Semiconductor Device Modeling and

Characterization – EE5342 Lecture 22 – Spring 2011

Professor Ronald L. Carterronc@uta.edu

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

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2

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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E-M model equations

BB

BC2i

CSRSESFBB

BE2i

S

t

BCCSR

t

BEESE

t

BEESF

t

BCCSC

xNDAqn

IIIxN

DAqn

I gives iprelationsh yreciprocit The

VV

fIV

VfII

V

VfI

VV

fII

expexp

expexp

4

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Common emitter current gain, F

lim. , V2

Vexp

Dn2

xxn ,

xDN

xDN

L2

x

lim. , V2

Vexp

Dn2

xxn ,

L2

xxDN

xDN

limited. or limited is BJT a Usually,

V2

Vexp

Dn2

xxn

L2

xxDN

xDN

1 so ,

1 ; III with ,

II

Tt

BE

0BBO

BBEi

EBE

BEB2B

2B

t

BE

0BBO

BBEi2B

2B

EBE

BEB

T

1

t

BE

0BBO

BBEi2B

2B

EBE

BEB

0

00CBE

B

C0

5

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Recombination/GenCurrents (FA)

CB

CBBCeff,

1gen

BCeff,

BCbiCBC

gen

BCiGC

1rec

BEt

BE

rec

iBERE

NNNN

N and

rate, ionrecombinat the is and DR CB

the is qN

VV2W where ,

2Wqn

J

.rate ionrecombinat the is and DR

EB the is W where ,V2

Vexp

2

nqWJ

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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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Charge componentsin the BJT **From Getreau, Modeling the

Bipolar Transistor, Tektronix, Inc.

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Gummel-Poon Staticnpn Circuit Model

C

E

B

B’

ILC

ILEIBF

IBRICC - IEC = {IS/QB}*

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

RC

RE

RBB

IntrinsicTransistor

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Gummel-PoonModelGeneral FormQXXXXXXX NC NB NE <NS> MNAME <AREA> <OFF> <IC=VBE, VCE> <TEMP=T>Netlist Examples

Q5 11 26 4 Q2N3904 IC=0.6, 5.0Q3 5 2 6 9 QNPN .67

NC, NB and NE are the collector, base and emitter nodes

NS is the optional substrate node; if unspecified, the ground is used. MNAME is the model name, AREA is the area factor, and TEMP is the temperature at which this device operates, and overrides the specification in the Analog Options dialog.

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Gummel-PoonStatic ModelGummel Poon Model Parameters (NPN/PNP)

Adaptation of the integral charge control model of Gummel and Poon.

Extends the original model to include effects at high bias levels.

Simplifies to Ebers-Moll model when certain parameters not specified.

Defined by parameters

IS, BF, NF, ISE, IKF, NE determine forward characteristics

IS, BR, NR, ISC, IKR, NC determine reverse characteristics

VAF and VAR determine output conductance for for and rev

RB(depends on iB), RC, and RE are also included

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NAME PARAMETER UNIT DEFAULTIS transport saturation current A 1.0e-16BF ideal maximum forward beta - 100NF forward current emission coef. - 1.0VAF forward Early voltage V infiniteISE B-E leakage saturation current A 0NE B-E leakage emission coefficient - 1.5BR ideal maximum reverse beta - 1NR reverse current emission coeff. - 1VAR reverse Early voltage V infiniteISC B-C leakage saturation current A 0NC B-C leakage emission coefficient - 2EG energy gap (IS dep on T) eV 1.11XTI temperature exponent for IS - 3

Gummel-Poon Static Par.

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Gummel-Poon StaticModel ParametersNAME PARAMETER UNIT DEFAULTIKF corner for forward beta A infinite

high current roll-offIKR corner for reverse beta A infinite

high current roll-offRB zero bias base resistance W 0IRB current where base resistance A

infinitefalls halfway to its min value

RBM minimum base resistance W RBat high currents

RE emitter resistance W 0RC collector resistance W 0TNOM parameter - meas. temperature °C

27

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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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Gummel Poon npnModel Equations

IBF = IS expf(vBE/NFVt)/BF

ILE = ISE expf(vBE/NEVt)

IBR = IS expf(vBC/NRVt)/BR

ILC = ISC expf(vBC/NCVt)

ICC - IEC = IS(exp(vBE/NFVt - exp(vBC/NRVt)/QB

QB = {½ +¼ +(BF IBF/IKF + BR IBR/IKR)1/2} (1 - vBC/VAF - vBE/VAR )-1

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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))

[+iB/(IRB)]1/2- (/)(iB/IRB)1/2

z =

Regarding (i) RBB and (x) RTh on slide 23,

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

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If IRB = 0, RBB = RBM+(RB-RBM)/QB

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

[+iB/(IRB)]1/2-

Gummel PoonBase Resistance

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

Regarding (i) RBB and (x) RTh on previous slide,

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

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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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BJT CharacterizationForward GummelvBCx= 0 = vBC + iBRB - iCRC

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

iB = IBF + ILE =

ISexpf(vBE/NFVt)/BF

+ ISEexpf(vBE/NEVt)

iC = FIBF/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 = RIBR/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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emitter

base

collector

reg 4reg 3reg 2reg 1

coll. base & emitter contact regions

Distributed resis-tance in a planar BJT

• The base current must flow lateral to the wafer surface

• Assume E & C cur-rents perpendicular

• Each region of the base adds a term of lateral res.

vBE diminishes as current flows

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Simulation of 2-dim. current flow

• Distributed device is repr. by Q1, Q2, … Qn

• Area of Q is same as the total area of the distributed device.

• Both devices have the same vCE = VCC

• Both sources have same current

iB1 = iB.• The effective value of

the 2-dim. base resistance isRbb’(iB) = V/iB = RBBTh

VCC

QnRR

Q2iBiB1

Q Q1R

=

V

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Analytical solutionfor distributed Rbb

• Analytical solution and SPICE simulation both fit

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

xi

Lr

dx

xdv

NEV

vLJ

NFV

vLJ

dxxdi

BBiBE

t

BESE

t

BES

B

expexp

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Distributed baseresistance function

Normalized base resis-tance vs. current. (i) RBB/RBmax, (ii) RBBSPICE/RBmax, after fitting RBB and RBBSPICE to RBBTh (x) RBBTh/RBmax.

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

RBBTh = RBM +

R/(1+iB/IRB)RB

(R = RB - RBM )

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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).