Semiconductor Device Physics - Alexandria...

1

Lecture 9

Semiconductor Device Physics

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2 0 1 3

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Chapter 10BJT Fundamentals


3

Bipolar Junction Transistors (BJTs)

Chapter 10 BJT Fundamentals

Over the past decades, the higher layout density and low-power advantage of CMOS (Complementary Metal–Oxide–Semiconductor) has eroded away the BJT’s dominance in integrated-circuit products.

Higher circuit density better system performance

BJTs are still preferred in some digital-circuit and analog-circuit applications because of their high speed and superior gain

Faster circuit speed (+)

Larger power dissipation (–)

• Transistor: current flowing between two terminals is controlled by a third terminal

4

Introduction

EB E B

CB C B

EC E C

EB CB

V V V

V V V

V V V

V V

BE B E

BC B C

CE C E

CB EB

V V V

V V V

V V V

V V


There are two types of BJT: pnp and npn.

The convention used in the textbook does not follow IEEE convention, where currents flowing into a terminal is defined as positive.

We will follow the normal convention: . . . . . .

5

Common-Emitter

I–V Characteristics

Circuit Configurations

Most popular configuration

Saturation Mode

IC < bIB

Active Mode

In active mode, bdc is the common

emitter dc current gain


Cdc

B

100I

Ib

6

Mode E-B Junction C-B Junction

Saturation forward bias forward bias

Active/Forward forward bias reverse bias

Inverted reverse bias forward bias

Cutoff reverse bias reverse bias

Modes of Operation


Common-Emitter Output Characteristics

7

BJT Electrostatics

AE DB ACN N N

CB EBW W

B nEB nCBW W x x

W : quasineutral base width


Under equilibrium and normal operating conditions, the BJT may be viewed electrostatically as two independent pnjunctions.

8

BJT Electrostatics


Electrostatic potential, V(x)

Electric field, E(x)

Charge density, ρ(x)

9

pnp BJT, active mode

BJT Design


Important features of a good transistor:

Injected minority carriers do not recombine in the neutral base region short base, W << Lp for pnp transistor

Emitter current is comprised almost entirely of carriers injected into the base rather than carriers injected into the emitter the emitter must be doped heavier than the base

10

EMITTER BASE COLLECTOR

p-type n-type p-type3

1

4

2

Base Current (Active Bias)

CB0i


The base current consists of majority carriers (electrons) supplied for:

1. Recombination of injected minority carriers in the base

2. Injection of carriers into the emitter

3. Reverse saturation current in collector junction

4. Recombination in the base-emitter depletion region

11

Decrease relative to

to increase transport factor

Decrease relative to

and to increase efficiency

Cp

T

Ep

I

I

dc T Common base dc current gain:

BJT Performance Parameters (pnp)

Ep Ep

E Ep En

I I

I I I

IEn

IEp

ICn

ICp

Negligible compared to holes injected

from emitter

1

5

2

1 2


Emitter Efficiency Base Transport Factor

12

C dc C B CB0α ( )I I I I

C dc E CB0αI I I

Common emitter dc current gain:

dc Cdc

dc B1

I

I

b

ICB0 :collector current when IE = 0

2

3

dc CB0C B

dc dc

α

1 α 1 α

II I

Collector Current (Active Bias)

CB0I


The collector current is composed of:

Holes injected from emitter, which do not recombine in the base

Reverse saturation current of collector junction

C dc B CE0I β I I

13

Chapter 11BJT Static Characteristics


14

Notation (pnp BJT)

E AE

E N

E n

E N

E0 p0

2

i E

N N

D D

L L

n n

n N

B DB

B P

B p

B P

B0 n02

i B

N N

D D

L L

p p

n N

C AC

C N

C n

C N

C0 p0

2

i C

N N

D D

L L

n n

n N

Minority carrier

constants

Chapter 11 BJT Static Characteristics

15

2

E EE 2

E

0d n n

Ddx

EB

E

E E0

( ) 0

( 0) ( 1)qV kT

n x

n x n e

Emitter Region


Diffusion equation:

Boundary conditions:

16

2

B BB 2

B

0d p p

Ddx

EB

CB

B B0

B B0

(0) ( 1)

( ) ( 1)

qV kT

qV kT

p p e

p W p e

Base Region


Diffusion equation:


17

2

C CC 2

C

0d n n

Ddx

CB

C

C C0

( ' ) 0

( ' 0) ( 1)qV kT

n x

n x n e

Collector Region


Diffusion equation:


18

EEn E

0x

d nI qAD

dx

BEp B

0x

d pI qAD

dx

BCp B

x W

d pI qAD

dx

Cn C

0

C

x

d nI qAD

dx

E

B

C

( ),

( ),

( )

n x

p x

n x

IC

IB

IE

E Ep En

C Cp Cn

B E C

I I I

I I I

I I I

Ideal Transistor Analysis


Solve the minority-carrier diffusion equation in each quasi-neutral region to obtain excess minority-carrier profilesEach region has different set of boundary conditions

Evaluate minority-carrier diffusion currents at edges of depletion regions

Add hole and electron components together terminal currents is obtained

19

2

E EE 2

E

0d n n

Ddx

E E

E 1 2( ) x L x Ln x Ae A e

EB

E

E E0

( ) 0

( 0) ( 1)qV kT

n x

n x n e

EB E

E E0( ) ( 1)qV kT x Ln x n e e

EEn E

0x

d nI qAD

dx

Emitter Region Solution


Diffusion equation:

General solution:


Solution

EBEE0

E

( 1)qV kTDqA n e

L

20

C C

C 1 2( )x L x L

n x Ae A e

CB C

C C0( ) ( 1)qV kT x L

n x n e e

2

C CC 2

C

0d n n

Ddx

CB

C

C C0

( ) 0

( 0) ( 1)qV kT

n x

n x n e

CCn C

0x

d nI qAD

dx

Collector Region Solution


Diffusion equation:

General solution:


Solution

CBCC0

C

( 1)qV kTD

qA n eL

21

B B

B 1 2( ) x L x Lp x Ae A e

2

B BB 2

B

0d n p

Ddx

EB

CB

B B0

B B0

(0) ( 1)

( ) ( 1)

qV kT

qV kT

p p e

p W p e

B B

EB

B B

B B

CB

B B

( ) ( )

B B0

B0

( ) ( 1)

( 1)

W x L W x LqV kT

W L W L

x L x LqV kT

W L W L

e ep x p e

e e

e ep e

e e

Base Region Solution


Diffusion equation:

General solution:


Solution

22

sinh( )2

e e

EB

CB

B

B B0

B

BB0

B

sinh ( )( ) ( 1)

sinh( )

sinh( ) ( 1)

sinh( )

qV kT

qV kT

W x Lp x p e

W L

x Lp e

W L

as

B B

EB

B B

B B

CB

B B

( ) ( )

B B0

B0

( ) ( 1)

( 1)

W x L W x LqV kT

W L W L

x L x LqV kT

W L W L

e ep x p e

e e

e ep e

e e



Since

We can write

23

CBEB

BEp B

0

B BB0

B B B

cosh( ) 1( 1) ( 1)

sinh( ) sinh( )

x

qV kTqV kT

d pI qAD

dx

D W LqA p e e

L W L W L

CBEB

BCp B

B BB0

B B B

cosh( )1( 1) ( 1)

sinh( ) sinh( )

x W

qV kTqV kT

d pI qAD

dx

D W LqA p e e

L W L W L

sinh( ) cosh( )2 2

d d e e e e

d d



Since

24

EB

CB

E B BE E0 B0

E B B

BB0

B B

cosh( )( 1)

sinh( )

1 ( 1)

sinh( )

qV kT

qV kT

D D W LI qA n p e

L L W L

Dp e

L W L

EB

CB

BC B0

B B

C B BC0 B0

C B B

1( 1)

sinh

cosh( ) ( 1)

sinh( )

qV kT

qV kT

DI qA p e

L W L

D D W Ln p e

L L W L

E En Ep ,I I I C Cn CpI I I

B E CI I I

Terminal Currents


Since

Then

25

EB

CB

/

B B0

/

B0

( ) ( 1) 1

( 1)

qV kT

qV kT

xp x p e

W

xp e

W

Due to VEB

Due to VCB

Simplified Relationships

02

0

limsinh( )

limcosh( ) 12

B B B B( ) (0) ( ) (0)x

p x p p W pW


To achieve high current gain, a typical BJT will be constructed so that W << LB.

Using the limit value

We will have

ΔpB(0)

ΔpB(W)

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E B

B E E

1

1D N W

D N L

dc 2

E B

B E E B

1

1

2

D N W W

D N L L

b

T 2

B

1

11

2

W

L

dc 2

E B

B E E B

1,

11

2

D N W W

D N L L

Performance Parameters


For specific condition of

“Active Mode”: emitter junction is forward biased and collector junction is reverse biased

W << LB, nE0/pB0 NB/NE

27

Ebers-Moll BJT Equations

EB

CB

E B BE E0 B0

E B B

BB0

B B

cosh( )( 1)

sinh( )

1 ( 1)

sinh( )

qV kT

qV kT

D D W LI qA n p e

L L W L

Dp e

L W L

EB

CB

BC B0

B B

C B BC0 B0

C B B

1( 1)

sinh

cosh( ) ( 1)

sinh( )

qV kT

qV kT

DI qA p e

L W L

D D W Ln p e

L L W L

IF0

IR0

αFIF0=

αRIR0

IF0, IR0: Emitter and Collector

Diode Saturation CurrentsαF and αR: Forward

and Reverse Gains

28

Ebers-Moll BJT Model

• Rewriting IE and IC equations yields:

• Those equations can be represented by the

Ebers-Moll BJT model shown below:

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