Institute of Solid State PhysicsTechnische Universität Graz

13. Bipolar transistors

Jan. 15, 2019

Institute of Solid State Physics

bipolar transistorsTechnische Universität Graz

collector base emitter

np

n+

lightly doped p substrate

npn transistor

Used in front-end high-frequency receivers (mobile telephones).

p+n+

bipolar transistors

p+

abrupt junction

x

E-xp xn

Ap

eNE x x

Dn

eNE x x

x

-xp

xn

+

-

eND

eNA

2

2

02

02

Ap p

Dn n

eN xV xx x x

eN xV xx x x

0

0

p

n

x x

x x

2ln D Abi B

i

N NeV k Tn

dEdx

dV Edx

Forward bias, V > 0

Electrons and holes are driven towards the junction.The depletion region becomes narrower

Minority electrons are injected into the p-regionMinority holes are injected into the n-region

np(xp) pn(xn)

+

0

0

( ) exp

( ) exp

p p pB

n n nB

eVn x nk T

eVp x pk T

0 exp bee

B

eVpk T

Reverse bias, V < 0

Electrons and holes are driven away from the junction.The depletion region becomes wider

Minority electrons are extracted from the p-region by the electric fieldMinority holes are extracted from the n-region by the electric field

+

np(xp) pn(xn)

0

0

( ) exp

( ) exp

p p pB

n n nB

eVn x nk T

eVp x pk T

pnp transistor, no bias

pnp transistor, forward active bias

The base-emitter voltage controls the minority carriers injected from the emitter to the base. These diffuse to the base-collector junction and are swept into the collector.

Always dissipate power due to the forward bias

Long/Short diode

n-type

,diff p pdpJ eDdx

0,

( )n n ndiff p p p

n

p x pdpJ eD eDdx d

pn(xn)

pn0

dn x

pn(x)Short diode

dn << Lp

Metal contact is much closer to the depletion region than the diffusion length

Long diode dn >> Lppn(xn)

Minority carrier concentration

emitter (n+) base (p) collector (n)contact contact

pe0

nb0 pc0

/0 1be BeV k T

eEp be p

e e

p eI eA D

W x

xe We Web WbcxcWc

/ /0

be B bc BeV k T eV k Tb

En be nbc be

n e eI eA D

W W

0 exp beb

B

eVnk T

0 exp bcb

B

eVnk T

0 exp bee

B

eVpk T

0 exp bcc

B

eVpk T

Emitter current

0 / /0 01 1be B bc Bbe p e eV k T eV k Tbe n b be n bE En Ep

eb e bc be bc be

eA D p eA D n eA D nI I I e eW x W W W W

/ /1 1be B bc BeV k T eV k TE ES R CSI I e I e

pe0

nb0 pc0

xe We Web WbcxcWc

0 exp bcb

B

eVnk T

0 exp bee

B

eVpk T

0 exp beb

B

eVnk T

Collector current

emitter (n+) base (p) collector (n)contact contact

/0 1bc BeV k T

ccp bc p

c c

p eI eA D

x W

/ /0

be B bc BeV k T eV k Tb

cn bc nbc eb

n e eI eA D

W W

pe0

nb0 pc0

xe We Web WbcxcWc

0 exp beb

B

eVnk T

0 exp bcb

B

eVnk T

0 exp bee

B

eVpk T

0 exp bcc

B

eVpk T

Collector current

0/ /0 01 1be B bc Bbc p ceV k T eV k Tbc n b bc n bc cp cn

bc be c c bc be

eA D peA D n eA D nI I I e eW W x W W W

/ /1 1be B bc BeV k T eV k Tc cp cn F ES CSI I I I e I e

pe0

nb0 pc0

xe We Web WbcxcWc

0 exp bcb

B

eVnk T

0 exp bee

B

eVpk T

0 exp beb

B

eVnk T

Ebers-Moll model

/ /1 1be B bc BeV k T eV k TC F ES CSI I e I e

/ /1 1be B bc BeV k T eV k TE ES R CSI I e I e

IE

IB

IC

/ 1be BeV k TF ESI I e / 1bc BeV k T

R CSI I e

R RI F FI

B E CI I I

emitter (n+) base (p) collector (n)contact contact

pe0

nb0 pc0

xe We Web WbcxcWc

0 exp beb

B

eVnk T

0 exp bcb

B

eVnk T

0 exp bee

B

eVpk T

0 exp bcc

B

eVpk T

Not an npn transistor

Emitter efficiency

/0 1be BeV k T

eEp be p

eb e

p eI eA D

W x

/ /0

be B bc BeV k T eV k Tb

En be nbc be

n e eI eA D

W W

For e ~ 1, Wbc - Wbe << Lb, Web - xe and nb0 >> pe0

Small base width and heavy emitter doping

for npn

2i

De

nN

2i

Ab

nN

11 /

Ene

En Ep Ep En

II I I I

neutral base width

Base transport factor

c

En

IBI

ratio of the injected current to the collected current

recombination in the base would reduce the base transport factor

A thin base with low doping results in a base transport factor ~ 1

Current transfer ratio

Ce

E

I BI

~ 1 for a good BJT

Transistor modes

1. Forward active: emitter-base forward, base-collector reverse2. Saturation: emitter-base forward, base-collector forward3. Reverse active: emitter-base reverse, base-collector forward4. Cut-off: emitter-base reverse, base-collector reverse

Ebers-Moll model

/ /1 1be B bc BeV k T eV k TC F ES CSI I e I e

/ /1 1be B bc BeV k T eV k TE ES R CSI I e I e

IE

IB

IC

/ 1be BeV k TF ESI I e / 1bc BeV k T

R CSI I e

R RI F FI

B E CI I I

Common base configuration

/ /1 1be B bc BeV k T eV k Tc F ES CSI I e I e

/ /1 1be B bc BeV k T eV k TE ES R CSI I e I e

solve for Vbe

saturation

active

cutoff IE < 0

http://lamp.tu-graz.ac.at/~hadley/psd/L13/commonbase/pnp_current.html

0 0

0

be p e be n bES

eb e bc be

be n bR CS

bc be

eA D p eA D nIW x W WeA D nIW W

Ebers - Moll Model

0

0 0

bc n bF ES

bc be

bc p c bc n bCS

c c bc be

eA D nIW W

eA D p eA D nIx W W W

Common emitter configuration

/ /1 1be B bc BeV k T eV k TE ES R CSI I e I e

/ /1 1be B bc BeV k T eV k Tc F ES CSI I e I e

B E CI I I

http

://la

mp.

tu-g

raz.

ac.a

t/~ha

dley

/psd

/L13

/com

mon

emitt

er.p

hp

current amplification ~100

Current amplification factor

Cfe

B

IhI

B E CI I I

1 1B CI I

1 1C e

B e

I BI B

~ 50 - 500

C EI I

for common emitter configuration

The Art of ElectronicsHorowitz and Hill

Transconductance

Cm

be

IgV

The transconductance can be very high.

/ /1 1be B bc BeV k T eV k Tc F ES CSI I e I e

/be BeV k TF ES C Bm

B B B

e I eI e Ig ek T k T k T

The first term depends on Vbe

Early effect

/ /1 1be B bc BeV k T eV k Tc F ES CSI I e I e

/ /1 1be B bc BeV k T eV k TE ES R CSI I e I e

B E CI I I

Ebers - Moll:

0 0be p e be n bES

eb e bc be

eA D p eA D nIW x W W

0 0bc p c bc n bCS

c c bc be

eA D p eA D nIx W W W

IES and ICS are treated as constants but the depletion widths Wbc, Wbe, Wc,and We depend on the voltages.

pe0

nb0 pc0

xe We Web WbcxcWc

0 exp beb

B

eVnk T

0 exp bcb

B

eVnk T

0 exp bee

B

eVpk T

0 exp bcc

B

eVpk T

Minority carrier concentration

pe0

pc0

xe xc

0 exp beb

B

eVnk T

0 exp bcb

B

eVnk T

0 exp bee

B

eVpk T

0 exp bcc

B

eVpk T

xn1 xp1 xn2xp2

Early effect

Common emitter configurationBase width modulation: smaller width increases the diffusion current and increases the gain.

Punchthrough: The neutral base width goes to zero and all gain is lost.Lightly dope the collector -> voltage drops in collector. Makes circuit slower.

http

://la

mpx

.tugr

az.a

t/~ha

dley

/psd

/L13

/com

mon

_e_e

arly

.php

IC ~ IB

Common emitter configuration

IC ~ IB amplifier

Small signal response

Low input impedance amplifier

Vcc

VresistorVtransistor

Small signal response

input conductance: cm

EB

igv

transconductance:

c B EB EBi i g v transistor man

BEB

EB

igv

Small signal response

01f f 0Tf f

1

Heterojunction bipolar transistors