Bjt Description

EEE 531: Semiconductor Device Theory I


Instructor: Dragica Vasileska

Department of Electrical Engineering

Arizona State University

Bipolar Junction Transistor


Outline

1. Introduction

2. IV Characteristics of a BJT

3. Breakdown in BJT

4. Geometry Effects in BJT


1. Introduction

Inventors of the transistor:William Shockley, John Bardeen

and Walter Brattain

Originalpoint-contacttransistor(1947)

First grown transistor (1950)


(A) Terminology and symbols

� Both, pnp and npn transistors can be thought as two very closely spaced pn-junctions.

� The base must be small to allow interaction between the two pn-junctions.

p+ n pE C

B

+ +

VEB VCB

n+ p nE C

B

+ +VBE VBC

PNP - transistor

E

B

C

NPN - transistor

E

B

C


� There are four regions of operation of a BJT transistor (example for a pnp BJT):

� Since it has three leads, there are three possible amplifier types:

VEB

VCB

Saturation region(both junctions forward biased)

Cutoff region(both junctions reverse biased)

Forward active region(emitter-base FB, collector-base RB)

Inverted active region(emitter-base RB, collector-base FB)

B

p+ n pE C

VEB VCB

p

p+

n

C

E

B

VEB

VEC

p+

p

n

E

C

B

VCB

VEC

(a) Common-base (b) Common-emitter (c) Common-collector


(B) Qualitative description of transistor operation

p+ n p� Emitter doping is much larger than

base doping

� Base doping larger than collector doping

� Current components:

� IB1 = current from electrons being back injected into the forward-biased emiter-base junction

� IB2 = current due to electrons that replace the recombined electrons in the base

� IB3 = collector current due to thermally-generated electrons in the collector that go in the base

IEp

IEn

ICp

Icn

IB1

IEn ICn

IB3

{IEp ICp

IB2

321 BBBCEB

CnCpC

EnEpE

IIIIII

III

III

EC

EF

EV


(C) Circuit definitions

Base transport factor T:

Emitter injection efficiency :

Alpha-dc:

Beta-dc:

EpCpT II / Ideally it would be equal to unity

(recombination in the base reduces its value)

E

Ep

EpCp

Ep

I

I

II

I

Approaches unity if emitter doping is

much larger than base doping

T

EnEp

Cp

EnEp

CnCp

E

Cdc

II

I

II

II

I

I

dc

dc

CE

C

B

Cdc

II

I

I

I

1Current gain is large when dc

approaches unity


Collector-reverse saturation current:

Collector current in common-emitter configuration:

Large current gain capability:

Small base current IB forces the E-B junction to be forward biased and inject large number of holes which travel through the base to the collector.

00 BCEdcCnCpCCnBC IIIIIII

dc

BCB

dc

dcCBCBCdcC

IIIIIII

11

00

0ECBdcC III

00 1 BCdcEC II


(D) Types of transistors

� Discrete (double-diffused)

p+np transistor

Emitter Base

Collector

5 m

200 m

� Integrated-circuit

n+pn transistor

6 m

200 m


2. IV-Characteristics of a BJT

(A) General Considerations

� Approximations made for derivation of the ideal IV-characteristics of a BJT:

(1) no recombination in the base quasi-neutral region

(2) no generation-recombination in the E-B and C-B

depletion regions

(3) one-dimensional current flow

(4) no external sources

� Notation:

NAE = NE

Ln = LE

Dn = DE

np0 = nE0

n = E

NDB = NB

Lp = LB

Dp = DB

pn0 = pB0

p = B

NAC = NC

Ln = LC

Dn = DC

np0 = nC0

n = C

p+ n p


� The carrier concentration variation for various regions of operation is shown below:

� Assuming long emitter and collector regions, the solutions of the minority electrons continuity equation in the emitter and collector are of the form:

nE0

nE(0�)

x�0� 0 W 0�

x�

nC(0�)

nC0

E-B C-BpB(0)

pB(W)

saturation

Forwardactive

pB0

Cut-off

nE(x�)

pB(x)

pB(W)

nC(x�)

CTCB

ETEB

LxVV

CC

LxVVEE

eenxn

eenxn

/'/

0

/"/0

1)'(

1)"(


� For the base region, the steady-state solution of the continuity equation for minority holes, of the form:

using the boundary conditions:

is given by:

Note: The presence of the sinh() terms means that recombination in

the base quasi-neutral region is allowed.

022

2

B

BB

L

p

dx

pd

1)(,1)0(/

0/

0 TCBTEB VV

BBVV

BB epWpepp

1/sinh

/sinh

1/sinh

/)(sinh)(

/

0

/0

TCB

TEB

VV

B

BB

VV

B

BBB

eLW

Lxp

eLW

LxWpxp


� Once we have the variation of nE(x�), pB(x) and nC(x�), we can

calculate the corresponding diffusion current components:

� Expressions for various diffusion current components:

x�0� 0 W 0�

x�

E-B C-B

InE(0�)

IpB(0)

IpB(W)

InC(0�)InE(x�) InC(x�)

IpB(x)

IB2=IpB(0)-IpB(W)

IE=InE(0�)+IpB(0) IC=InC(0�)+IpB(W)

Base recombination current

Wx

BBpB

x

BBpB

x

CCnC

x

EEnE

dx

pdAqDWI

dx

pdAqDI

dx

ndAqDI

dx

ndAqDI

)(,)0(

')'0(,

")"0(

0

'0'"0"


� Final results for the emitter, base and collector currents:

1)/sinh(

1)/coth(

1)/sinh(

1)/coth(

1)/coth(

1)/sinh(

1

1)/sinh(

1

1)/coth(

/2

/2

/2

/2

/2

/2

TCB

TEB

TCB

TEB

TCB

TEB

VV

BB

BB

B

CC

Ci

VV

BB

BB

B

EE

EiB

VV

BBB

B

CC

Ci

VV

BBB

BiC

VV

BBB

Bi

VV

BBB

B

EE

EiE

eLW

LWNL

D

NL

DAqn

eLW

LWNL

D

NL

DAqnI

eLWNL

D

NL

DAqn

eLWNL

DAqnI

eLWNL

DAqn

eLWNL

D

NL

DAqnI


� For short-base diodes, for which W/LB<<1, we have:

� Therefore, for short-base diodes, the base current simplifies to:

� As W/LB0 (or B ), the recombination base current IB2 0 .

2)sinh(

1)coth(;)sinh(;

21)cosh(

2x

xx xx

xx

12

12

/2

/2

TCB

TEB

VV

BBB

B

CC

Ci

VV

BBB

B

EE

EiB

eL

W

NL

D

NL

DAqn

eL

W

NL

D

NL

DAqnI

IB1

IB2

-IB3

IB2


(B) Current expressions for different biasing regimes

Forward-active region:

� E-B junction is forward biased, C-B junction is reverse-biased:

)/sinh(

1)/cosh(

)/sinh(

1)/cosh(

)/sinh(

1

)/coth(

2

/2

/2

/2

B

B

BB

B

CC

Ci

VV

B

B

BB

B

EE

EiB

Cp

VV

BBB

BiC

EpEn

VV

BBB

B

EE

EiE

LW

LW

NL

D

NL

DAqn

eLW

LW

NL

D

NL

DAqnI

IeLWNL

DAqnI

IIeLWNL

D

NL

DAqnI

TEB

TEB

TEB

These terms vanish if

there is no recombi-

nation in the base


� Graphical description of various current components:

� The emitter injection efficiency is given by:

p+ n p

{IEp

{IEn

}ICp

ICn

IB1 IB3

IEIC

IB

Recombination in the base

is ignored in this diagram.

EB

BEE

EB

BEE

baseshort

BEBB

BEE

BEBB

BEE

EnEp

Ep

DWN

DNL

DWN

DNL

LWDNL

DNL

LWDNL

DNL

II

I

1)/coth(1

)/coth(


� The base transport factor is given by:

� Common-emitter current gain:

� For a more general case of a non-uniform doping in the base, the

Gummel number is given by:

2

2

21

)/cosh(

1

Bbaseshort

BEp

CpT

L

W

LWI

I

EB

BEE

baseshort

BBEBB

BEE

BEBB

BEE

dcDWN

DNL

LWLWDNL

DNL

LWDNL

DNL

)2/(sinh)/coth(21

)/coth(

2

GB = WNB (Gummel number)

W

BB dxxNG

0

)( Typical values of GB:


Saturation region:

� E-B and C-B junctions are both forward biased:

CEB

CpCnCp

VV

BBB

B

CC

Ci

VV

BBB

BiC

Ep' EpEn

VV

BBB

Bi

VV

BBB

B

EE

EiE

III

IIIeLWNL

D

NL

DAqn

eLWNL

DAqnI

I-IIeLWNL

DAqn

eLWNL

D

NL

DAqnI

TCB

TEB

TCB

TEB

'

/2

/2

/2

/2

)/coth(

)/sinh(

1

)/coth(

)/coth(

3BCn II

Base current much larger

than in forward-active regime


� Graphical description of various current components:

� Important note:

As VCB becomes more positive, the number of holes injected from

the collector into the base and afterwards in the emitter increases.

The collector hole flux is opposite to the flux of holes arriving from

the emitter, and the two currents subtract, which leads to a reduction of

the emitter as well as the collector currents.

p+ n p

{IEp

{IEn

}ICp

ICn

IB1IB3

IEIC

IB



} ICp�IEp�{


Cutoff region:

� E-B and C-B junctions are both reverse biased. For short-base diode with no recombination in the base, this leads to:

CC

Ci

CC

C

EE

EiCEB

CnCC

CiCEn

EE

EiE

NL

DAqn

NL

D

NL

DAqnIII

INL

DAqnII

NL

DAqnI

22

22,

p+ n p

IB1 IB3

IEIC

IB



IEn ICn


(C) Form of the input and output characteristics

Common-base configuration:

Common-emitter configuration:

IE

VEB

VCB=0

VCB<-3VT

IC

VBC

IE0

IE=0

saturation

Forward active

cutoff

IBC0

IB

VEB

VEC > 3VT

VEC= 0

VEC

IB0

IB=0

saturation

Forward active

cutoff

IEC0

ICVCB= 0


� Note on the collector-base reverse saturation current:

ICn

VBC>0

IB=IBC0

C

B

E

VBC

Minority electrons in

the collector that are

within LC from the C-B

junction are collected

by the high electric

field into the base.


� Why is IEC0 much larger than IBC0?

ICn

VEC > 0

IE = IEC0

C

B

E

IB=0

IEn

IEp ICp

Cn

EpdcBCdcEpBCCpCnEC

I

IIIIIII ,1 000

The electrons injected from the collector into the base and

then into the emitter forward bias the E-B junction .

This leads to large hole injection from the emitter into the base and

then into the collector.

In summary, relatively small number of electrons into the emitter

forces injection of large number of holes into the base (transistor

action) which gives IEC0 >> IBC0 .


(D) Ebers-Moll equations

� The simplest large-signal equivalent circuit of an ideal (intrinsic) BJT consists of two diodes and two current-controlled current sources:

� Using the results for IE and IC, we can calculate various coefficient:

� The reciprocity relation for a two-port network requires that:

IF IR

RIR FIF

IE IC

IB

1

1

/

0

/0

TCB

TEB

VV

RR

VVFF

eII

eII

11

11

/

0/

0

/

0/

0

TCBTEB

TCBTEB

VV

RVV

FFC

VV

RRVV

FE

eIeII

eIeII

00 RRFF II


(E) Early effect

� In deriving the IV-characteristics of a BJT, we have assumed that dc, dc, IBC0 and IEC0 to be constant and independent of the applied voltage.

� If we consider a BJT in the forward active mode, when the reverse bias of the C-B junction increases, the width of the C-B depletion region increases, which makes the width of the base quasi-neutral region Weff

to decrease:

� The common-emitter current gain, taking into account the effective width of the base quasi-neutral region (assuming =1) is then given by:

� The common-emitter current gain can be approximated with:

dcbdebeff xxWW ical)(metallurg

22

11 BeffTdc LW

2

21

eff

B

dc

dcdc

W

L


� Graphical illustration of the Early (base-width modulation) effect:

� If we approximate the collector current with the hole current:

we find:

� Since WB/ VBC <0, we have that IC/ VBC > 0, i.e. IC increases.

E C

B

Weff

Weff�

TEBTEB

B

VV

BB

Bi

VV

W

oB

BiCpC e

WG

DAqne

dxxN

DAqnII

/2/2

)()(

A

C

BC

B

B

BC

BC

C

V

I

V

W

G

WnI

V

I

)(

Early voltage


� Empirically, it is found that a linear interpolation of the collector current dependence on VEC is adequate in most cases:

where the Early voltage is given by:

� Graphical illustration of the Early effect:

AECECBdcAECECBdcC VVIIVVIII /1/1 00

0

s

BBAA

k

WqGkV

VEC

IC

-|VA|

Another effect contributing

to the slope is due to generation

currents in the C-B junction:

Generated holes drift to the

collector.

Generated electrons drift into

the base and then the emitter,

thus forcing much larger hole

injection (transistor action).


(F) Deviations from the ideal model:

There are several factors that lead to deviation from the ideal model predictions:

Breakdown effects

Geometry effects

Generation-recombination in the depletion regions

3. Breakdown in BJT�s

� There are two important mechanisms for breakdown in BJT�s:

(1) punch-through breakdown

(2) avalanche breakdown (similar to the one in pn-junctions)


� The punch-through breakdown occurs when the reverse-bias C-B voltage is so large that the C-B and the E-B depletion regions merge.

� The emitter-base barrier height for holes is affected by VBC , i.e. small increase in VBC is needed for large increase in IC .

� The mechanism of avalanche breakdown in BJT�s depend on the circuit configuration (common-emitter or common-base configuration).

p+ n p

VBC increasing

Note: Punch-through voltage is

usually much larger than the

avalanche breakdown voltage.


� For a common-base configuration, the avalanche breakdown in the C-B junction (open emitter) BVBC is obtained via the maximum (breakdown) electric field FBR (~300 kV/cm for Si and 400 kV/cm for GaAs):

� The increase in current for voltages higher than BVBC is reflected via the multiplication factor in the current expres-sion. It equals one under normal operating conditions, and exceeds unity when avalanche breakdown occurs.

� When the emitter is open, the multiplication factor for the C-B junction is:

C

BRs

CB

BRsBC

qN

Fk

NNq

FkBV

2

11

2

20

20

1

1

bm

BC

BCCB

BV

VM


� For a common-emitter configuration, the collector-emitter breakdown voltage BVEC is related to BVBC :

bmdcBCEC

BCdc

dcBCEC

ECECBCdc

BCBCCBCEdcBCC

CE

BVBVM

MM

IMM

IMIIIMI

II

/1

00

0

11

)1(

1

Open base configuration

Much smaller than BVBC

due to transistor action.

Mu

ltip

licati

on f

acto

r

Reverse voltage

10

20

30

40

50

20 40

MEC MBC


VEC

IC

BVEC0

Common-emitter output

characteristics

IC

VBCBVBC0

Common-base output

characteristics


4. Geometry effects

� The geometry effects include:

(1) Bulk and contact resistance effects

(2) Current crowding effect

� Base current flows in the direction parallel to the E-B junction, which gives rise to base spreading resistance.

� When VBB� is much larger than VT, most of the emitter current is concentrated near the edges of the E-B junction.

p+ p+n+

p

n

n+

collector

B BE

Emitter contacts

Base contacts


Generation-recombination in the depletion region

VEB

ln(IC)

ln(IB)

� Reverse-biased C-B junction adds a generation current to IC.

� Forward-biased E-B junction has recombination current. IC is not affected by the recombina-tion in the E-B junction.

IC

IB

dc

g-r current

Current crowding, high-level injection series resistence

ln(IC)

dc

g-r

Currentcrowding or rC

dc modification:

� Low-current levels recombination current

� large current levels high-level injection and series resistance

Documents

Bjt Description