ if emitter is narrow


Ebers-Moll Model

The Ebers-Moll model is a large-signal equivalent circuit which describes both the active and saturation regions of BJT operation.•Use this model to calculate IB and IC given VBE and VBC


increasing

(npn) or VEC (pnp)

If only VEB is applied (VCB = 0):

)1(1

)1(

)1(

/0

/0

/0

kTqVFFB

kTqVFFC

kTqVFE

EB

EB

EB

eII

eII

eII

If only VCB is applied (VEB = 0): :

)1)(1(

)1(

)1(

/0

/0

/0

kTqVRRB

kTqVRRE

kTqVRC

CB

CB

CB

eII

eII

eII

aR : reverse common base gainaF : forward common base gain

I C

V CBV EB

I B

E B C

1)1( /)/sinh(

10

/)/sinh(

/cosh(

00) kTqV

LWBLDkTqV

LW

LW

BLD

ELD

ECB

BB

BEB

B

B

B

B

E

E epepnqAI

1)1( /)/sinh(

/cosh(

00/

)/sinh(1

0) kTqV

LW

LW

BLD

CLDkTqV

LWBLD

CCB

B

B

B

B

C

CEB

BB

B epnepqAI

)/sinh(0

00B

B

B

BRRFF LW

p

L

DqAII

Reciprocity relationship:


)1()1( /0

/0 kTqV

RRkTqV

FECBEB eIeII

In the general case, both VEB and VCB are non-zero:

IE: E-B diode current + fraction of C-B diode current that makes it to the E-B junction

)1()1( /0

/0 kTqV

RkTqV

FFCCBEB eIeII

IC: C-B diode current + fraction of E-B diode current that makes it to the C-B junction

Large-signal equivalent circuit for a pnp BJT


Base-Width Modulation

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

P+

N P

W

W(VBC)x

pB(x)

1/0 kTqVB

EBep(VCB=0)

0

+ VEB

IE IC

Common Emitter Configuration, Active Mode Operation

VEC

IC


Ways to Reduce Base-Width Modulation

1. Increase the base width, W

2. Increase the base dopant concentration NB

3. Decrease the collector dopant concentration NC

Which of the above is the most acceptable action?


Early Voltage, VA

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

VA


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


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


• 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


Date post:	31-Dec-2015
Category:	Documents
Upload:	kirby-terrell
View:	11 times
Download:	0 times

Lecture 25

Documents