BIPOLARTRANSISTOR

1

Bibliography:

2

• H. Mathieu, « Physique des semi-conducteurs et des composantsélectroniques », 4° édition, Masson 1998.

• D.A. Neamen, « semiconductor physics and devices », McGraw-Hill, Inc 2003.• P. Leturcq et G.Rey, « Physique des composants actifs à semi-conducteurs »,

Dunod Université, 1985.• J. Singh, « semiconductors devices :an introduction », McGraw-Hill, Inc 1994.• Y. Taur et T.H. Ning, « Fundamentals of Modern VLSI devices », Cambridge

University Press, 1998.• K.K. Ng, « complete guide to semiconductor devices », McGraw-Hill, Inc 1995.• D.J. Roulston, « Bipolar semiconductor devices », McGraw-Hill, Inc 1990.

Plan• Geometry• Principle of operating• Static characteristics• Ebers-Moll Equations• Static parameters ( gain…)• Second order effects• Switching performances• Transistor in HF domain• Hetero-junction Bipolar Transistor (HBT or TBH)

3

Geometry

• Geometry:• Lateral• Vertical

• For digital circuits, vertical design

4

lateral

vertical

npn

BC

E

Geometry for IC

5

Muller et Kamins, « device electronics for IC »,2nd Ed., Wiley, 1986

Geometry with insulating oxide

6

Muller et Kamins, « device electronics for IC »,2nd Ed., Wiley, 1986

BJT always present: why?• speed• Low noise• High gain• Low output resistance

• Still present in mobile phone ( analog part)• Low density, mainly in power stage• BiCMOS

7

Analogueamplifier

Working principle

• 2 PN Junctions with one common region (base)• The first Junction (EB) will

inject carriers• The second one (CB) will

collect carriers• The base must be thin (lower than diffusion length)

8

• Reverse biased Junction:• Low current due to empty

tank , reservoir.• By modifying the filling of the

tank, we can modulate the collected current (collector)

• We fill the reservoir ( the base) par a forward bias of the EB junction.

9

Working principle

• The reverve biasing CB junctioncreates a favorable electric fieldfor the collect

• Conditions: • Thin base:

• Avoid recombination effects• Ligthly doped base compared to

emitter• favors one type of injected

carriers (better injection efficiency)

10

Working principle

Statics characteristics

11

NPN Transistor NPN Transistor 

12

Minority carrier distribution in a forward biased npntransistor

ideal

With recombination

13

PNP Transistor

No recombination in the Base  ! (        )

1D Approximation

Homogeneous doping in the Base

Low Injection

Statics characteristics + simplifying hypotheses

Current components in the NPN Transistor• In the neutral Base region:

• Fundamental equation

• and ,

• Integrating from E-B to C-B:

• finally:

• In forward active regime, Jn is negative ( e- vers x<0)

14

dxnpd

eDJ

neDJ

pp

p

n

n ).(

dxnpd

eDJ

neDJ

pp

p

n

n ).(

pn JJ pn

dxnpd

eDJ

pn

n ).(

dxnpd

eDJ

pn

n ).(

'

'

)(

)exp()exp(2

C

E

BCBE

iBnbn

dxxp

kTeV

kTeV

neDJ

'

'

)(

)exp()exp(2

C

E

BCBE

iBnbn

dxxp

kTeV

kTeV

neDJ

'

'

)(

)1()1(2

C

E

kTeV

kTeV

iBnbn

dxxp

eeneDJ

BCBE

'

'

)(

)1()1(2

C

E

kTeV

kTeV

iBnbn

dxxp

eeneDJ

BCBE( )( )

( )( )

P P

N N

dp xJ eD p x

kT dxdn x

J eD n xkT dx

15

)1(

)()1(

)()(

)1()1(

'

'

'

'

'

'

222 kT

eV

C

E

iBnbkTeV

C

E

iBnbC

E

kTeV

kTeV

iBnbn

BCBE

BCBE

edxxp

neDedxxp

neD

dxxp

eeneDJ

)1(

)()1(

)()(

)1()1(

'

'

'

'

'

'

222 kT

eV

C

E

iBnbkTeV

C

E

iBnbC

E

kTeV

kTeV

iBnbn

BCBE

BCBE

edxxp

neDedxxp

neD

dxxp

eeneDJ

and:BeffA

C

E

WNdxxpB

'

'

)( BeffA

C

E

WNdxxpB

'

'

)(

So:

)1()1()1()1(

22kT

eVkT

eV

SnkT

eV

BeffA

nbiBkTeV

BeffA

nbiBEn

BCBEBC

B

BE

B

eeIeWNDene

WNDenAI

)1()1()1()1(

22kT

eVkT

eV

SnkT

eV

BeffA

nbiBkTeV

BeffA

nbiBEn

BCBEBC

B

BE

B

eeIeWNDene

WNDenAI

with :B

iE

BeffA

nbiBESn G

enAWNDenAI

B

22

B

iE

BeffA

nbiBESn G

enAWNDenAI

B

22

Saturation current of electrons in the PN narrowjunction ( or without recombination in the Base).

BeffnbiB

iBeff

nb

A

iB

iB W

Dp

nnW

DN

nnG B

2

2

2

2

BeffnbiB

iBeff

nb

A

iB

iB W

Dp

nnW

DN

nnG B

2

2

2

2

Gummel number in the Base (s/cm4)

Current components in the NPN Transistor

in the case of uniform base doping

• Emitter current • Collector current

16

1)exp(

kTeVJJ BE

spEpE

1)exp(

kTeVJJ BC

spCpC

finally

pCpEECB

npCC

npEE

IIIII

III

III

E B C

JpE Jn JpCIE

IB

IC

NPN

Current components in the NPN Transistor

• And :

17

)1(exp)1](exp[ kT

eVIkT

eVIIIII BCsn

BEspEsnpEnE

)1](exp[)1(exp kT

eVIIkT

eVIIII BCspCsn

BEsnpCnC

1)exp(1)exp(

kTeVI

kTeVIIIIII BC

spCBE

spEpCpECEB

Current components in the NPN Transistor

• Forward active region:• E‐B (forward) and C‐B (reverse)

18

kTeVII

kTeVI

QQDnAeI BE

SpESnBE

SpESB

nBiE exp)(exp)(

22

2 2

( )exp expi nB BE BEC Sn

B S

Ae n D eV eVI I

Q Q kT kT

kTeVIIII BE

SpECEB exp*

Statics characteristics

• Emitter injection efficiency:

• DC common base current gain:

• DC common emitter current gain :

19

exp( / )exp( / )

Sn BE SnnE

pE SpE BE Sp

I eV kT III I eV kT I

1 to close but    1).(

1

1

22

SpSn

Sn

nBi

SBSpE

C

III

DneQQJI

I

ESp

Sn

B

C

II

II

1

NB:if we neglect recombinationprocess and         are equivalent E

Statics characteristics

• Base transport factor:• Take into account recombination

in neutral base region

20

( (0) ) / 2effB p ps

rBn n

AeW n nQI

t

sC

QI

2

2

21

eff

C n n

rB t B

I LI W

Statics characteristics

• Recombination factor:• Take into account recombination in

depleted base region

21

exp2 2

i BErD T

Aen eVI W

kT

withWT, width of E‐B space charges.

When we add up all the contribution to the base currentwe get:

rDrBBB IIII *

Statics characteristics

• The common emitter gain can be expressed as:

22

C

rD

EC

rDrBB

C

B

II

IIII

II

111 *

Statics characteristics

2 5

2 8

2 101000

10eff

n

B

LW

2

2 1000E E

B B

D DEeffSn iB nBE

SpE iE pE A Beff A

N NWI n DI n D N W N

2

5

80

expexp 2 10exp exp

2 10 2exp exp

2 2 2

B

B

i nB BEBE

Sn A BeffC i nB BE BE

rD A Beff TBE i BEGR T

Aen D eVeVI N W kTI nD eV eVkTI N W W kT kTeV Aen eVI W

kT kT

• IB intrisic base current (no recombination)

• IrB recombination current in the neutral base region

• IrD recombination current in the depletionzone of EB junction

If VBE>0,72V then exp() larger than 106

Modern Transistors:

Other modes of operation

• Saturation mode (regime):• The two junctions are forward biased.

23

kTeV

BS

nBikTeV

spEBS

nBiE

BCBE

eQQDnAe

eIQQDnAe

I

2222

kTeV

spCBS

nBikTeV

BS

nBiC

BCBE

eIQQDnAee

QQDnAeI

2222

QS1

nex(0)

WB

QS2

nex(W)

WB

nex(0)nex(W)

QS1+QS2

WB

• Low injection : (QS<<QB):• Current is due to saturation charge injected into the base, ie

QST = QS1 +QS2

• If we deal with « narrow » junction, this charge is simplygiven by the surface of ½ trapeze (linear decay)

24

kTeV

sntkT

eV

A

iBBBS

kTeV

sntkT

eV

A

iBBS

BCBC

BEBE

eJeNnWWxenWQ

eJeNnWxenWQ

2

2

2

1

21)(

21

21)0(

21

Saturation mode

Saturation mode

• Low injection: (QS<<QB):• An other « view » of saturation charge (from Ablard):

• We consider transistor in active mode with a charge QSN and a charge QSAT (we have to determine) which supply the samesaturation current Icsat.

25

0 WB

n(x)

)0(exn

)( Bex Wn

Base

)()0( Bexex Wnn

QSN

QSAT

kTeV

sntkT

eV

sntSN

BBSN

BCBE

eJeJQ

WWnneQ

))()0((21

kTeV

sntkT

eV

sntSN

BBSN

BCBE

eJeJQ

WWnneQ

))()0((21

We get :

kTeV

sntSAT

BC

eJQ 2 kTeV

sntSAT

BC

eJQ 2

Responsible for the degradation of dynamic performance

QST = QSN+QSAT

Nonideal Effects

• « Gummel plot »:• Graph of IC and IB versusVBE

26

1

2

3

• Early effect / collector punchthrough

• Base – collector junction breakdown

• Emitter and Base serie resistance

• Ic « collapse » fort high current

• « crowding effect »

• Early effect / collector punchthrough

• Base – collector junction breakdown

• Emitter and Base serie resistance

• Ic « collapse » fort high current

• « crowding effect »

27

Nonideal Effects

• At "first glance" Ic is independent of VCB

• In fact we have the modulation of the width of the neutral region in the base, so in the same wayQB+QS , and so Ic !

28

'

'

2 2 2 2 2 2

( )exp exp exp

( ) B

i nB BE i nB BE i nB BEC C

B S A Beff

E

Ae n D eV Ae n D eV Ae n D eVI

Q Q kT kT N W kTp x dx

if VBC WB QB+QS

Ic

ZCE B-C

Early effect / collector punchthrough

29

BCZCE

SC

BB

dBC

pBA

W

WeNCQ

V

Early effect / base punchthrough

Collector current is due to diffusion of electrons in the base

• At the limit:• The space charge BC

« depletes » totaly the neutral base

• collector injects directlycurrent into the emitterbecause energy barrier islowering

• Current only limited by serieresistance Rserie from E and C

30

C

CBB

DSC

DAABpt N

NNNeWV

2)(2

Early effect / base punchthrough

Base - Collector junction breakdown

• Avalanche of BC:• Often occurs before punchthrough

• How to prevent it?• Lowering the electric field:

• Reduce the doping gradient in the collector

• Lightly doped layer between base and collector

31

Ionisation par impacts

BrBfB III BrBfB III

Emitter and Base resistance (effet 3)

• At low current negligeableeffects

• In high speed circuits, B-C allways reverse biased (rc2 and rc3 as low as possible)• Resistances rc have no

effects on current flow• Only re and rb play a major role .

• IR drop Voltage

32

)exp(

)(

'

'

kTVeII

VVV

rrIIrrIIrV

BEBB

BEBEBE

beBCebBEeBE

0 BEC III

Measured current:IB’

Collector « collapse » for high injection level (effect 1)

• Numbers of physicalmechanisms can cause thisfalloff of IC0:• Increase of the charge (holes)

into the base (maintainneutrality)

• Increase the width of the quasineutral base layer (push off the space charge into the collector): Kirk effect

33

kTeV

dxxpneDAI

kTeVJAI

BEC

E p

ieBnBEC

BECEC

exp)(

exp

'

'

2

0

Nc

Nb

x)

Wb0

E’ C’

Nc-n

Nb+n

x)

Wb0

E’ C’

34

And the effect #2  ????????????????

« crowding effect »

• The view of a 1D devices is an approximation

• Drop voltage IR in the base. • The edge of the emitter contact is

more biased than the core/center• Favour a high density of current

essentially along the edges• Not a good thing for high power

devices

• Solutions: interdigitatedapproach

35

Bipolar Transistor: a switch ?

• ON state: the switch isclosed (saturation mode)

• OFF state: the switch is open (cutoff mode)

• ON state: the switch isclosed (saturation mode)

• OFF state: the switch is open (cutoff mode)

36

• Input signal as low as possible

• input power as low as possible

common emitter

• Input signal as low as possible

• input power as low as possible

common emitter

37

Bipolar Transistor: a switch ?

• Switching velocity?• Limiting factors?

38

Turn on transient: Continuity equation

for the charge:

B BB

n

Q dQI

dt

Base charge can bewritten:

Collector current is givenby:

transit time

in the base (narrow)

( ) [1 exp( )]B B nn

tQ t I

( )( ) B

Ct

Q tI t

( )[1 exp( )]B n

c Bt t n

Q t tI I

Bipolar Transistor: a switch ?

• Turn on:• IC increases until the saturation

regime is reached:(we neglect VCEsat)

• The limit charge QB(ton) to saturate the transistor is givenby :

• The on state time is given by:

39

C

DDC R

VIsat

C

DDC R

VIsat

nB

pBCS D

dIQ sat

2

2

nB

pBCS D

dIQ sat

2

2

)(1

1ln)(1

1ln

Bc

nnBS

nON IIIQt

)(1

1ln)(1

1ln

Bc

nnBS

nON IIIQt

)]exp(1[)(n

nBBtItQ

Bipolar Transistor: a switch ?

• Remark: the charge can increaseover QB(ON) to over saturate the transistor.this charge is injectedfrom the collector

• Turn off time : input with a « 0 »:• Evacuation of the stored charge

• This is the storage time ts

• after, this is the samemechanism than for PN Junction

40

S

nBnS Q

It

ln

S

nBnS Q

It

ln

Final value:

Bn I

Bipolar Transistor: a switch ?

• Storage time (desaturation) limits the switching time

• 2 ways to reduce it:• Add impurities which

decrease strongly the lifetimeinto the base (pb withtransport factor)

• Schottky Diode in // with CB junction: avoid saturation of the transistor

41

Bipolar Transistor: a switch ?

AC signal : equivalent circuitAC signal : equivalent circuit

42

CµIB Ib Ic

Transistor and ac signal: equivalent circuit

• Transconductance :links the variation of the collector current to the base – emiter voltage:

• Input resistance : links the variation of Base current to the base – emitervoltage:

• Output resistance:

43

   .C Cm c m BE

BE

I eIg i g v

V kT

1

11B

BE B m

I kTr h

V eI g

1

22

1C Ao

CE C

I Vr

V I h

• Capacitance :

• Storage capacitance

• transit time

• Capacitance : CB junction capacitance reverse biased

• Collector –substrate (depletion layer) capacitance:

44

EBTSE CCC

CBTCC

dCSC

mFSE gC

BCBEB tttEF tttt

C

C

Transistor and ac signal: equivalent circuit

• Cut off frequency (current gain =1 when short circuit load)• We neglect r0

• Current gain is given by:

45

beµb

beµbemc

vCjCjr

i

vCjvgi

1

21)()/1()( h

CCjrCjg

ii

µ

µm

b

c

21)()/1()( h

CCjrCjg

ii

µ

µm

b

c

Transistor and ac signal: equivalent circuit

21 00 then  (0)  static gain(1 / )

c mm

b

i gif g r h

i r

21 00 then  (0)  static gain(1 / )

c mm

b

i gif g r h

i r

• In modern devices , in general• At low frequency:

• At high frequency, the imaginary term dominates and :

46

mµ gC

)(1)(

µ

m

b

c

CCrjrg

ii

)(1)(

µ

m

b

c

CCrjrg

ii

)()(

µ

m

CCjg

)(

)(µ

m

CCjg

Transistor and ac signal: equivalent circuit

Transistor en ac: schéma équivalent

• We get the « cutoff frequency » by considering iC/iB=1

• By replacing all the terms by their expressions

47

µ

mT CC

gf

2

)()(2

1ceTTSE

CF

T

rrCCCeIkT

f BCBC

Forward Transit time

12 ( )

m

T µ

gf C C

12 ( )

m

T µ

gf C C

Resistance neglected

Transistor en ac: schéma équivalent

• Maximun oscillation frequencyPower gain=1• Laborious and tedious calculation/ we have to take into account the

base resistance

48

dBCb

T

Crff

8max dBCb

T

Crff

8max

Heterojunction Bipolar Transistor

• Current gain:

• In the case of narrow base:

49

2 2

2 21 12

E E B

E B B E B

i p A Beff Beff

D n i p n

n D N W WN D n L L

2 2

2 21 12

E E B

E B B E B

i p A Beff Beff

D n i p n

n D N W WN D n L L

2

21 E E B

E B B E

i p A Beff

D n i p

n D N WN D n L

2

21 E E B

E B B E

i p A Beff

D n i p

n D N WN D n L

• If we want a gain with a high value, we need close to 1. It means: • Lowering base doping• Lowering base width (careful with punchthrough!)

50

Increase of the base resistance fmax decreases

2

21 E E B

E B B E

i p A Beff

D n i p

n D N WN D n L

2

21 E E B

E B B E

i p A Beff

D n i p

n D N WN D n L

Heterojunction Bipolar Transistor

• Other solution:• Increase emitter doping

• Improve emitter efficiency• Problem: « gap shrinking »

• This « problem » can be transform in opportunity !! (next twoslides)

51

2

21 E E B

E B B E

i p A Beff

D n i p

n D N WN D n L

2

21 E E B

E B B E

i p A Beff

D n i p

n D N WN D n L

)exp()()( 22

kTE

Basenémetteurn gii

.0)()( émetteurgbasegg EEE

Heterojunction Bipolar Transistor

52

kTE

LW

nN

DD

Nn g

p

Beff

i

A

n

p

D

i

EB

B

B

E

E

e exp1 2

2

kTE

LW

nN

DD

Nn g

p

Beff

i

A

n

p

D

i

EB

B

B

E

E

e exp1 2

2

1)exp(

1 kTE

WL

DD

NN g

Beff

p

p

n

A

D E

E

B

B

E

1)exp(

1 kTE

WL

DD

NN g

Beff

p

p

n

A

D E

E

B

B

E

We see that it is difficult to have at the same time a large emitter doping, a lightly doped and thin base and a large gain

Heterojunction Bipolar Transistor

• We design a structure with a negative energy gap difference: this is an HBT

53

eb EgEgEg

Heterojunction Bipolar Transistor

54

Requirements for a bipolar device

•High gain

•High emitter efficiency

•High speed

Demands and Problems for a BJT

Demands Problems

Heavy emitter doping Bandgap shrinkage causingbase injection

Low base dopingNarrow base width High base resistance

Solution: Heterojunction Bipolar Transistors

•Emitter can be heavely doped using a SC with Eg larger than the base semiconductor•Base can be heavely doped and be made narrow without increasing base resistance•Collector can be chosen from a material to increase breakdown voltage

(From Singh)

55

Transistor with a Silicon –Germanium base

56

Electrons density

kTeV

IQQDnAe

I BESpE

SB

nBiE exp)(

22

kTeV

QQDnAeI BE

SB

nBiC exp)(

22

emettir collector

base

)(2 Sini

)(2 SiGeni

Improve gainImprove transist timeIncrease Early voltage