Chapter 8 Bipolar Junction Transistors

Slide 8-1

Chapter 8 Bipolar Junction Transistors

• Since 1970, the high density and low-power advantage of the MOS technology steadily eroded the BJT’s early dominance.

• BJTs are still preferred in some high-frequency and analog applications because of their high speed and high power output.

Question: What is the meaning of “bipolar” ?

Modern Semiconductor Devices for Integrated Circuits (C. Hu)

Slide 8-2

8.1 Introduction to the BJT

IC is an exponential function of forward VBE and independent of reverse VCB.


N+ P N

emitter collector base

VB E VCB

-

-

Efn

Efp

VCB

VB E

(a)

(b)

(c)

VB E IC

0VCB

B

CE

Ec

Ev

EfnNPN BJT:

N+ P NE C

B

VBE VCB

Emitter Base Collector

Slide 8-3

Common-Emitter Configuration

Question: Why is IB often preferred as a parameter over VBE?


Slide 8-4Modern Semiconductor Devices for Integrated Circuits (C. Hu)

8.2 Collector Current

BBB

B

DL

L

n

dx

nd

22

2

B : base recombination lifetime DB : base minority carrier (electron)

diffusion constant Boundary conditions :

)1()0( /0 kTqV

BBEenn

0)1()( 0/

0 BkTqV

BB nenWn BC

N+ P N

emitter base collector

x0 W

depletion layers

B

Slide 8-5

BB

B

B

kTqVB LW

LxW

enxn BE

/sinh

sinh

)1()( /0

)1( /2

kTqV

B

iB

B

BE

BEC

BEeN

n

W

DqA

dx

dnqDAI

)1( / kTqVSC

BEeII

B

BE

W

BiB

iB

kTqV

B

iEC

dxD

p

n

nG

eG

qnAI

02

2

/2

)1(

It can be shown

GB (s·cm4) is the base Gummel number

8.2 Collector Current

ni2

NB-------e

qVBE kT1–

n n 0-------------

)0(/)( nxn

0 1

1)1()( /

2

kTqV

B

iB BEeN

nxn

x/x/WB

)/1)(1(

)/1)(0()(

/2

BkTqV

B

iB

B

WxeN

n

Wxnxn

BE


Slide 8-6

•At low-level injection, inverse slope is 60 mV/decade

•High-level injection effect :

8.2.1 High Level Injection Effect

0 0.2 0.4 0.6 0.8 1.0 10-12

10-10

10-8

10-6

10-4

10-2

VBE

I C (

A)

IkF

60 mV/decadeAt large VBE, BNpn

pnpn

kTqVi

BEenpn 2/kTqV

iBBEenpG 2/ kTqV

iBEenI 2/

C

When p > NB , inverse slope is 120mV/decade.

kTqVi

kTEEqi

BEFpFn enennp /2/)(2


Slide 8-7

8.3 Base Current

Some holes are injected from the P-type base into the N+ emitter.The holes are provided by the base current, IB .

pE' nB'

WE WB

(b)

emitter base collectorcontact

IE IC

electron flow –

+hole flow

IB

(a) contact


Slide 8-8

E

BE

W

EiE

iE

kTqV

E

iEB

dxD

n

n

nG

eG

qnAI

02

2

/2

)1(

Is a large IB desirable? Why?

8.3 Base Current emitter base collectorcontact

IE IC

electron flow –

+hole flow

IB

(a) contact


)1( /2

kTqV

EE

iEEEB

BEeNW

nDqAI

For a uniform emitter,

Slide 8-9

8.4 Current Gain

B

CF I

I

How can F be maximized?

Common-emitter current gain, F :

Common-base current gain:

F

F

BC

BC

CB

C

E

CF

EFC

II

II

II

I

I

I

II

1/1

/

It can be shown that F

FF

1

2

2

iEBBE

iBEEB

B

EF nNWD

nNWD

G

G


Slide 8-10

EXAMPLE: Current Gain

A BJT has IC = 1 mA and IB = 10 A. What are IE, F and F?

Solution:

9901.0mA 01.1/mA 1/

100μA 10/mA 1/

mA 01.1μA 10mA 1

ECF

BCF

BCE

II

II

III

We can confirm

F

FF

1 F

FF

1

and


Slide 8-11

8.4.1 Emitter Bandgap Narrowing

Emitter bandgap narrowing makes it difficult to raise F by doping the emitter very heavily.


2

2

iE

iB

B

E

n

n

N

N

To raise F, NE is typically very large. Unfortunately, large NE makes

22iiE nn

(heavy doping effect).

kTEVCi

geNNn /2 Since ni is related to Eg , this effect is also known as band-gap narrowing.

kTEiiE

gEenn /22 EgE is negligible for NE < 1018 cm-3, is 50 meV at 1019cm-3, 95 meV at 1020cm-3, and 140 meV at 1021 cm-3.

Slide 8-12

2

2

iE

iB

B

E

n

n

N

N To further elevate F, we can raise niB by

using an epitaxial Si1-Ge base.

With = 0.2, EgB is reduced by 0.1eV and niE2 by

30x.

8.4.2 Narrow-Bandgap Base and Heterojuncion BJT


Slide 8-13

Assume DB = 3DE , WE = 3WB , NB = 1018 cm-3, and niB2 = ni

2. What is F for (a) NE = 1019 cm-3, (b) NE = 1020 cm-3, and (c) NE = 1020 cm-3 and a SiGe base with EgB = 60 meV ?

(a) At NE = 1019 cm-3, EgE 50 meV,

(b) At NE = 1020 cm-3, EgE 95 meV

(c)

292.12meV 26/meV 502/22 8.6 iiikTE

iiE nenenenn gE

138.610

109218

219

2

2

i

i

iEB

iE

BE

EBF n

n

nN

nN

WD

WD

22 38 iiE nn 24F2meV 26/meV 602/22 10 ii

kTEiiB nenenn gB

237F

EXAMPLE: Emitter Bandgap Narrowing and SiGe Base


Slide 8-14

A high-performance BJT typically has a layer of As-doped N+ poly-silicon film in the emitter.

F is larger due to the large WE , mostly made of the N+ poly-silicon. (A deep diffused emitter junction tends to cause emitter-collector shorts.)

N-collector

P-base

SiO2

emitter

N+-poly-Si

8.4.3 Poly-Silicon Emitter


Slide 8-15

Why does one want to operate BJTs at low IC and high IC?Why is F a function of VBC in the right figure?

F

From top to bottom:VBC = 2V, 1V, 0V

8.4.4 Gummel Plot and F Fall-off at High and Low Ic

Hint: See Sec. 8.5 and Sec. 8.9.

SCR BE current


Slide 8-16

8.5 Base-Width Modulation by Collector Voltage

Output resistance :

C

A

CE

C

I

V

V

Ir

1

0

Large VA (large ro ) is desirable for a large voltage gain

IB3IC

VCE0VA

VA : Early Voltage

IB2

IB1


Slide 8-17

How can we reduce the base-width modulation effect?


N+ P N

emitter base collector VCE

WB 3

WB 2

WB 1

x

n'

} V

CE1< V

CE2<V

CE3

VBE


Slide 8-18

The base-width modulation effect is reduced if we

(A) Increase the base width,(B) Increase the base doping concentration, NB , or(C) Decrease the collector doping concentration, NC .

Which of the above is the most acceptable action?


N+ P N emitter base collector

VCE

WB3

WB2

WB1

x

n'} VCE1< VCE2<VCE3

VBE


Slide 8-19

8.6 Ebers-Moll Model

The Ebers-Moll model describes both the active and the saturation regions of BJT operation.


IB IC

0 VCE

saturationregion

active region

Slide 8-20

IC is driven by two two forces, VBE and VBC .

When only VBE is present :

)1(

)1(

/

/

kTqV

F

SB

kTqVSC

BE

BE

eI

I

eII

Now reverse the roles of emitter and collector.When only VBC is present :

)1)(1

1(

)1(

)1(

/

/

/

kTqV

RSBEC

kTqV

R

SB

kTqVSE

BC

BC

BC

eIIII

eI

I

eII

R : reverse current gainF : forward current gain


IC

VB CVB E

IB

E B C


Slide 8-21

)1()1(

)1)(1

1()1(

//

//

kTqV

F

SkTqV

F

SB

kTqV

RS

kTqVSC

BCBE

BCBE

eI

eI

I

eIeII

In general, both VBE and VBC are present :

In saturation, the BC junction becomes forward-biased, too.

VBC causes a lot of holes to be injected into the collector. This uses up much of IB. As a result, IC drops.

VCE (V)



Slide 8-22

8.7 Transit Time and Charge Storage

C

FF I

Q

When the BE junction is forward-biased, excess holes are stored

in the emitter, the base, and even in the depletion layers.

QF is all the stored excess hole charge

F determines the high-frequency limit of BJT operation.

F is difficult to be predicted accurately but can be measured.


Slide 8-23

8.7.1 Base Charge Storage and Base Transit Time

Let’s analyze the excess hole charge and transit time in the base only.

WB0

n 0 n iB2

NB------- e

qVBE kT1– =

x

p' = n'

)1()0( /2

kTqV

B

iB BEeN

nn

pn B

BFB

C

FB

BEFB

D

W

I

Q

WnqAQ

2

2/)0(2


Slide 8-24

What is FB if WB = 70 nm and DB = 10 cm2/s?

Answer:

2.5 ps is a very short time. Since light speed is 3108 m/s, light travels only 1.5 mm in 5 ps.

EXAMPLE: Base Transit Time

ps 5.2s105.2/scm 102

)cm 107(

212

2

262

B

BFB D

W


Slide 8-25

The base transit time can be reduced by building into the base a drift field that aids the flow of electrons. Two methods:

• Fixed EgB , NB decreases from emitter end to collector end.

• Fixed NB , EgB decreases from emitter end to collector end.

dx

dE

qc1E

8.7.2 Drift Transistor–Built-in Base Field


-E B C

Ec

Ev

Ef

-E B C

Ec

Ev

Ef

Slide 8-26

8.7.3 Emitter-to-Collector Transit Time and Kirk Effect

Top to bottom : VCE = 0.5V, 0.8V, 1.5V, 3V.

• To reduce the total transit time, emitter and depletion layers must be thin, too.

• Kirk effect or base widening: At high IC the base widens into the collector. Wider

base means larger F .


Slide 8-27

Base Widening at Large Ic

satEC qnvAI

satE

CC

C

vA

IqN

qnqN

sdx

dE /

x

E

baseNcollector

N+

collector

basewidth

depletionlayer

x

E

baseN N+

collector

“basewidth”

depletionlayer

collector


Slide 8-28

8.8 Small-Signal Model

kTqVSC

BEeII /

Transconductance:

)//(

)(

/

/

qkTIeIkT

q

eIdV

d

dV

dIg

CkTqV

S

kTqVS

BEBE

Cm

BE

BE

At 300 K, for example, gm=IC /26mV.)//( qkTIg Cm

vber gmvbe

C

E

B

E

C

+


Slide 8-29

F

m

BE

C

FBE

B g

dV

dI

dV

dI

r

11

mFCFBEBE

F gIdV

d

dV

dQC

This is the charge-storage capacitance, better known as the diffusion capacitance.

Add the depletion-layer capacitance, CdBE :

dBEmF CgC

8.8 Small-Signal Model

mF gr /

vber gmvbe

C

E

B

E

C

+


Slide 8-30

EXAMPLE: Small-Signal Model Parameters

A BJT is biased at IC = 1 mA and VCE = 3 V. F=90, F=5 ps, and T = 300 K. Find (a) gm , (b) r, (c) C.

Solution:

(a)

(b)

(c)

siemens)(milliqkTIg Cm mS 39V

mA39

mV 26

mA 1)//(

kΩ 3.2mS 39

90/ mF gr

ad)(femto fargC mF fF 19F109.1039.0105 1412


Slide 8-31

Once the model parameters are determined, one can analyze circuits with arbitrary source and load impedances.

The parameters are routinely determined through comprehensivemeasurement of the BJT ACand DC characteristics.


Slide 8-32

8.9 Cutoff Frequency

The load is a short circuit. The signal source is a current source,ib , at frequency, f. At what frequency does the current gain fall to unity?)/( bc ii

CdBEFF

m

b

c

bemc

bbbe

qIkTCjjCjr

g

i

i

vgi

Cjr

iiv

//1

1

/1)(

, /1admittanceinput

)/(2

1at 1

CdBEFT qIkTC

f

vbe

r gmvbe

C

E

B

E

C

+

-

Signalsource

Load

dBEmF CgC


Slide 8-33

fT is commonly used to compare the speed of transistors.• Why does fT increase with increasing IC?

• Why does fT fall at high IC?

fT = 1/2(F + CdBEkT/qIC)

8.9 Cutoff Frequency


Slide 8-34

• Poly-Si emitter• Thin base• Self-aligned poly-Si base contact• Narrow emitter opening• Lightly-doped collector• Heavily-doped epitaxial subcollector• Shallow trench and deep trench for electrical isolation

BJT Structure for Minimum Parasitics and High Speed


Slide 8-35

•In order to sustain an excess hole charge in the transistor, holes must be supplied through IB to susbtain recombination at the above rate.•What if IB is larger than ? FFFQ /

FF

FB

F QtI

dt

dQ

)(

Step 1: Solve it for any given IB(t) to find QF(t).

8.10 Charge Control Model

•For the DC condition,FF

FFCB

QII

/

Step 2: Can then find IC(t) through IC(t) = QF(t)/F .

IC(t) = QF(t)/F


Slide 8-36

Visualization of QF(t)

FF

FB

F QtI

dt

dQ

)(

QF(t)

QF/FF

IB( t) )(tIB

FF

FQ


Slide 8-37

EXAMPLE : Find IC(t) for a Step IB(t)

The solution of isFF

FB

F QtI

dt

dQ

)(

)1(/)()(

)1(/

0

/0

FF

FF

tBFFFC

tBFFF

eItQtI

eIQ

What is ?)( )?0( ?)( FFB QQI

IB(t)

IC(t)

IC(t)

t

t

IB IB0

E B Cn

t

QF


Slide 8-38

8.11 Model for Large-Signal Circuit Simulation

• Compact (SPICE) model contains dozens of parameters, mostly determined from measured BJT data.

• Circuits containing tens of thousands of transistors can be simulated.

• Compact model is a “contract” between device/manufacturing engineers and

circuit designers.

)1(1)( ///

kTqV

F

S

A

CBkTqVkTqVSC

BCBCBE eI

V

VeeII

C

B

E

QF

CCS

rB

rC

rE

CBE

QR

CBC

IC


Slide 8-39

A commonly used BJT compact model is the Gummel-Poon model, consisting of•Ebers-Moll model

•Current-dependent beta

•Early effect

•Transit times

•Kirk effect

• Voltage-dependent capacitances

• Parasitic resistances

•Other effects

8.11 Model for Large-Signal Circuit Simulation


Slide 8-40

8.12 Chapter Summary

• The base-emitter junction is usually forward-biased while the base-collector is reverse-biased. VBE determines the collector current, IC .

B

BE

W

BiB

iB

kTqV

B

iEC

dxD

p

n

nG

eG

qnAI

02

2

/2

)1(

• GB is the base Gummel number, which represents all the subtleties of BJT design that affect IC.


Slide 8-41

8.12 Chapter Summary• The base (input) current, IB , is related to IC by the common-

emitter current gain, F . This can be related to the common-base current gain, F .

B

E

B

CF G

G

I

I

• The Gummel plot shows that F falls off in the high IC region due to high-level injection in the base. It also falls off in the low IC region due to excess base current.

F

F

E

CF I

I

1

• Base-width modulation by VCB results in a significant slope of the IC vs. VCE curve in the active region (known as the Early effect).


Slide 8-42

8.12 Chapter Summary• Due to the forward bias VBE , a BJT stores a certain amount

of excess carrier charge QF which is proportional to IC.

FCF IQ

F is the forward transit time. If no excess carriers are stored outside the base, then

• The charge-control model first calculates QF(t) from IB(t) and then calculates IC(t).

B

BFBF D

W

2

2

FF

FB

F QtI

dt

dQ

)(

FFC tQtI /)()(

, the base transit time.


Slide 8-43

8.12 Chapter Summary

The small-signal models employ parameters such as transconductance,

q

kTI

dV

dIg C

BE

Cm /

input capacitance,

and input resistance.

mFBE

F gdV

dQC

mFB

BE gdI

dVr /


Documents

Chapter 8 Bipolar Junction Transistors