Chapter 10 BJT Fundamentals

President University Erwin Sitompul SDP 9/1

Lecture 9Semiconductor Device Physics

Dr.-Ing. Erwin SitompulPresident University

http://zitompul.wordpress.com

2 0 1 3


Chapter 10BJT Fundamentals

Semiconductor Device Physics


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 gainFaster circuit speed (+)Larger power dissipation (–)

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


EB E B

CB C B

EC E C

EB CB

V V VV V VV V V

V V

BE B E

BC B C

CE C E

CB EB

V V VV V VV V V

V V

IntroductionChapter 10 BJT Fundamentals

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: . . . . . .


Common-Emitter I–V Characteristics

Cdc

B

100II

Most popular configuration

Saturation ModeIC < IB

Active Mode

In active mode, dc is the common

emitter dc current gain

Circuit ConfigurationsChapter 10 BJT Fundamentals


Mode E-B Junction C-B JunctionSaturation forward bias forward bias

Active/Forward forward bias reverse biasInverted reverse bias forward bias

Cutoff reverse bias reverse bias

Modes of OperationChapter 10 BJT Fundamentals

Common-Emitter Output Characteristics


AE DB ACN N N

CB EBW W

B nEB nCBW W x x

W : quasineutral base width

BJT ElectrostaticsChapter 10 BJT Fundamentals

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


BJT ElectrostaticsChapter 10 BJT Fundamentals

Electrostatic potential, V(x)

Electric field, E(x)

Charge density, ρ(x)


pnp BJT, active mode

BJT DesignChapter 10 BJT Fundamentals

Important features of a good transistor: Injected minority carriers do not recombine in the neutral

base region short base, W << Lp for pnp transistorEmitter 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


EMITTER BASE COLLECTOR

p-type n-type p-type3

1

4

2

CB0i

Base Current (Active Bias)Chapter 10 BJT Fundamentals

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

1. Recombination of injected minority carriers in the base2. Injection of carriers into the emitter3. Reverse saturation current in collector junction4. Recombination in the base-emitter depletion region


Decrease relative to to increase transport factor

Decrease relative to and to increase efficiency

CpT

Ep

II

dc T Common base dc current gain:

Ep Ep

E Ep En

I II I I

IEn

IEp

ICn

ICp

Negligible compared to holes injected

from emitter

15

21 2

BJT Performance Parameters (pnp)Chapter 10 BJT Fundamentals

Emitter Efficiency Base Transport Factor


C dc C B CB0α ( )I I I I

C dc E CB0αI I I

Common emitter dc current gain:dc C

dcdc B1

II

ICB0 :collector current when IE = 0

23

dc CB0C B

dc dc

α1 α 1 α

II I

CB0I

Collector Current (Active Bias)Chapter 10 BJT Fundamentals

The collector current is comprised 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


Chapter 11BJT Static Characteristics

Semiconductor Device Physics


E AE

E N

E n

E N

E0 p02i E

N ND D

L Ln n

n N

B DB

B P

B p

B P

B0 n02i B

N ND D

L Lp p

n N

C AC

C N

C n

C N

C0 p02i C

N ND D

L Ln n

n N

Minority carrier

constants

Notation (pnp BJT)Chapter 11 BJT Static Characteristics


2E E

E 2E

0 d n nDdx

EB

E

E E0

( ) 0( 0) ( 1)qV kT

n xn x n e

Emitter RegionChapter 11 BJT Static Characteristics

Diffusion equation:

Boundary conditions:


2B B

B 2B

0 d p pDdx

EB

CB

B B0

B B0

(0) ( 1)( ) ( 1)

qV kT

qV kTp p ep W p e

Base RegionChapter 11 BJT Static Characteristics

Diffusion equation:



2C C

C 2C

0 d n nDdx

CB

C

C C0

( ' ) 0( ' 0) ( 1)qV kT

n xn x n e

Collector RegionChapter 11 BJT Static Characteristics

Diffusion equation:



EEn E

0x

d nI qADdx

B

Ep B0x

d pI qADdx

BCp B

x W

d pI qADdx

Cn C

0

C

x

d nI qADdx

E

B

C

( ), ( ),( )

n xp xn x

ICIB

IEE Ep En

C Cp Cn

B E C

I I II I II I I

Ideal Transistor AnalysisChapter 11 BJT Static Characteristics

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


2E E

E 2E

0 d n nDdx

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

EB

E

E E0

( ) 0( 0) ( 1)qV kTn x

n x n e

EB EE E0( ) ( 1)qV kT x Ln x n e e

EEn E

0x

d nI qADdx

Emitter Region SolutionChapter 11 BJT Static Characteristics

Diffusion equation:

General solution:


Solution

EBEE0

E

( 1)qV kTDqA n eL


C CC 1 2( ) x L x Ln x Ae A e

CB CC C0( ) ( 1)qV kT x Ln x n e e

2C C

C 2C

0 d n nDdx

CB

C

C C0

( ) 0( 0) ( 1)qV kTn x

n x n e

CCn C

0x

d nI qAD

dx

Collector Region SolutionChapter 11 BJT Static Characteristics

Diffusion equation:

General solution:


Solution

CBCC0

C

( 1)qV kTDqA n eL


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

2B B

B 2B

0 d n pDdx

EB

CB

B B0

B B0

(0) ( 1)( ) ( 1)

qV kT

qV kTp p ep W p e

B BEB

B B

B BCB

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 ee e

e ep ee e

Base Region SolutionChapter 11 BJT Static Characteristics

Diffusion equation:

General solution:


Solution


sinh( )2

e e

EB

CB

BB B0

B

BB0

B

sinh ( )( ) ( 1)

sinh( )sinh( ) ( 1)sinh( )

qV kT

qV kT

W x Lp x p e

W Lx Lp eW L

as

B BEB

B B

B BCB

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 ee e

e ep ee e


Since

We can write


CBEB

BEp B

0

B BB0

B B B

cosh( ) 1( 1) ( 1)sinh( ) sinh( )

x

qV kTqV kT

d pI qADdx

D W LqA p e eL 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 qADdx

D W LqA p e eL W L W L

sinh( ) cosh( )2 2

d d e e e ed d


Since


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 eL L W L

D p eL 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 eL W L

D D W Ln p eL L W L

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

B E CI I I

Terminal CurrentsChapter 11 BJT Static Characteristics

Since

Then


EB

CB

/B B0

/B0

( ) ( 1) 1

( 1)

qV kT

qV kT

xp x p eWxp eW

Due to VEB

Due to VCB

0 2

0

limsinh( )

lim cosh( ) 12

B B B0 B( ) (0) ( ) (0) xp x p p W pW

Simplified RelationshipsChapter 11 BJT Static Characteristics

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

Using the limit value

We will have


E B

B E E

1

1 D N WD N L

dc 2

E B

B E E B

1

12

D N W WD N L L

T 2

B

1

112WL

dc 2

E B

B E E B

1 ,112

D N W WD N L L

Performance ParametersChapter 11 BJT Static Characteristics

For specific condition of “Active Mode”: emitter junction is forward biased and

collector junction is reverse biasedW << LB, nE0/pB0 NB/NE


Homework 7

Due: Monday, 25.11.2013.

1.(10.17)Consider a silicon pnp bipolar transistor at T = 300 K with uniform dopings of NE = 5×1018 cm–3, NB = 1017 cm–3, and NC = 5×1015 cm–3 . Let DB = 10 cm2/s, xB = 0.7 μm, and assume xB << LB. The transistor is operating in saturation with JP = 165 A/cm2 and VEB = 0.75 V. Determine:(a) VCB, (b) VEC(sat), (c) the number/cm2 of excess minority carrier holes in the base, and (d) the number/cm2 of excess minority carrier electrons in the long collector, take LC = 35 μm.

2.(10.14)Problem 10.4, Pierret’s “Semiconductor Device Fundamentals”.

Chapter 11 BJT Static Characteristics

Chapter 10 BJT Fundamentals

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Transcript of Chapter 10 BJT Fundamentals