Semiconductor Device Modeling and

Characterization – EE5342 Lecture 21 – Spring 2011

Professor Ronald L. Carterronc@uta.edu

http://www.uta.edu/ronc/

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Linking current E-M circuit model

ECCC

CTEC

I-I

II

CB

t

BC

R

S

R

EC

I

V

Vfexp

II

t

BE

F

S

F

CC

EB

V

Vfexp

II

I

B

E

C

2

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Non-ideal effects in BJTs• Recombination/Generation effects

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

• 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

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npn Base-width mod.(Early Effect) Fig 9.15*

xn

qDJ nn

BC

B

BBC

BB

BC

BBjC

BC

j

Vx

xJ

VJ

xJ

xJ

Vx

AqNCV

Q

pn

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Base-width modulation(Early Effect, cont.)

Fig 9.16*

ACEB

jC

CE

B

jC

B

BC

B

BCB

VVI

Q

C

VI

AqN

C

xJ

Vx

AxJ

VI

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Emitter currentcrowding in baseFig 9.21*

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Interdigitated basefixes emitter crowdingFig 9.23*

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Base region high-level injection (npn)

HLI in ennp :Note

Nennp when

n

NlnV2V when HLI aseB

npennp

edges DR @ Junction the of Law

tBE

tBE

tBE

V/V2i0BB

BV2/V

i0B0B

i

BtBE

0xBBV/V2

i0'xEE

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Effect of HLI innpn base regionFig 9.17*

BB np ,

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Effect of HLI in npnbase region (cont)

HLI).-E for changes J (notice markedly

change to factor JJ/J causing

, L/xsinh

V/VfexpnL/xtanh

V2/Vexpn

LqD

J

:as region) HLI the (in rewritten be must

, L/xsinhV/Vfexp

L/xtanh

V/Vfexp

LnqD

J

0x at current electron the lyConsequent

pE

pEnEnE

BB

tBCB0

BB

tBEi

B

BnE

BB

tBC

BB

tBE

B

B0BnE

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Effect of HLI in npnbase region (cont)

markedly. change

to /JJ factor the causing

, L/xtanh

V/VfexpnL/xsinh

V2/Vexpn

LqD

J

:as region) HLI the (in rewritten be must

, L/xtanhV/Vfexp

L/xsinh

V/Vfexp

LnqD

J

xx at current electron the eFurthermor

nEnCT

BB

tBCB0

BB

tBEi

B

BnC

BB

tBC

BB

tBE

B

B0BnC

B

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Emitter region high-level injection (npn)

HLI in ennp :Note

Nennp so

n

NlnV2V when HLI Emitter

npennp

edges DR @ Junction the of Law

tBE

tBE

tBE

V/V2i0EE

EV2/V

i0E0E

i

EtBE

0xBBV/V2

i0'xEE

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Effect of HLI innpn emitter region

HLI).-B for changes the to addition in

change to factor JJ/J causing

, V2

Vexp

L/xtanhL

nqDJ as

n/NlnVV (for rewritten be must

, 1V

Vexp

L/xtanhL

pqDJ

0x' at current hole the lyConsequent

pEnEnE

t

BE

EEE

iEpE

iEtBE

t

BE

EEE

E0EpE

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Effect of HLI innpn base regionFigs 9.18 and 9.19*

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Bandgap narrowing effects Fig 9.20*

kT

Eexpnn

17e2

NmV10E

E0NEE

g2i

2iE

dg

gdgg

21

slope Replaces ni2

throughout

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Junction breakdown at BC junction• Reach-through or punch-through

when WCB and/or WEB become large enough to reduce xB to zero

• Avalanche breakdown when Emax at EB junction or CB junction reaches Ecrit.

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The npn Gummel-Poon Static ModelC

E

B

B’

ILC

ILEIBF

IBRICC - IEC =

IS(exp(vBE/NFVt

- exp(vBC/NRVt)/QB

RC

RE

RBB

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Gummel Poon npnModel Equations

IBF = ISexpf(vBE/NFVt)/BF

ILE = ISEexpf(vBE/NEVt)

IBR = ISexpf(vBC/NRVt)/BR

ILC = ISCexpf(vBC/NCVt)

QB = (1 + vBC/VAF + vBE/VAR )

{½ + ¼ + (BFIBF/IKF + BRIBR/IKR)}

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Making a diode from the GP BJT modelC

E

B

B’

ILC

ILEIBF

IBRICC - IEC =

IS(exp(vBE/NFVt

- exp(vBC/NRVt)/QB

RC

RE

RBB

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Making a completediode with G-P BJT• RB = RC = 0• Set RE to the desired

RS value• Set ILE and NE to ISR

and NR so this is the rec. current

• Set BR=BF>>1, ~1e8 so IBR, IBF are neglibigle

• Set ISC = 0 so ILC is = 0

• Set IS to IS for diode so ICC-IEC is the injection curr.

• Set VAR = VAF = 0• IKF gives the desired

high level injection, set IKR = 0

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Charge componentsin the BJT **From Getreau, Modeling the

Bipolar Transistor, Tektronix, Inc.

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References1 OrCAD PSpice A/D Manual, Version 9.1,

November, 1999, OrCAD, Inc.2 Semiconductor Device Modeling with

SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993.

* Semiconductor Physics & Devices, by Donald A. Neamen, Irwin, Chicago, 1997.

** Modeling the Bipolar Transistor, by Ian Getreau, Tektronix, Inc., (out of print).