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Page 1: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

BIPOLARTRANSISTOR

1

Page 2: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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.

Page 3: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

Page 4: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

Geometry

• Geometry:• Lateral• Vertical

• For digital circuits, vertical design

4

lateral

vertical

npn

BC

E

Page 5: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

Geometry for IC

5

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

Page 6: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

Geometry with insulating oxide

6

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

Page 7: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

Page 8: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

Page 9: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• Reverse biased Junction:• Low current due to empty

« tank »• En modulant le remplissage

du réservoir, modulation du courant inverse collecté (collecteur)

• On remplit le réservoir (la base) en polarisant en direct la jonction EB

9

Working principle

Page 10: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• 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

Page 11: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

Statics characteristics

11

NPN Transistor NPN Transistor 

Page 12: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

12

Minority carrier distribution in a forward biased npntransistor

ideal

With recombination

Page 13: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

13

PNP Transistor

No recombination in the Base  ! (   )

1D Approximation

Homogeneous doping in the Base

Low Injection

Statics characteristics + simplifying hypotheses

Page 14: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

Current components in the NPN Transistor

• In the neutral Base region:• Continuity 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

Page 15: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

Page 16: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• 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

Page 17: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• And (!) :

17

)1(exp)(

)1](exp)(

[ '

'

'

'

22

kT

eV

dxxp

DAenkT

eVIdxxp

DAenIII BCC

E

nbiBEspEC

E

nbipEnE

)1](exp)(

[)1(exp)(

'

'

'

'

22

kT

eVIdxxp

DAenkT

eV

dxxp

DAenIII BCspCC

E

nbiBEC

E

nbipCnC

1)exp(1)exp(

kTeVI

kTeVIIIIII BC

spCBE

spEpCpECEB

Isn

Current components in the NPN Transistor

Page 18: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

18

kTeVII

kTeVI

QQDnAeI BE

SpESnBE

SpESB

nBiE exp)(exp)(

22

kTeVI

kTeV

QQDnAeI BE

SnBE

SB

nBiC expexp)(

22

kTeVIIII BE

SpECEB exp*

Statics characteristics

Page 19: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• Emitter injection efficiency:

• DC common base current gain:

• DC common emitter current gain :

19

Ep

nE I

I

SpSn

Sn

nBi

SBSpE

C

III

DneQQJI

I

22

).(1

1

1B

C

II NB:if we neglect recombination

process and         are equivalent E

Statics characteristics

Page 20: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• Base transport factor:• Take into account recombination

in neutral base region

20

n

ppB

n

srB

nnAeXQI eff

2/))0((

t

sC

QI

12

2

2

effB

n

t

n

rB

C

XL

II

Statics characteristics

Page 21: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• Recombination factor:• Take into account recombination in

depleted base region

21

kTeVW

AenI BE

Ti

rD 2exp

2

withWT, width of E‐B space charges.

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

rDrBBB IIII *

Statics characteristics

Page 22: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• The common emitter gain can be expressed as:

• intriseque base current (no recombination)• recombination current in the neutral base region• recombination current in the depletion zone of EB junction

22

C

rD

EC

rDrBB

C

B

II

IIII

II

111 *

*BI

rBIrDI

Statics characteristics

Page 23: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

n(x)

)0(exn

)( Bex Wn

QS1

QS2

Base

0 WB

Page 24: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• 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

Page 25: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

Impossible d’afficher l’image.Impossible d’afficher l’image.

We get :Impossible d’afficher l’image.

Responsible for the degradation of dynamic performance

QST = QSN+QSAT

Page 26: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• High injection level

• In this case, injected electron density reaches holes density into the base ( )

• Equivalent study leads to the following result :

• .

26

BkT

eVkT

eV

iS WeeenQBCBE

)(21 22 B

kTeV

kTeV

iS WeeenQBCBE

)(21 22

kTeV

iB

nBkTeV

iB

nBn

BCBE

enWeDen

WeDJ 22 22

kTeV

iB

nBkTeV

iB

nBn

BCBE

enWeDen

WeDJ 22 22

pn

Saturation mode

Page 27: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

Nonideal Effects

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

27

1

2

3

Page 28: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• 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 »

28

Nonideal Effects

Page 29: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• 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 !

29

kTeV

QQDnAeI BE

SB

nBiC exp)(

22

if VBC WB QB+QS

Ic

ZCE B-C

Early effect / collector punchthrough

Page 30: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• At the limit:• The space charge BC

« depletes » totaly the neutral base

• collector injects directlycurrent into the emitter.

• Current only limited by serieresistance Rserie form E and C

30

BCZCE

SC

BB

dBC

pBA

W

WeNCQ

V

C

CBB

DSC

DAABpt N

NNNeWV

2)(2

Early effect / collector punchthrough

Page 31: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

Page 32: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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’

Page 33: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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 of 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’

Page 34: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

34

And the effect #2  ????????????????

Page 35: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

« 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• Favour a high density of current

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

devices

• Solutions: interdigitatedapproach

35

Page 36: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

Page 37: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• 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 ?

Page 38: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• Switching velocity?• Limiting factors?

38

Turn on transient: Continuity equation fir

the charge:

IdQdt

Qn

B B

n

Base charge can bewritten:

Collector current is givenby:

transit time

in the base (narrow)

)]exp(1[)(n

nBBtItQ

t

BC

tQtI

)(

)(

)]exp(1[)(

nt

nBc

t

B tIItQ

Bipolar Transistor: a switch ?

Page 39: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• 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 ?

Page 40: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• Remark: the charge can increasesover QB(ON) to over saturate the transistor

• 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 ?

Page 41: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• Storage time (desaturation) limits the switching time

• 2 ways to reduce it:• Add impurities which

decrease strongly the lifetimeinto the base

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

41

Bipolar Transistor: a switch ?

Page 42: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

AC signal : equivalent circuitAC signal : equivalent circuit

42

CµIB Ib Ic

Page 43: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

kTeI

VI

g C

BE

Cm

11

1

hgeI

kTVIr

mBBE

B

11

1

hgeI

kTVIr

mBBE

B

22

11

hIV

VIr

C

A

CE

Co

22

11

hIV

VIr

C

A

CE

Co

Page 44: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• 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

Page 45: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• Cut off frequency (current gain =1)• 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

Ib Ic

x

Transistor and ac signal: equivalent circuit

Page 46: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

• At high frequecy, 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

Page 47: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

Transistor en ac: schéma équivalent

• On obtient alors la fréquence de coupure (« cutoff frequency ») en faisant iC/iB=1

• Soit encore

47

µ

mT CC

gf

2

)()(2

1ceTTSE

CF

T

rrCCCeIkT

f BCBC

Temps de transit en direct

Page 48: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

Page 49: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

Heterojunction Bipolar Transistor

• Current gain:

• In the case of narrow base:

49

2

2

2

2

2111

1BEB

B

B

E

E

E

n

Beff

p

Beff

i

A

n

p

D

i

E

E

LW

LW

nN

DD

Nn

2

2

2

2

2111

1BEB

B

B

E

E

E

n

Beff

p

Beff

i

A

n

p

D

i

E

E

LW

LW

nN

DD

Nn

EB

B

B

E

E

E

p

Beff

i

A

n

p

D

i

E

E

LW

nN

DD

Nn

2

2

111

EB

B

B

E

E

E

p

Beff

i

A

n

p

D

i

E

E

LW

nN

DD

Nn

2

2

111

Page 50: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• 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

EB

B

B

E

E

E

p

Beff

i

A

n

p

D

i

E

E

LW

nN

DD

Nn

2

2

111

EB

B

B

E

E

E

p

Beff

i

A

n

p

D

i

E

E

LW

nN

DD

Nn

2

2

111

Heterojunction Bipolar Transistor

Page 51: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

• Other solution:• Increase emitter doping

• Improve emitter efficiency• Problem: « gap shrinking »

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

51

EB

B

B

E

E

E

p

Beff

i

A

n

p

D

i

E

E

LW

nN

DD

Nn

2

2

111

EB

B

B

E

E

E

p

Beff

i

A

n

p

D

i

E

E

LW

nN

DD

Nn

2

2

111

)exp()()( 22

kTE

Basenémetteurn gii

.0)()( émetteurgbasegg EEE

Heterojunction Bipolar Transistor

Page 52: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

Page 53: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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

53

eb EgEgEg

Heterojunction Bipolar Transistor

Page 54: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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 beheavely doped and be made narrow without increasingbase resistance•Collector can be chosen from a material to increase breakdown voltage

(From Singh)

Page 55: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

55

Page 56: Transistor Bipolaire eng - Polytech Niceusers.polytech.unice.fr/~lorenz/Bipolar_Transistor_eng.pdf · • Ebers-Moll Equations ... • Transistor in HF domain • Hetero-junction

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 gain gainImprove transist timeIncrease Early voltage