Chenming Hu Ch8 Slides

7/30/2019 Chenming Hu Ch8 Slides

1/43

Slide 8-1

Chapter 8 Bipolar Junction Transistors

Since 1970, the high density and low-power advantage of

the MOS technology steadily eroded the BJTs 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)


2/43

Slide 8-2

8.1 I ntroduction to the BJT

IC is an exponential

function of forwardVBE and independent

of reverse VCB.


VB EIC

0VCB

NPN BJT:

N+ P NE C

B

VBE VCB

Emitter Base Collector


3/43

Slide 8-3

Common-Emitter Configuration

Question: Why isIB often preferred as a parameter overVBE?



4/43

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

8.2 Collector Cur rent

BBB

B

DL

L

n

dx

nd

22

2

B : base recombination lifetimeDB : base minority carrier (electron)

diffusion constant

Boundary conditions :

)1()0( /0 kTqVBBEenn

0)1()( 0/

0 BkTqV

BB nenWnBC

N+ P N

emitter base collector

x0 W

depletion layers

B


5/43

Slide 8-5

BBB

B

kTqV

BLW

L

xW

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

0

2

2

/2

)1(

It can be shown

GB (scm4) is the base Gummel number

8.2 Collector Cur rent

ni2

NB-------e

qVBE kT1

nn 0-------------

)0(/)( nxn

0 1

1)1()( /

2

kTqV

B

iB BEeN

nxn

x/

x/WB

)/1)(1(

)/1)(0()(

/2

B

kTqV

B

iB

B

WxeN

n

Wxnxn

BE



6/43

Slide 8-6

At low-level injection,

inverse slope is 60 mV/decadeHigh-level injection effect :

8.2.1 H igh Level I njection Effect

0 0.2 0.4 0.6 0.8 1.010-12

10-10

10-8

10-6

10-4

10-2

VBE

IC

(A

)IkF

60 mV/decadeAt large VBE, BNpn

pnpn

kTqV

iBEenpn 2/

kTqV

iBBE

enpG2/

kTqViBEenI 2/C

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

kTqV

i

kTEEq

iBEFpFn enennp /

2/)(2



7/43

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



8/43

Slide 8-8

E

BE

W

EiE

iE

kTqV

E

iEB

dx

D

n

n

nG

eG

qnAI

0

2

2

/2

)1(

Is a large IBdesirable? 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,


9/43

Slide 8-9

8.4 Current Gain

B

C

F I

I

How canFbe maximized?

Common-emittercurrent 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 thatF

FF

1

2

2

iEBBE

iBEEB

B

EF

nNWDnNWD

GG



10/43

Slide 8-10

EXAMPLE: Current Gain

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

Solution:

9901.0mA01.1/mA1/

100A10/mA1/

mA01.1A10mA1

ECF

BCF

BCE

II

II

III

We can confirm

F

F

F

1

F

F

F

1and



11/43

Slide 8-11

8.4.1 Emitter Bandgap Narrowing

Emitter bandgap narrowing makes it difficult to raiseFby

doping the emitter very heavily.


2

2

iE

iB

B

En

n

N

N

To raiseF,NE is typically very large.

Unfortunately, largeNEmakes22iiE nn

(heavy doping effect).

kTE

VCigeNNn

/2 Since ni is related toEg, this effect is

also known as band-gapnarrowing.

kTE

iiEgEenn

/22 EgE is negligible forNE< 1018 cm-3,is 50 meV at 1019cm-3, 95 meV at 1020cm-3,

and 140 meV at 1021 cm-3.


12/43

Slide 8-12

2

2

iE

iB

B

E

n

n

N

N

To further elevateF, we can raise niB by

using an epitaxial Si1-hGehbase.

With h= 0.2,EgB is reduced by 0.1eV and niE2 by 30x.

8.4.2 Narrow-Bandgap Base and Heterojuncion BJT



13/43

Slide 8-13

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

2 = ni2.What is

F for (a) NE= 1019 cm-3, (b) NE= 1020 cm-3, and (c) NE= 1020 cm-3and 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)

292.12meV26/meV502/22 8.6 iiikTE

iiE nenenenngE

138.610

109218

219

2

2

i

i

iEB

iE

BE

EBF

n

n

nN

nN

WD

WD

22 38 iiE nn 24F

2meV26/meV602/22 10 iikTE

iiB nenenngB 237F

EXAMPLE: Emi tter Bandgap Narrowing and SiGe Base



14/43

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



15/43

Slide 8-15

Why does one want to operate BJTs at lowICand highIC?

Why isFa function ofVBC in the right figure?

F

From top to bottom:

VBC= 2V, 1V, 0V

8.4.4 Gummel Plot and FFall-off at High and Low Ic

Hint: See Sec. 8.5 and Sec. 8.9.

SCR BE current



16/43

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



17/43

Slide 8-17

How can we reduce the base-width modulation effect?


N+

P N

emitter base collectorVCE

WB3

WB2

WB1

x

n' }V

CE1

< VCE2


18/43

Slide 8-18

The base-width modulation

effect is reduced if we

(A) Increase the base width,

(B) Increase the base dopingconcentration,NB , or

(C) Decrease the collector doping

concentration,NC.

Which of the above is the most acceptable action?


N+ P Nemitter base collector

VCE

WB3

WB2

WB1

x

n'

}VCE1


19/43

Slide 8-19

8.6 Ebers-Moll Model

The Ebers-Moll model describes both the active

and the saturation regions of BJT operation.


IBIC

0VCE

saturationregion

active region


20/43

Slide 8-20

ICis driven by two two forces, VBEand VBC.

When only VBE is present :

)1(

)1(

/

/

kTqV

F

SB

kTqV

SC

BE

BE

eI

I

eII

Now reverse the roles of emitter and collector.

When only VBC is present :

)1)(1

1(

)1(

)1(

/

/

/

kTqV

R

SBEC

kTqV

R

SB

kTqV

SE

BC

BC

BC

eIIII

eII

eII

R : reverse current gain

F: forward current gain


IC

VB CVB E

IB

E B C



21/43

Slide 8-21

)1()1(

)1)(11()1(

//

//

kTqV

F

SkTqV

F

SB

kTqV

R

SkTqV

SC

BCBE

BCBE

eI

eI

I

eIeII

In general, both VBEand VBCare 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

ofIB. As a result,ICdrops.

VCE(V)




22/43

Slide 8-22

8.7 Transit Time and Charge Storage

C

FF

IQ

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

Fdetermines the high-f requency limit of BJT operation.Fis difficult to be predicted accurately but can be measured.



23/43

Slide 8-23

8.7.1 Base Charge Storage and Base Transit Time

Lets analyze the excess hole charge and transit time in

the base only.

WB0

n 0 n iB2

NB------- e

qV BE kT1 =

x

p' = n'

)1()0( /2

kTqV

B

iB BEeNnn

pn B

BFB

C

FB

BEFB

D

W

I

Q

WnqAQ

2

2/)0(

2



24/43

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

ps5.2s105.2/scm102

)cm107(

2

12

2

262

B

B

FB D

W



25/43

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:

FixedEgB ,NB decreasesfrom emitter end to collector end.

FixedNB ,EgB decreasesfrom emitter end to collector end.

dx

dE

q

c1

8.7.2 Drift TransistorBuilt-in Base Field


-E B C

Ec

Ev

Ef

-E B C

Ec

Ev

Ef


26/43

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. Widerbase means largerF.



27/43

Slide 8-27

Base Widening at Large Ic

satEC qnvAI

satE

C

C

C

vA

I

qN

qnqN

sdx

dEe/

x

Ebase

Ncollector

N+collector

base

width

depletion

layer

x

Ebase

N N+collector

basewidth

depletionlayer

collector



28/43

Slide 8-28

8.8 Small-Signal Model

kTqVSC

BEeII /

Transconductance:

)//(

)(

/

/

qkTIeIkT

q

eIdV

ddVdIg

C

kTqV

S

kTqV

S

BEBE

Cm

BE

BE

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

vbe r gmvbe

C

E

B

E

C

+



29/43

Slide 8-29

F

m

BE

C

FBE

B g

dV

dI

dV

dI

r

11

mFCF

BEBE

F gIdV

ddVdQC

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

dif fusion capacitance.

Add the depletion-layer capacitance, CdBE:

dBEmF CgC

8.8 Small-Signal Model

mF gr /

vbe r gmvbe

C

E

B

E

C

+



30/43

Slide 8-30

EXAMPLE: Small-Signal M odel 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 mS39V

mA

39mV26

mA1

)//(

k3.2mS39

90/ mF gr

ad)(femto fargC mF fF19F109.1039.01051412



31/43

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 comprehensive

measurement of the BJT AC

and DC characteristics.



32/43

Slide 8-32

8.9 Cutoff F requency

The load is a short circuit. The signal source is a current source,

ib , at frequency,f. At what frequency does the current gainfall to unity?)/( bc ii

CdBEFF

m

b

c

bemc

bbbe

qIkTCjjCjr

g

i

i

vgi

Cjr

iiv

//1

1

/1)(

,/1admittanceinput

)/(2

1at1

CdBEF

TqIkTC

f

vbe r gmvbe

C

E

B

E

C

+

-

Signalsource

Load

dBEmF CgC



33/43

Slide 8-33

fTis commonly used to compare the speed of transistors.

Why doesfTincrease with increasingIC?

Why doesfTfall at highIC?

fT

= 1/2(F

+ CdBE

kT/qIC

)

8.9 Cutoff F requency



34/43

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 M inimum Parasitics and High Speed



35/43

Slide 8-35

In order to sustain an excess hole charge in the transistor,

holes must be supplied throughIB to susbtain recombination at

the above rate.

What ifIB is larger than ?FFFQ /

FF

FB

F QtIdt

dQ

)(

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

8.10 Charge Control Model

For the DC condition,FF

FFCB

QII

/

Step 2: Can then findIC(t) throughIC(t) = QF(t)/F.

IC(t) = QF(t)/F



36/43

Slide 8-36

Visual ization of QF(t)

FF

FB

F QtIdt

dQ

)(

QF(t)

QF

/F

F

IB

( t) )(tIB

FF

FQ



37/43

Slide 8-37

EXAMPLE : F ind IC(t) f or a Step IB(t)

The solution of isFF

FB

F QtIdt

dQ

)(

)1(/)()(

)1(

/

0

/

0

FF

FF

t

BFFFC

t

BFFF

eItQtI

eIQ

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

IB(t)

IC(t)

IC(t)

t

t

IB

IB0

E B C

n

t

QF



38/43

Slide 8-38

8.11 Model for Large-Signal Circui t 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

CBkTqVkTqV

SCBCBCBE e

I

V

VeeII

C

B

E

QF

CCS

rB

rC

rE

CBE

QRCBC

IC



39/43

Slide 8-39

A commonly used BJT compact model is the Gummel-Poonmodel, 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 Circui t Simulation



40/43

Slide 8-40

8.12 Chapter Summary

The base-emitter junction is usually forward-biased while

the base-collector is reverse-biased. VBEdetermines thecollector current,IC.

B

BE

W

BiB

iB

kTqV

B

iEC

dxD

p

n

nG

eG

qnAI

0

2

2

/2

)1(

GB is the base Gummel number, which represents all thesubtleties of BJT design that affectIC.



41/43

Slide 8-41


The base (input) current,IB, is related toICby the

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

B

E

B

CF

G

G

I

I

The Gummel plot shows thatF falls off in the highIC

region due to high-level injection in the base. It also falls

off in the lowICregion due to excess base current.

F

F

E

CF

I

I

1

Base-width modulation by VCB results in a significant slopeof theICvs. VCEcurve in the active region (known as the

Early effect).



42/43

Slide 8-42


Due to the forward bias VBE, a BJT stores a certain amount

of excess carrier charge QFwhich is proportional toIC.

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) fromIB(t)

and then calculatesIC(t).

B

BFBF

DW2

2

FF

FB

F QtIdt

dQ

)(

FFC tQtI /)()(

, the base transit time.



43/43

Slide 8-43


The small-signal models employ parameters such as

transconductance,

q

kTI

dV

dIg C

BE

Cm /

input capacitance,

and input resistance.

mF

BE

F gdVdQC

mF

B

BE gdI

dVr /


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Chenming Hu Ch8 Slides