Lundstrom ECE-606 S13

Notes for ECE-606: Spring 2013

Bipolar Junction

Transistors (BJTs)

Professor Mark Lundstrom Electrical and Computer Engineering

Purdue University, West Lafayette, IN USA lundstro@purdue.edu

1 3/21/13

2

Reversve biased PN junction

Fig. 6.9, Semiconductor Device Fundamentals, R.F. Pierret

Current is small

3

PN junction in reverse bias

Lundstrom ECE-606 S13

Fp

EC

Fn

EV

hf > EG

Large currents can flow when there are excess minority carriers on the P-side (or N-side).

4

excess carriers another way

Lundstrom ECE-606 S13

FpEC

FnEV

Fn VBE > 0

p0P ≈ NA

Fp

E

C B

VCB > 0

25

generic transistor

Lundstrom ECE-606 S13

I1

3

V32

ΔI1 = gmΔV32

gm =∂I1∂V32 V12

1

I2

6

BJT

Lundstrom ECE-606 S13

IC

VBE

ΔIC = gmΔVBE

gm = ∂IC∂VBE VCE

IE

E

C

B VCE

VCB =VCE −VBE

7

invention of the transistor

1926

C.T. Sah, “Evolution of the Field-Effect Transistor – From Conception to VLSI,” Proc. IEEE, 76, 1280, 1988

8

“discovery” of the bipolar transistor

0http://www.porticus.org/bell/images/transistor1.jpg

9

inventors of the bipolar transistor

http://en.wikipedia.org/wiki/File:Bardeen_Shockley_Brattain_1948.JPG

NPN bipolar transistor

10

IC

IB VCE

VBE

VCB

IE

IB + IC = IE

VBE +VCB = VCE

KCL:

KVL:

NPN bipolar transistor

11

IC

IB VCE

VBE

VCB

IE n+ emitter

p base

n collector

n+

C

B

E

transistor structures

12

n+ emitter

p base

n collector

n+

p base n-collector

n+

n+

double

diffused

BJT

common base (active region)

13

IC

IB VCE

VBE

VCB

IE

IC

VCBVEB IB

IE

BE: FB BC: RB

VEB < 0VCB > 0

common emitter (active region)

14

IC

IB VCE

VBE

VCB

IE

BE: FB BC: RB

VBE > 0VCB = VCE −VBE > 0

IC

IB VCE

IEVBE

BJT operation: active region

15 15

n+ emitter

p base

n collector

n+

FB RB

1) energy band diagram

BJT operation: active region currents

16 16

n+ emitter

p base

n collector

n+

FB RB IE IC

IB

IEn

IEpIE = IEn + IEp

ICn

ICp

ICn ≈ IEn >> ICp

IC ≈ IEn

IB ≈ IEp

(neglect base recombination)

2) currents

BJT operation: active region

17 17

n+ emitter

p base

n collector

n+

FB RB IE ICIEn

IEpIE = IEn + IEp

IEn

IC ≈ IEn

IB = IEp

3) Boundary conditions at the beginning and end of the base.

BJT operation: active region

18

18 xp

x

Δn x( )

WB+xp

n+ emitter

p base

n collector

n+

FB RB IE ICIEn

IEpIE = IEn + IEp

IEn

IC ≈ IEn

IB = IEp

Δn(0) = ni2

NAB

⎛⎝⎜

⎞⎠⎟eqVBE kBT −1( )

Δn(WB + xp ) =ni2

NAB

⎛⎝⎜

⎞⎠⎟eqVBC kBT −1( )

base diffusion current

19

0 x

Δn x( ) Δn 0( )

WB

Δn WB( ) ≈ 0Δn(0) = ni

2

NAB

⎛⎝⎜

⎞⎠⎟eqVBE kBT −1( )

IEn = qAEni2

NAB

⎛⎝⎜

⎞⎠⎟Dn

WB

eqVBE /kBT −1( )

IEn

IEn = −qAEDndn(x)dx

= qAEDnΔn(0)WB

BJT operation: beta

20 20

n+ emitter

p base

n collector

n+

FB RB IE ICIEn

IEpIE = IEn + IEp

ICn

IC ≈ IEn

IB = IEp

IEn = qAEni2

NAB

⎛⎝⎜

⎞⎠⎟Dn

WB

eqVBE /kBT −1( ) ≈ IC

IEp = qAEni2

NDE

⎛⎝⎜

⎞⎠⎟Dp

WE

eqVBE /kBT −1( ) ≈ IBβ =

ICIB

=NDE

NAE

Dn

Dp

WE

WB

BJT operation: transconductance

21

21

n+ emitter

p base

n collector

n+

FB RB IE ICIEn

IEpIE = IEn + IEp

IEn

IC ≈ IEn

IB = IEp

IC = qAEni2

NAB

⎛⎝⎜

⎞⎠⎟Dn

WB

eqVBE /kBT −1( )= IC0 e

qVBE /kBT −1( )

gm =∂IC∂VBE

=IC

kBT q( )

gm =ID

VGS −VT( )

BJT operation: gamma

22 22

n+ emitter

p base

n collector

n+

FB RB IE ICIEn

IEpIE = IEn + IEp

IEn

IC ≈ IEn

IB = IEp

IEn = qAEni2

NAB

⎛⎝⎜

⎞⎠⎟Dn

WB

eqVBE /kBT −1( ) ≈ IC

IEp = qAEni2

NDE

⎛⎝⎜

⎞⎠⎟Dp

WE

eqVBE /kBT −1( ) ≈ IBγ =

IEnIEn + IEp

< 1

BJT operation: base transport factor

23 23

n+ emitter

p base

n collector

n+

FB RB IE ICIEn

IEpIE = IEn + IEp

ICn

IC ≈ IEn

IB = IEp

IEn = qAEni2

NAB

⎛⎝⎜

⎞⎠⎟Dn

WB

eqVBE /kBT −1( )

IEp = qAEni2

NDE

⎛⎝⎜

⎞⎠⎟Dp

WE

eqVBE /kBT −1( ) ≈ IB

ICn = αT IEn ≈ IC

BJT operation: IE and IC

24 24

n+ emitter

p base

n collector

n+

FB RB IE ICIEn

IEpIE = IEn + IEp

ICn

IC ≈ IEn

IB = IEp

ICn = αT IEn = IC

γ =IEn

IEn + IEp=IEnIE

IC = αT IEn = αTγ IE = αdcIE

IB = IE − IC = IC β

IC = αdcIE

αdc = αTγ

β =αdc

1−αdc

common emitter (active region)

25

IC

IB VCE

VBE

VCB

IE

IC = βIB

IB VCE >VBE

IE = β +1( ) IB

VBE > 0

IV characteristics

Gummel plot

26

log J( )

VBE

JC = JC0 eqVBE /kBT −1( )

JB = JB0 eqVBE /nkBT −1( )

NPN bipolar transistor

27

BE: FB BC: RB

VBE > 0VCB = VCE −VBE > 0

IC

IB VCE

IEVBE

Pierret, Fig. 10.4

active saturation

cut-off inverted active

BJT operation: active region

28

28

xp x

Δn x( )

WB+xp

Δn(0) = ni2

NAB

⎛⎝⎜

⎞⎠⎟eqVBE kBT −1( )

Δn(WB + xp ) =ni2

NAB

⎛⎝⎜

⎞⎠⎟eqVBC kBT −1( )

Δn(WB + xp ) ≈ 0Pierret, Fig. 10.4

active saturation

cut-off inverted active

VBE > 0

VCB > 0

BJT operation: saturation region

29

29

xp x

Δn x( )

WB+xp

Δn(0) = ni2

NAB

⎛⎝⎜

⎞⎠⎟eqVBE kBT −1( )

Δn(WB + xp ) =ni2

NAB

⎛⎝⎜

⎞⎠⎟eqVBC kBT −1( )

Δn(WB + xp ) >> 0Pierret, Fig. 10.4

active saturation

cut-off inverted active

VBE > 0VCB < 0

BJT operation: cut-off region

30

30

xp x

Δn x( )

WB+xp

Δn(0) = ni2

NAB

⎛⎝⎜

⎞⎠⎟eqVBE kBT −1( )

Δn(WB + xp ) =ni2

NAB

⎛⎝⎜

⎞⎠⎟eqVBC kBT −1( )

Pierret, Fig. 10.4

active saturation

cut-off inverted active

VBE ≤ 0

VCB ≥ 0

BJT operation: inverted active region

31

31

xp x

Δn x( )

WB+xp

Δn(0) = ni2

NAB

⎛⎝⎜

⎞⎠⎟eqVBE kBT −1( ) ≈ 0

Δn(WB + xp ) =ni2

NAB

⎛⎝⎜

⎞⎠⎟eqVBC kBT −1( )

Δn(WB + xp ) >> 0 Pierret, Fig. 10.4

active saturation

cut-off inverted active

VBE ≤ 0VCB < 0

NPN bipolar transistor (active region)

32

1)  Base recombination (base transport factor)

2)  Speed (frequency response)

3)  Base width modulation (Early effect)

4)  Typical doping profiles

5)  Kirk effect

base recombination

33

0 x

Δn x( )

Δn 0( )

WB

Δn WB( ) ≈ 0

IEn

quasi-neutral base

ICn ≈ IEn

IEn − ICn ≈ AEqΔn 0( )WB

2τ n

IEn −αT IEn ≈ AEqΔn 0( )WB

2τ n

1−αT ≈AE

qΔn 0( )WB

2τ nIEn

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

IEn = qAEDnΔn 0( )WB

αT ≈ 1− 12

WB

Ln

⎛⎝⎜

⎞⎠⎟

2

speed (base transit time)

34

0 x

Δn x( )

Δn 0( )

WB

Δn WB( ) ≈ 0

IEn

quasi-neutral base

ICn ≈ IEn

IC = qAEDnΔn 0( )WB

IC =QB

tt

QB =qΔn 0( )WB

2

tt =WB

2

2Dn

fT =12πtt

effects of saturation on speed

35 Pierret, Fig. 12.7

Early effect (base width modulation)

36

BE: FB BC: RB

VBE > 0VCB = VCE −VBE > 0

IC

IB VCE

IEVBE

Pierret, Fig. 10.4

active saturation

cut-off inverted active

Why is there an output conductance (resistance)?

Early effect (base width modulation)

37

n+ emitter

p base

n collector

n+

FB RB IE ICIEn ICn

IC ≈ IEn

Width of the quasi-neutral base is what matters. Width of the CB depletion region depends on base doping, collector doping, and revers bias across the C-B junction.

IC ∝ DnΔn 0( )WB

typical doping profiles

38 38

n+ emitter

p base

n collector

n+

FB RB IEn

IEp

IEn ∝ni2

NAB

IEp ∝ni2

NDE

γ =IEn

IEp + IEn≈

1

1+ NAB

NDE

⎛⎝⎜

⎞⎠⎟

Emitter must be doped more heavily than the base.

HBT

39 39

n+ emitter

p base

n collector

n+

FB RB

EGE EGB EGC

IEn

IEp

IEn ∝niB2

NAB

IEp ∝niE2

NDE

γ =IEn

IEp + IEn≈

1

1+ niE2

niB2NAB

NDE

⎛⎝⎜

⎞⎠⎟

Freedom to dope the base heavily

collector doping

40 40

n+ emitter

p base

n coll

n+

FB RB IEn

IEp

ρ = qNDJC = q Dn

WB

Δn 0( )

JC = qnυsatn ≈ ND

“base push out” Kirk effect

common base (active region)

41

IC

IB VCE

VBE

VCB

IE

IC = αdcIE

VCB > 0VEB < 0

IE

IB = IC β

IV characteristics

common base (active region)

42

IC

VCBVEB IB

IE

BE: FB BC: RB

VEB < 0VCB > 0

Pierret, Fig. 10.4

active

cut-off

saturation