ece606: solid state devices lecture 18 bipolar transistors...

Klimeck – ECE606 Fall 2012 – notes adopted from Alam

ECE606: Solid State DevicesLecture 18

Bipolar Transistorsa) Introductionb) Design (I)

Gerhard [email protected]

1


Background

2

Point contact Germanium transistor

Ralph Bray from Purdue missed the invention of transistors.http://www.electronicsweekly.com/blogs/david-manners-semiconductor-blog/2009/02/how-purdue-university-nearly-i.htmlhttp://www.physics.purdue.edu/about_us/history/semi_conductor_research.shtml

Transistor research was also in advanced stages in Europe (radar).

E C

Base!

E B C


Shockley’s Bipolar Transistors …

n+emitter

pbase

ncollector

n+

Double

Diffused BJT

p basen-collector

n+

n+

n+ emitter


Modern Bipolar Junction Transistors (BJTs)

4

SiGe Layer

Transistor speed increases as the electron's travel distance is reduced

SiGe intrinsic base Dielectric trench

N+P+N

P-

N-

CollectorEmitterBaseN+

Why do we need all these design?


Symbols and Convention

5

Poly emitter

Low-doped base

Collector dopingoptimization

N+

P

N

Symbols

NPN PNP

Collector

Emitter

Base

Collector

Emitter

Base

IC+IB+IE=0

VEB+VBC+VCE=0

E

B

C

(DC)


Outline

6

1) Equilibrium and forward band-diagram

2) Currents in bipolar junction transistors

3) Eber’s Moll model

4) Intermediate Summary

5) Current gain in BJTs

6) Considerations for base doping

7) Considerations for collector doping

8) Conclusions

REF: SDF, Chapter 10


Topic Map

7

Equilibrium DC Small signal

Large Signal

Circuits

Diode

Schottky

BJT/HBT

MOS


Band Diagram at Equilibrium

8

1P P P

pr g

t q

∂ = − ∇ • − +∂

J

( )D AD q p n N N+ −∇ • = − + −

P P Pqp E qD pµ= − ∇J

1N N N

nr g

t q

∂ = ∇ • − +∂

J

J µ= + ∇N N Nqn E qD n

Equilibrium

DC dn/dt=0Small signal dn/dt ~ jωtn

Transient --- Charge control model


Band Diagram at Equilibrium

9

BaseEmitter Collector

Vacuum level

EC

EV

EF

χ2

χ1 χ3

NPN homojunction BJT


Electrostatics in Equilibrium

10

( )0

,

2 s Bn E bi

E B E

k Nx V

q N N N=

+ε

( )0

,

2 s Ep BE bi

B E B

k Nx V

q N N N=

+ε

( )0

,

2 s Bn C bi

C C B

k Nx V

q N N N=

+ε

( )0

,

2 s Cp BC bi

B C B

k Nx V

q N N N=

+ε


Two back to back p-n junction


Outline

11








8) Conclusions



Topic Map

12

Equilibrium

DC Small signal

Large Signal

Circuits

Diode

Schottky

BJT/HBT

MOS


Band Diagram with Bias

13

1P P P

pr g

t q

∂ = ∇ • − +∂

J

( )D AD q p n N N+ −∇ • = − + −

P P Pqp E qD pµ= − ∇J

1N N N

nr g

t q

∂ = ∇ • − +∂

J

J µ= + ∇N N Nqn E qD n

Non-equilibrium

DC dn/dt=0Small signal dn/dt ~ jωtn

Transient --- Charge control model


Electrostatics in Equilibrium

14

( ) ( )0,

2 s Bn E bi EB

E B E

k Nx V V

q N N N

ε= −+

( ) ( )0,

2 s Ep BE bi EB

B E B

k Nx V V

q N N N

ε= −+

( ) ( )0,

2 s Bn C bi CB

C C B

k Nx V V

q N N N

ε= −+

( ) ( )0,

2 s Cp BC bi CB

B C B

k Nx V V

q N N N

ε= −+


VEB VCB

Assume current flow is small…fermi level is flat


Current flow with Bias

15

EC-Fn,C

Fp,B-EV

EC-Fn,EV

Input small amount of holes results in large amount of electron output


Vg↑

Modern MOSFET - “Fundamental” Limitlooks similar to BJT

p

Metal

n+ n+

Oxide

DSVg

x

E

S≥60 mV/dec

Threshold

VgVdd

log Id

0


Vg↑

Modern MOSFET - “Fundamental” Limitlooks similar to BJT

p

Metal

n+ n+

Oxide

DSVg

x

E

S≥60 mV/dec

Threshold

VgVdd

log Id

0

DOS(E), log f(E)

Ef

`̀


Coordinates and Convention

18


N+ P N

0 WX’’ X’X

, , ,

0 0 0 0 0 0

, . . . . , . . . .

, . . . . . . . . , . . . . . .

, . . . . . . . , . . . . . .

E D E B A B C D C

E P B N C P

E p B n C p

N N N N N N

D D D D D D

n n p p n n

= = == = == = =

Doping

Minority carrier diffusion

Majority carriers


Carrier Distribution in Base

19

( )2,(0 ) 1BEi B qV

B

nn e

Nβ+∆ = − ( )

2,( ) 1BCi B qV

BB

nn x W e

Nβ∆ = = −

( ) ( )2,

2,1) 1( 1BE BCi B qV

B

B

B

i qV

B B

x xn x

W W

ne

ne

N Nβ β

∆ = − +

−

−

VEBVCB

( ) 1B B

x xn x Ax B

W WDC

∆ = + = − +

DC

Assume no recombination. Start from minority carrier


Collector and Emitter Electron Current

20

( ) ( )2,

2,1) 1( 1BE BCi B qV

B

B

B

i qV

B B

x xn x

W W

ne

ne

N Nβ β

∆ = − +

−

−

( ) ( )2,

,

2, 1 1BBE

B

Ci B qVn i B qn C

Vn

BBn

BW B

nqDe

W

dnJ qD

dx

nqDe

W NNββ= = −− −+

( )

,

2

1BE

p E p

p qVi

n D

dpJ qD

dxD n

eW N

β

= −

= − −

VBE

VBE


Current-Voltage Characteristics

21

JC

VCE

IB

VBE

log10 JC

> 60 mV/dec.

High-level injectionseries resistance, etc.

Normal, Active RegionEB: Forward biasedBC: Reverse biased

( ) ( )2 2, ,

, 1 1BCBEi B i B qVqVn nn C

B B B B

n nqD qDJ e e

W N W N= − − + −ββ

WB is not independent of bias=> Early Effect same physics of diode , rollover


Outline

22








8) Conclusions



Ebers Moll Model

23

( )( )

0

0

1

1

BE

BC

qVF F

qVR R

I I e

I I e

β

β

= −

= −

IC=Ic,n+Ic,p

( ) ( )

( ) ( )

2 2 2, , ,

0 0

1 1

1 1

BCBE

BCBE

pi B i B i C qVqVn n

B B B B C C

qVqVF F R

C

qDn n nqD qDI A e A e

W N W N W N

I e I e

ββ

ββα

= − − + + −

≡ − − −

( ) ( )

( ) ( )

2 2 2, , ,

0 0

1 1

1 1

BCBE

BCBE

p i E i B i B qVqVn n

E E B B E B

qVqVF R

E

R

qD n n nqD qDA e A e

W N W N W N

I e I e

I ββ

ββ α

= − + − + −

≡ − − −

IE

IF

IB

IC

E

B

C

IR

αFIF

αRIR

Hole diffusion in collector

IE=IE,n+IE,p

Temperature dependent


Common Base Configuration

24

P NE

IE ICC

BB

VEB(in)

VCB(out)

How would the model change if this was a Schottky barrier BJT?

IE

IF

IB

IC

E

B

C

IR

CBE CBC

αRIR αFIFN

Junction capacitance and diffusion capacitance

The original transistor was a metal/ semicond / metal deviceNo minority carriers, no diffusion capacitance but the “rest” about the same.

Common base configuration provides power gain, but no current gain. => Emitter and collector current are identical => no current gain=> Collector current IC can be driven through large resistor => power gainIs there another configuration that can deliver current gain?


Common Emitter Configuration

25

αRIR

αFIF

CBE

CBC

E

BIB

IE

IC

IF

IR

( )1

1

F F F FF F B

FF

F

I II I= = − =

−

α α ααβα

F F

F

Iαβ

F F R RI I−α α

Cµ

Cπ

IR

P+

N

P

C

E E

B

VEB(in)

VEC(out)

ICIB

This is a practice problem …


Intermediate Summary

26

• The physics of BJT is most easily understood with

reference to the physics of junction diodes.

• The equations can be encapsulated in simple

equivalent circuit appropriate for dc, ac, and large

signal applications.

• Design of transistors is far more complicated than this

simple model suggests => the next lecture elements

• For a terrific and interesting history of invention of the

bipolar transistor, read the book “Crystal Fire”.


Outline

27








8) Conclusions



Ebers Moll Model

28

IE

IF

IB

ICE

B

C

IR

αFIFαRIR

( )( )

0

0

1

1

BE

BC

qVF F

qVR R

I I e

I I e

= −

= −

β

β

( ) ( )

( ) ( )

2, , ,

00

2 2

1 1

1 1

BCB

BE

E

BC

pi B i E i B qVqVn nE E E

B B E E

qVR R

V

B

F

B

q

qDn n nqD qDI A e A

I e

eW N W N W N

I e β β

ββ

α

= − + − + −

= − −−

( ) ( )

( ) ( )

2 2 2, , ,

0 0

1 1

1 1

BCBE

BCBE

i B i B i C qVqVn n nC C C

B B B B C C

qVqVF F R

n n nqD qD qDI A e A e

W N W N W N

I e I e

ββ

ββα

= − − + + −

= − − −

( ) ( )2 2, ,1 1BCBEp pi E i C qVqV

BE E C C

qD qDn nI A e A e

W N W Nββ= − + −


Ebers Moll Model (Basic definition)

29

IB IC

0 VCE

saturationregion

active region

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


Gummel Plot and Output Characteristics

30

• The simultaneous plot of collector and base current vs.the base-emitter voltage on a semi-logarithmic scale isknown as a Gummel Plot.

• This plot is extremely useful in device characterizationbecause it reflects on the quality of the emitter-basejunction while the base-collector bias is kept at aconstant.

• A number of other device parameters can be ascertainedeither quantitatively or qualitatively directly from theGummel plot because of its semi-logarithmic nature

− For example the d.c gain β, base and collector idealityfactors, series resistances and leakage currents.


Gummel Plot and Output Characteristics

31

2 2, , //( 1) ( 1)BCBEi B i B q kTq kTn n

B B B B

C VVn nqD qDe e

A W N W N

I − − + −≃

2, /( 1)BEp i E V kT

E E

B qqD ne

A W N

I = −

CDC

BI

Iβ =

DCβ Common emitter Current Gain

VBE


Current Gain

32

P+

N

P

C

E E

B

VEB(in)

ICIBCommon Emitter current gain ..

CDC

B

I

Iβ =

2 2( / )/, ,

2/,

( 1) ( 1)

( 1)

BCBE

BE

qV kTqV kTi B i Bn n

B B B B

qV kTi En

E E

n nqD qDe e

W N W N

nqDe

W N

− + −=

−

2,

2,

i Bn E E

B p i E B

nD W N

W D n N≈

Common Base current gain ..P+ N P

E

IE IC

C

BB

VEB(in)

VCB(out)

CDC

E

I

Iα = C C

DC

B E C

I I

I I Iβ = =

− 1DC

DC

αα

=−

DC transfer gain

Will examine

Properties are related – (transistor did not change ☺)


Current Gain

33

2,

2,

i Bn E EDC

B p i E B

nD W N

W D n Nβ ≈

Hig

h in

ject

ion

colle

ctor

cur

rent

=>

roll-

off

Bas

e cu

rren

t do

es n

ot r

oll o

ff


How to make a Good Silicon Transistor

34

Emitter doping higherthan Base doping

Base doping hard to controlEmitter doping easier

~1, same materialprimarily determined by bandgap

Make-Base short …(few mm in 1950s, 200 A now)Want high gradient of carrier density

For a given Emitter length

2,

2,

i Bn E EDC

B p i E B

nD W N

W D n Nβ ≈


Doping for Gain …

35

NE

NB

NC

N+

P

N

2,

2,

i Bn E EDC

B p i E B

nD W N

W D n Nβ ≈


Outline

36







what’s wrong with the previous recipe?


8) Conclusions



Problem of Low Base Doping: Current Crowding

37

( )

( )

' ( )

' ( )

2,

2,

1( )

( )1

BE

BE

qi Bn V

CC B B

p qi EB B

E E

x

V x

nqDe dxJ x dxI W N

qD nI J x dxe dx

W N

β

β

β−

= = =−

∫∫∫ ∫

p base

n-collector

n+

n+VBE

VBEDouble diffused junction configuration:Emitter doping must compensate / overcome the base doping

Low doping in base=> resistance along the current path=> potential drop

=> Determines the injection => Spatially dependent=> More current in the corners


Low Base Doping: Non-uniform Turn-on

38

n+ p base

n-collectorn+

B

E

Interdigitated designs for almost all high power transistors (E-B distance minimized)

Non-uniform current inefficientHigh current at the edge can cause burn-out

Sketches from text book


Low Base Doping: Current Crowding

39

p base

n-collector

n+

n+VBE

We talked about how low doping for the base enhances the current gain.

But there is a potential downside to this approach

If the base doping is kept to small values, it will have a high resistance: Lesser ability to conduct means higher resistance



40

p base

n-collector

n+

n+VBE

Non-zero base resistance results in a lateral potential difference under the emitter region

For an n-p-n transistor as shown, the potential decreases from edge of the emitter towards the centre (the emitter is highly doped and can be considered an equipotential region)



41

p base

n-collector

n+

n+VBE

The number of electrons injected from emitter to base is exponentially dependent on base-emitter voltage

With the lateral drop in the voltage in the base between the edge and centre of emitter, more carriers will be injected at the edge than the emitter centre.



42

Key facts:

1. Current crowding is due to 2D nature of BJTs

2. It is a function of the doping concentration

3. As doping concentration increases, resistivity decreases

− Consequence: Current gain goes smaller � Emitter current injection efficiency decreases

The larger current density near the emitter may cause localized heating and high injection effects

Possible Solution: Emitter widths are fabricated with an inter-digitated design � Many narrow emitters connected in parallel to achieve the required emitter area


Low Base Doping: Non-uniform Turn-on

43

n+ p base

n-collectorn+

B

E

Interdigitated designs for almost all high power transistors (E-B distance minimized)

Non-uniform current inefficientHigh current at the edge can cause burn-out

Sketches from text book


Problem of Low Base Doping: Punch-through

44

NE

NB

NC

( ) ( )0,

2 s Ep BE bi BE

B E B

k Nx V V

q N N N= −

+ε

( ) ( )0,

2 s Cp BC bi BC

B C B

k Nx V V

q N N N= −

+ε

NN+

Low base doping is not a good idea!


Problem of low Base-doping: Base Width Modulation

45

2,

2,, ,

E i Bn EDC

p i EB p B p c B

D W n N

W x x D n Nβ ≈

− −

N+

P N

( ) ( )0,

2 s Ep BE bi BE

B E B

k Nx V V

q N N N= −

+ε

( ) ( )0,

2 s Cp BC bi BC

B C B

k Nx V V

q N N N= −

+ε

Gain depends on collector voltage (bad) …Depletion region width modulation

NB

NC

NE

Electrical base region is smaller than the metallurgical region!


Problem of Low Base-doping: Early Voltage

46

2,

2. . ,

i Bn E EDC

p B p C i EB p B

D W n N

W x x D n Nβ ≈

− −

2 2, ,( / ) ( / )

, ( 1) 1' '

( )BE BCi B i BqV kT qV kTn nn

BC

B B B

qD n qD nI e e

NW W N= − − + −

C C C

BC BC A A

dI I I

dV V V V= ≈

+

VBC

VA

IC

Ideally

In practice

VBC about 1VVA ideally infinity

Jim Early device pioneer


The Early Voltage PS1

47

VA

VBC

IC

Ideally

In practice

• The collector current depends on VCE:

• For a fixed value of VBE, as VCE increases, the reverse bias on the collector-base junction increases, hence the width of the depletion region increases.

− The quasi-neutral base width decreases � collector current increases.

Due to the Early effect, collector current increases with increasing VCE, for a fixed value of VBE.


The Early Voltage PS2

48

VA

VBC

IC

Ideally

In practice

• The Early voltage is obtained by drawing a line tangential to the transistor I-V characteristic at the point of interest.

• The Early voltage equals the horizontal distance between the point chosen on the I-V characteristics and the intersection between the tangential line and the horizontal axis.

• Early voltage is indicated on the figure by the horizontal dotted line


Punch-through and Early Voltage

49

C C

B A

B BA

CB

C

B

B I I

q W V

W

C

N

qNV

C

− ≈

⇒ = −

C C C

BC BC A A

dI I I

dV V V V= ≈

+

Need higher NB and WB or …

( ) ( )2 2, ,1 1BCBEi B i B qVqVn n

CB B B B

n nqD qDI e e

W N W Nββ= − + −

( )( )

1

C C

BC B

B B

B

B BC

C

B BCB

ddI dI

dV d q W dV

dI d

q

qN W

Q

dW dV

N

N

=

=

∞→

1 C

BCB

BqN

IC

W

= −

2C

B B B B

dI d

dW dW W W

ξ ζ = = −

C

B

I

W= −

BW

ξ=


Outline

50








8) Conclusions



Collector Doping

51

2,

2, , ,

i Bn E E

B p B p C p i E B

nD W N

W x x D n N≈

− −β

0

, ,

sCB

n C p B

Cx x

=+

κ ε

If you want low base dopingthen reduce collector doping even more to increase Collector depletion…..

B BA

CB

qN WV

C= −

N+

P N

NB

NC

NE

Base-Collector in reverse bias⇒Majority carriers only⇒No diffusion capacitance

⇒Reduce capacitance⇒Increase xnC


… but (!) Kirk Effect and Base Pushout

52

+

-

Nc

NB

WCWB

p-Base n-Collector

n+

xSpa

ce-C

harg

e D

ensi

ty

Nc

NB

WCWB

p-Base n-Collectorn+

xSpa

ce-C

harg

e D

ensi

ty

B B C CN x N x=

2 2

02bi BC B B C Cs

qV V N x N x − = + κ ε

( ) ( )2 2

0

' '2bi BC B B C C

s

qV V N n x N n x − = + + − κ ε

( ) ( )' 'B B C CN n x N n x+ = −

'

11

1 1

C

sat BBC C C

C

C sat C

J

q NNx x x

N q N

n

n Jυ

υ

++= =

− −

C satnJ qυ=Additional charge!Can be large compared to low doping


Kirk Effect and Base Pushout

53

n+emitter

pbase

ncollector

n+

x

Nc

NB

p-Base n-Collector n+

Spa

ce-C

harg

e D

ensi

ty

WCWB

n+

x

Nc

NB

p-Base n-Collector

Spa

ce-C

harg

e

WCWB

p-Base n-Collector n+

x

Spa

ce-C

harg

e

WCWB

WCIB WS

C

nc-Nc

E

⇒Increase bias & current

⇒Junction lost⇒High current dominates collector doping


Kirk Effect and Base Pushout

54

'

1

1

C

sat BC

sat

CC

C

J

q N

J

q Nx x

υ

υ

−

+=

,C crit sat C KJ q N Jυ= ≡

Can not reduce collector doping arbitrarily without causing base pushout


Kirk Effect

The Kirk effect occurs at high current densities in a bipolar transistor. The effect is dueto the charge density associated with the current passing through the base-collectorregion. As this charge density exceeds the charge density in the depletion region thedepletion region ceases to exist. Instead, there will be a build-up of majority carriersfrom the base in the base-collector depletion region. The dipole formed by thepositively and negatively charged ionized donors and acceptors is pushed into thecollector and replaced by positively charged ionized donors and a negatively chargedelectron accumulation layer, which is referred to as base push out. This effect occurs ifthe charge density associated with the current is larger than the ionized impuritydensity in the base-collector depletion region. Assuming full ionization, this translatesinto the following condition on the collector current density.

Key point : Under high current and low collector doping the depletion approximation is invalid in the C-B junction!


Perhaps High Doping in Emitter?

56

2,

2,

i Bn E

B p i E B

EnD W

W D n

N

Nβ ≈

Band-gap narrowing reduces gain significantly …

(Easki-like) Tunneling cause loss of base control …

,

,

/

/

B

g E

gE kT

n C VE

B p BC V

EE

kT

D N NW e

W D N e NN

N−

−= /gE kT E

B

Ne

N−∆≈


Summary

57

While basic transistor operation is simple, its optimum design is not.

In general, good transistor gain requires that the emitter doping be larger than base doping, which in turn should be larger than collector doping.

If the base doping is too low, however, the transistor suffers from current crowding, Early effects. If the collector doping is too low, then we have Kirk effect (base push out) with reduced high-frequency operation and if the emitter doping is too high then the gain is reduced.

ece606: solid state devices lecture 18 bipolar transistors...

Documents