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Dr.-Ing. Erwin SitompulPresident University

Lecture 9Semiconductor Device Physics

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Chapter 10BJT Fundamentals

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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

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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: . . . . . .

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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

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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

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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.

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BJT ElectrostaticsChapter 10 BJT Fundamentals

Electrostatic potential, V(x)

Electric field, E(x)

Charge density, ρ(x)

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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

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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

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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

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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

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Chapter 11BJT Static Characteristics

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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

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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:

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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:

Boundary conditions:

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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:

Boundary conditions:

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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

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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:

Boundary conditions:

Solution

EBEE0

E

( 1)qV kTDqA n eL

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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:

Boundary conditions:

Solution

CBCC0

C

( 1)qV kTDqA n eL

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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:

Boundary conditions:

Solution

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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

Base Region SolutionChapter 11 BJT Static Characteristics

Since

We can write

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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

Base Region SolutionChapter 11 BJT Static Characteristics

Since

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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

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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

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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

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Homework 7

Deadline: 21.06.2012, at 08:00.

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