EE 5340Semiconductor Device TheoryLecture 21 – Spring 2011

Professor Ronald L. Carterronc@uta.edu

http://www.uta.edu/ronc

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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

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IC =

JCAC

IB=-(IE+IC )

JnE JnC

IE = -JEAE

JRB=JnE-JnC

JpE

JGC

JREJpC

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E-M linking current 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

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t

BC

t

BESEC

t

BCS

t

BE

F

SE

t

BES

t

BC

R

SC

S

V

Vexp

V

VexpII

branch E-C the links"" that current The

V

VfexpI

V

Vfexp

II

V

VfexpI

V

Vfexp

II

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

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E-M linking current model (cont)

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E-M linking current model (cont)

EBECE

CBECC

F

FF

t

BE

F

SEB

R

RR

t

BC

R

SCB

I-II and

III sdefinition with eqns

M-E the for values same the give still

1

with V

Vfexp

II

& 1

with VV

fexpI

I

:Similarly

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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

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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 current crowding in base

Fig 9.21*

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Interdigitated base fixes emitter crowding

Fig 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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Hybrid-picircuit model• Adapted from linking current version

of E-M model with parasitic Rs and CSubstr

• C-E branch is linking current• B-E branch is the reduced B-E diode

with diffusion (for and rev) resistance and capacitance and junction cap.

• B-C branch is the reduced B-C diode with diffusion (for and rev) resistance and capacitance and junction cap.

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Hybrid-piCircuit modelFig 9.33*

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Gummel-Poon Staticnpn Circuit Model

C

E

B

B’

ILC

ILEIBF

IBR ICC - IEC =

IS(exp(vBE/NFVt

- exp(vBC/NRVt)/QB

RC

RE

RBB

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Gummel-Poon Staticnpn Circuit Model

C

E

B

B’

ILC

ILEIBF

IBR ICC - IEC = {IS/QB}*

{exp(vBE/NFVt)-exp(vBC/NRVt)}

RC

RE

RBB

IntrinsicTransistor

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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)]1/2 }

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Charge componentsin the BJT **From Getreau,

Modeling the Bipolar Transistor,

Tektronix, Inc.

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Gummel PoonBase ResistanceIf IRB = 0, RBB = RBM+(RB-RBM)/QB

If IRB > 0RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z))

[1+144iB/(p2IRB)]1/2-1

(24/p2)(iB/IRB)1/2z =

From An Accurate Mathematical Model for the Intrinsic Base Resistance of Bipolar Transistors, by Ciubotaru and Carter, Sol.-St.Electr. 41, pp. 655-658, 1997.

RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB

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BJT CharacterizationForward GummelvBCx= 0 = vBC + iBRB -

iCRC

vBEx = vBE +iBRB +(iB+iC)RE

iB = IBF + ILE =

ISexpf(vBE/NFVt)/BF

+ ISEexpf(vBE/NEVt)

iC = bFIBF/QB =

ISexpf(vBE/NFVt)/QB

+

-

iC RC

iB

RE

RB

vBEx

vBC

vBE

++

-

-

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Ideal F-G DataiC and iB (A)

vs. vBE (V)

N = 1 1/slope = 59.5 mV/dec

N = 2 1/slope = 119 mV/dec

BJ T I (A) vs. Vbe (V) for the G-P model Forward Gummel configuration (Vbcx=0)

1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

0.0 0.2 0.4 0.6 0.8

I c

I b

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BJT CharacterizationReverse Gummel

+

-

iE

RC

iB

RE

RB

vBCxvBC

vBE

++

-

-

vBEx= 0 = vBE + iBRB - iERE

vBCx = vBC +iBRB +(iB+iE)RC

iB = IBR + ILC =

ISexpf(vBC/NRVt)/BR

+ ISCexpf(vBC/NCVt)

iE = bRIBR/QB =

ISexpf(vBC/NRVt)/QB

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Ideal R-G DataiE and iB (A)

vs. vBE (V)

N = 1 1/slope = 59.5 mV/dec

N = 2 1/slope = 119 mV/dec

BJ T I (A) vs. Vbe (V) for the G-P model Forward Gummel configuration (Vbcx=0)

1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

0.0 0.2 0.4 0.6 0.8

I c

I b

Ie

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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.

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