ece606: solid state devices lecture 19 bipolar transistors ...ee606/downloads/... · ... solid...

Klimeck – ECE606 Fall 2012 – notes adopted from Alam

ECE606: Solid State DevicesLecture 19

Bipolar TransistorsDesign

Gerhard [email protected]

1


Outline

2

1) Current gain in BJTs

2) Considerations for base doping

3) Considerations for collector doping

4) Intermediate Summary

5) Problems of classical transistor

6) Poly-Si emitter

7) Short base transport

8) High frequency response

9) Conclusions

REF: SDF, Chapter 10


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

`̀


Current flow with Bias

5

EC-Fn,C

Fp,B-EV

EC-Fn,EV

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


Gummel Plot and Output Characteristics

6

CDC

BI

Iβ =

DCβ Common emitter Current Gain

VBE

2,

2,

i Bn E EDC

B p i E B

nD W N

W D n Nβ ≈


How to make a Good Silicon Transistor

7

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 ≈


Electrostatics in Equilibrium

8

( )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

BaseEmitter Collector

Two back to back p-n junction


Electrostatics in Equilibrium

9

( ) ( )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= −+

BaseEmitter Collector

VEB VCB

Assume current flow is small…fermi level is flat


Problem of Low Base Doping: Punch-through

10

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!

VBE is positive (forward bias) VBC is negative (reverse bias) => xp,BC grows


Problem of low Base-doping: Base Width Modulation

11

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!


The Early Voltage

12

• 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.

collector current increases with increasing VCE, for a fixed value of VBE.

VA

VBC

IC

Ideally

In practice

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

Device PioneerJim Early

VBC about 1VVA ideally infinity


The Early Voltage

13

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




Problem of Low Base-doping: Early Voltage

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= ≈

+


VA

VBC

IC

Ideally

In practice



Punch-through and Early Voltage

15

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

16






6) Poly-Si emitter



9) Conclusions



Collector Doping

17

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

18

+

-

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

19

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

20

'

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!


,

,

/

/

B

g E

gE kT

n C VE

B p BC V

EE

kT

D N NW e

W D N e NN

N−

−=

Perhaps High Doping in Emitter?

22

2,

2,

i Bn E

B p i E B

EnD W

W D n

N

Nβ ≈

Band-gap narrowing reduces gain significantly …

/gE kT E

B

Ne

N−∆≈

Very high doping can narrow the bandgap of a semiconductor!

If the emitter is extremely highly doped, then the bandgap in the emitter may be smaller than the base

=> Reduction in gain


Perhaps High Doping in Emitter?

23

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


Intermediate Summary

24

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.


Outline

25






6) Poly-Si emitter



9) Conclusions



Doping for Gain

26

2,

2,

i Bn E Edc

B p i E B

nD W N

W D n Nβ ≈

NE

NB

NC

Emitter doping: As high as possible withoutband gap narrowing

Base doping: As low as possible, withoutcurrent crowding, Early effect

Collector doping: Lower than base dopingwithout Kirk Effect

Base Width: As thin as possible withoutpunch through


How to make better Transistor

27

2,

2,

i Bn E E

B p i E B

nD W N

W D n Nβ ≈

Classical Shockley Transistor

Hetero-junction Bipolar Transistor

Graded Base transport

Polysilicon Emitter


Poly-silicon Emitter

28

N+

P N

SiGe intrinsic base Dielectric trench

N+P+N

P-

N-N+

CollectorEmitterBase

N+

Poly-silicon

emitter


Poly-silicon Emitter

29

1, ,

22p E pol s

E

y p

pI q qD

W

ppυ−= − = −

( )2,

, 1 1 1BEi B qVnn E

B B

nqDI n n e

W N= ≡ −β

N+ P

1

2 p E

p E s

D W

Dp W

p

υ=

+

, , 2 1p E

p E pp

o ys

ssE

lID

q p qpW

D W

υυ

υ= − = −

+×

( ), , 1pp si EEI Dq W p= −

, ,

, ,

p E poly

p E si p

s

sE

I

DI W

υυ

=+

WE

poly

p2p1

vs

Question: Why does poly only suppress the hole current, not electron current?

Ans. Polysilicon is not a ohmic contact and acts as rectifying contact. It blocks the easy passage of holes but lets electrons

pass through

vs Infinite at metal

Finite at poly


Gain in Poly-silicon Transistor

30

, , 1 , ,p E poly p B pols

s

p E

Ey

p

D WI p

Wq I

D

υυ

×= − =

+

( ), , 1pp si EEI Dq W p= −

, , ,

, , ,

p B poly B poly

p B s p BE

s

ssi iD

I I

I IW

υυ

=+≃

,

, ,,B si

B siC Cpoly

B poly B polyI

II I

I Iβ

= = ×

Poly suppresses base current, increases gain …

2,2,

( )1

si Bn E

B i Ep

sE

B

nD N

W n ND Wυ

υ→ × <<∵

2,

2,

i Bn E E

B p i E B s

p sEnD W N

W D n N

D W υυ

+ ≈ ×


Outline

31






6) Poly-Si emitter



9) Conclusions



How to make better Transistor

32

2 2, ,

2 2, ,

1i E i Bn E E n E

B p i B B B i E B s

n nD W N D N

W D n N W n Nβ

υ≈ → ×

Classical Shockley transistor

Heterojunction bipolar transistor

Graded Base transport

Polysilicon Emitter


Short-base Quasi-ballistic Transistor

33

N+ P

1 2, 2thE n

Bn

nnI qD

Wnq υ−= − = −

1

2 n B

n thB

D W

D W

n

n υ=

+, ,

, ,

n E ballistic

n E s n hi tB

th

D

I

WI

υυ

=+

∆nn1

υth

n2


Gain in short-base Poly-silicon Transistor

34

, , ,

, , ,

p B poly B poly

p B s p BE

s

ssi iD

I I

I IW

υυ

=+≃

, , , ,,

, , , ,

C ballistic C ballistic C si B sipoly ballistic

B poly C si B si B poly

I I I I

I I I Iβ

= = × ×

, ,

, ,

n E ballistic

n E s

th

thi n B

I

I D W

υυ

=+

Large devices, dinite diffusion length => small diffusion velocity=> thermal velocity is large => neglect diffusion velocity

2,

2,

i Bn E E

n B B p i E

th

th

E s

s

p

B

nD W N

D W W D n N

D W υυυυ

+ ≈ × × +

2,2,

i B E

i E B s

thn N

n N υυ→ × × vs Assume small

vs

Assume smallCompared to diffusion velocity

Quasi-Ballistic transport in very short base limits the gain …


Outline

35






6) Poly-Si emitter



9) Conclusions



Topic Map

36

Equilibrium DC Small signal

Large Signal

Circuits

Diode

Schottky

BJT/HBT

MOS


Small Signal Response

37

P+

N

P

C

E E

B

VEB(in)

VEC(out)

ICIB

log10 β

log10 f

fT

1

fβ

2

, ,

1

2 2 2B BC B

j BC j BET n sat C

W W k TC C

f D qI

= + + +

π υ

β ω( ) ≈ βDC

ωβ

ω

Desire high fT⇒High IC⇒Low capacitances⇒Low widths


Frequency Response

38

� The gain of an amplifier is affected by the capacitance associated with its circuit.� This capacitance reduces the gain in both the low and high frequency ranges of

operation.� The reduction of gain in the low frequency band is due to the coupling

and bypass capacitors selected. They are essentially short circuits in themid and high bands.

� The reduction of gain in the high frequency band is due to the internalcapacitance of the amplifying device, e.g., BJT, FET, etc.

� This capacitance is represented by capacitors in the small signal equivalent circuit for these devices. They are essentially open circuits in the low and mid bands.


Small Signal Response (Common Emitter)From Ebers Moll Model

39

Cµ

( )1 F FIα−

Cπ

IRF F R RI Iα α−

( )/0 1BEqV kT

F FI I e= −

( )11 F F

BE

B B

BE B

Idd q

r dV dV T

I

k

I

π

α =−

= =

( )F C

BE Bm

Fd qI

dV Tg

I

k

α= =

( )F F B BEmm Eg VI gδ δα υ= =

P+

N

P

C

E E

B

VEB(in)

VEC(out)

ICIB

IB

1 C

DC B

qI

k Tβ=

DC Circuit => AC small signal CircuitBC In reverse bias, IR=0

Cµ

Cπrππππ gmVBE

IBIC

IE


Short Circuit Current Gain

40

( )( )1

1T

T mT

T

m j gf

j C Cj C j

g

Cr

C

π µπ µ

π

µωβ

ω ω ω−

≡ = ≈ +

+ +

( )1

m BE CB

BE BE BCB

Cj

f

j C j

C

Ci

r

gi

π µπ

µω υβ

υ ω υ ω

υ

υ

+= =

+ +

Cπrπ

m BEg υ

Cµ

( ) ( ), , , ,

1 1

2 j BC jT

BBE d B

B

m C CC d BE

T

C k T k T

g

CC C C C

f qI qIπ µ

πω+

≡ = = + + +

,,

d BCB Bd BC

C C BE C

Ck T dQC

qI dI dV dI= =

E

CB


Base Transit Time

43

B B

C C

dQ Q

dI I=

N+ P

∆n n1

21

1

12

2

BB

n

B

q nW Wn Dq

W

= =

Ref. Charge control model

Base transit time


Collector Transit Time

44

?BC

sat

W=τυ

N+ P

1

2qi τ× × =

, 2 2BC

eff BCsat

q W

i

ττυ

= = =

t

i τ

Electrons injected into collector depletion region – very high fields more than diffusion => drift => acceleration of carriersCharge imaged in collector


Putting the Terms Together

45

2

, ,

1

2 2 2B BC

T n sat

Bj BC j BE

C

W W

f D

k TC C

qI

= + +

+

π υ

Base transit time

Collector transit time

Junction charging time

10log Tf

10log CI

Kirk Current

Do you see the motivation to reduce WB and WBC as much as possible? What problem would you face if you push this too far ?

KI

Increasing IC too high reduces WBC and increases the overall capacitance=> frequency rolls off….


High Frequency Metrics

46

( ) ( )2

, ,

1

2 2 2B BC B

j BE j BCT n sat C

ex c cb

W W k T qC C R

f DR C

Iτ

π υ= = + + ++ +

(current-gain cutoff frequency, fT)

(power-gain cutoff frequency, fmax)

fmax =fT

8π RbbCcbi


Summary

47

We have discussed various modifications of the classical

BJTs and explained why improvement of performance

has become so difficult in recent years.

The small signal analysis illustrates the importance of

reduced junction capacitance, resistances, and transit

times.

Classical homojunctions BJTs can only go so far, further

improvement is possible with heterojunction bipolar

transistors.

ece606: solid state devices lecture 19 bipolar transistors ...ee606/downloads/... · ... solid...

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