EE 5340Semiconductor Device TheoryLecture 19 – Spring 2011

Professor Ronald L. Carterronc@uta.edu

http://www.uta.edu/ronc

©rlc L19-31Mar2011

2

Test 2 – Tuesday 05Apr11• 11 AM Room 129 ERB• Covering Lectures 11 to19• Open book - 1 legal text or ref.,

only.• You may write notes in your book.• Calculator allowed• A cover sheet will be included with

full instructions. For examples see http://www.uta.edu/ronc/5340/tests/.

npn BJT currents in the forward active region ©RLC

©rlc L19-31Mar2011

3

IC =

JCAC

IB=-(IE+IC )

JnE JnC

IE = -JEAE

JRB=JnE-JnC

JpE

JGC

JREJpC

©rlc L19-31Mar2011

4

E current equations mode npn BJT (w/o

gen/rec)

ditto. , L/xsinh

V/VfexpL/xtanhV/Vfexp

LnqDJ

dir. x' in , 1VVexpL/xtanhL

pqDJ

xxnqDJ- ,x'

'xp-qDJ

BBtBC

BBtBE

BB0B

nE

tBE

EEEE0E

pE

0xB

BnE0x'

EEpE

©rlc L19-31Mar2011

5

C current equations in npn BJT (w/o gen/rec)

BB

tBC

BB

tBE

B

B0BnC

tBC

CCC

C0CpC

xxB

BnC0x"

CCpC

LxVVf

LxVVf

LnqDJ

1VV

LxLpqDJ-

xxnqDJ- ,x"

xpqDJ-B

/tanh/exp

/sinh/exp

exp/tanh

"

©rlc L19-31Mar2011

6

Ebers-Moll Model(Neglecting G-R curr)

(Fig. 9.30*)

-JEAE=IE JCAC=IC

©rlc L19-31Mar2011

Source of Ebers-Moll Equations (E)

tBE

FF

BBB

B0B

tBC

RR

E

ES

BBB

B0B

EEE

E0EES

BB

tBC

BB

tBE

B

B0BnE

t

BE

EEE

E0EpE

EEnEpEE

V/VfexpJ

L/xsinhLnqD

V/VfexpJ

AI

L/xtanhLnqD

L/xtanhLpqDJ

L/xsinhV/Vfexp

L/xtanhV/Vfexp

LnqDJ

1VVexp

L/xtanhLpqDJ

A/IJJJ

αα

7

©rlc L19-31Mar2011

Source of Ebers-Moll Equations (C)

tBC

RR

BBB

B0B

tBE

FF

C

CS

BBB

B0B

CCC

C0CCS

BB

tBE

BB

tBC

B

B0BnC

t

BC

CCC

C0CpC

CCnCpCC

V/VfexpJ

L/xsinhLnqD

V/VfexpJ

AI

L/xtanhLnqD

L/xtanhLpqDJ

L/xsinhV/Vfexp

L/xtanhV/Vfexp

LnqDJ

1VVexp

L/xtanhLpqDJ-

A/IJJJ

αα

8

©rlc L19-31Mar2011

E-M model equations

BB

BC2i

CSRSESFBB

BE2i

S

tBC

CSRt

BEESE

tBE

ESFt

BCCSC

xNDAqnIIIxN

DAqnI gives iprelationsh yreciprocit The

VVfIV

VfII

VVfIV

VfII

expexp

expexp

9

©rlc L19-31Mar2011

Fig. 9.30*

-JEAE

= IE

JCAC

= IC

E

B

C

RIR FIF

Ebers-Moll Model (Neglecting G-R curr)

10

©rlc L19-31Mar2011

E-M linking current model

ECCCCTEC

I-III

CBt

BCRS

REC

IV

VfexpII

tBE

FS

FCC

EB

VVfexpII

I

B

E

C

11

©rlc L19-31Mar2011

tBC

tBESEC

tBCS

tBE

FSE

tBES

tBC

RSC

S

VVexpV

VexpII

branch E-C the links"" that current TheV

VfexpIVVfexpII

VVfexpIV

VfexpII

become eqns. M-E the ,I of terms In

12

E-M linking current model (cont)

©rlc L19-31Mar2011

E-M linking current model (cont)

EBECE

CBECC

FF

Ft

BEFS

EB

RR

Rt

BCRS

CB

I-II andIII sdefinition with eqns

M-E the for values same the give still

1 with VVfexpII

& 1 with VVfexpII

:Similarly

13

©rlc L19-31Mar2011

14

More non-ideal effects in BJTs

a Base-width modulation (FA: xB changes with changes in VBC)

a Current crowding in 2-dim base• High-level injection (minority

carriers g.t. dopant - especially in the base).

• Emitter Bandgap narrowing (NE ~ density of states at cond. band. edge)

• Junction breakdown at BC junction

©rlc L19-31Mar2011

15

Recombination/Generation

Currents (FA)

CBCB

BCeff,

1gen

BCeff,BCbiC

BCgen

BCiGC

1rec

BEt

BErec

iBERE

NNNNN and

rate, ionrecombinat the is and DR CB

the is qNVV2W where ,2

WqnJ

.rate ionrecombinat the is and DR

EB the is W where ,V2Vexp2

nqWJ

©rlc L19-31Mar2011

16

FA npn figure of merit – emitter efficiency

1L/x and L/x if ,xDNxDN1

L/xtanhLDnL/xtanhLDp1

VV if ,J/J11

JJJ

EEBB1

EBEBEB

1

EEEB0BBBBE0E

tBEnEPEPEnE

nE

©rlc L19-31Mar2011

17

FA npn figure of merit – base transport factor

2

BB

BBtBE

BBtBET

BBtBCtBE

nE

nCT

Lx1L

x0L

x , Lx1

LxVV1LxVV

Lx and VV , VV For

. JJ factor, transport base The

coshlim/cosh

/cosh/exp/cosh/exp

©rlc L19-31Mar2011

18

FA npn figure of merit – recombination factor

BB1

tBE

0BBOBBEi

nE1

0

BEtBE

0iBER

RnEnE

pERnEpEnE

Lx for ,V2VexpDn2

xxn1

,J from rate, ionrecombinat the is and DR

EB the is x where ,V2Vexp2

nqxJ

JJJ

JJJJJ

factor, Recomb

©rlc L19-31Mar2011

19

Common base current gain, F

TpEREnE

pEnE

nEnC

pEnEnE

EpCGC

pEREnEnC

EC

pEREnE

pCGCnC

EC

0

JJJJJ

JJ

JJJ as

Factors .I of fctns not are J and J

since , JJJJ

II :signal small

JJJJJJ

II gain, current DC

T

©rlc L19-31Mar2011

20

Common base current gain, F (continued)

1

tBE

0BBOBBEi

2B

2B

EBEBEB

1

tBE

0BBOBBEi

1

2B

2B

BBtBEBBtBE

T

1

EBEBEB

1

EEEB0BBBBE0E

V2VexpDn2

xxnL2

xxDNxDN1

V2VexpDn2

xxn1

L2x1L/xcoshV/Vexp1

L/xcoshV/Vexp

xDNxDN1L/xtanhLDn

L/xtanhLDp1

©rlc L19-31Mar2011

21

Common emitter current gain, F

lim. , V2VexpDn2

xxn , xDNxDN

L2x

lim. , V2VexpDn2

xxn , L2x

xDNxDN

limited. or limited is BJT a Usually,V2VexpDn2

xxnL2

xxDNxDN

1 so , 1 ; III with ,II

TtBE

0BBOBBEi

EBEBEB

2B

2B

tBE

0BBOBBEi

2B

2B

EBEBEB

T

1

tBE

0BBOBBEi

2B

2B

EBEBEB

00

0CBEBC

0

©rlc L19-31Mar2011

Common base current gain, F (cont.)

1

tBE

0BBOBBEi

2B

2B

EBEBEB

1

tBE

0BBOBBEi

1

2B

2B

BBtBEBBtBE

T

1

EBEBEB

1

EEEB0BBBBE0E

V2VexpDn2

xxnL2

xxDNxDN1

V2VexpDn2

xxn1

L2x1L/xcoshV/Vexp1

L/xcoshV/Vexp

xDNxDN1L/xtanhLDn

L/xtanhLDp1

22

©rlc L19-31Mar2011

Common emitter current gain, F

lim. , V2VexpDn2

xxn , xDNxDN

L2x

lim. , V2VexpDn2

xxn , L2

xxDNxDN

limited. or limited is BJT a Usually,V2VexpDn2

xxnL2

xxDNxDN

1 so , 1 ; III with ,II

TtBE

0BBOBBEi

EBEBEB

2B

2B

tBE

0BBOBBEi

2B

2B

EBEBEB

T

1

tBE

0BBOBBEi

2B

2B

EBEBEB

00

0CBEBC

0

23

©rlc L19-31Mar2011

References* Semiconductor Physics and

Devices, 2nd ed., by Neamen, Irwin, Boston, 1997.

**Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, John Wiley, New York, 1986.

24