Semiconductor Device Modeling and Characterization EE5342, Lecture 19 Spring 2003

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Semiconductor Device Modeling and CharacterizationEE5342, Lecture 19Spring 2003

Professor Ronald L. [email protected]

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

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

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iE = - IEC =

(IS/QB)exp(vBC/NRVt),

where ICC = 0, and

QB-1

=

(1-vBC/VAF-vBE/VAR )

{IKR terms}-1,

so since vBE = vBC - vEC,

VAR ~ iE/[iE/vBE]vBC

VAR ParameterExtraction (rEarly)

+

-+

-

iE

iB

vECvBC

0.2 < vEC < 5.0

0.7 < vBC < 0.9

Reverse Active Operation

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0.0000

0.0002

0.0004

0.0006

0 1 2 3 4 5

iE(A) vs. vEC (V)

Reverse EarlyData for VAR• At a particular data

point, an effective VAR value can be calculated

VAReff = iE/[iE/vBE]vBC

• The most accurate is at vBE = 0 (why?)

vBC = 0.85 V

vBC = 0.75 V

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198

200

202

204

0 1 2 3 4

VAReff(V) vs. vEC (V)

Reverse EarlyVAR extractionVAReff = iE/[iE/vBE]vBC

• VAR was set at 200V for this data

• When vBE = 0

vBC = 0.75VAR=200.5

vBC = 0.85VAR=200.2

vBC = 0.85 V

vBC = 0.75 V

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+

-+

-

VAF ParameterExtraction (fEarly)

iC

iB

vCEvBE

0.2 < vCE < 5.0

0.7 < vBE < 0.9

Forward Active Operation

iC = ICC =

(IS/QB)exp(vBE/NFVt),

where ICE = 0, and

QB-1

=

(1-vBC/VAF-vBE/VAR )*

{IKF terms}-1,

so since vBC = vBE - vCE,

VAF ~ iC/[iC/vBC]vBE

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0.000

0.001

0.002

0.003

0 1 2 3 4 5

iC(A) vs. vCE (V)

Forward EarlyData for VAF• At a particular data

point, an effective VAF value can be calculated

VAFeff = iC/[iC/vBC]vBE

• The most accurate is at vBC = 0 (why?)

vBE = 0.85 V

vBE = 0.75 V

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99

101

103

105

0 1 2 3 4VAFeff(V) vs. vCE (V)

Forward EarlyVAf extractionVAFeff = iC/[iC/vBC]vBE

• VAF was set at 100V for this data

• When vBC = 0

vBE = 0.75VAF=101.2

vBE = 0.85VAF=101.0

vBE = 0.85 V

vBE = 0.75 V

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BJT CharacterizationForward GummelvBCx= 0 = vBC + iBRB - iCRC

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

iB = IBF + ILE =

ISexp(vBE/NFVt)/BF

+ ISEexpf(vBE/NEVt)

iC = FIBF/QB =

ISexp(vBE/NFVt)


{IKF terms}-1

+

-

iC RC

iB

RE

RB

vBEx

vBC

vBE

++

-

-

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1.E-12

1.E-10

1.E-08

1.E-06

1.E-04

1.E-02

0.1 0.3 0.5 0.7 0.9

Sample fg data forparameter extraction

• IS = 10f• NF = 1• BF = 100• Ise = 10E-14• Ne = 2• Ikf = .1m• Var = 200• Re = 1• Rb = 100iC, iB vs. vBEext

iB data

iC data

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Definitions ofNeff and ISeff

• In a region where iC or iB is approxi-mately a single exponential term, then

iC or iB ~ ISeffexp (vBEext /(NFeffVt)

whereNeff = {dvBEext/d[ln(i)]}/Vt,

and ISeff = exp[ln(i) - vBEext/(NeffVt)]

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Region a - IKFIS, RB, RE, NF, VAR

Region b - IS, NF, VAR, RB, RE

Region c - IS/BF, NF, RB, RE

Region d - IS/BF, NFRegion e - ISE, NE

Forward GummelData Sensitivities

1.E-12

1.E-10

1.E-08

1.E-06

1.E-04

1.E-02

0.1 0.3 0.5 0.7 0.9iC(A),iB(A) vs. vBE(V)

iC

vBCx = 0

iB

a

b

c

d

e

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Region (b) fgData SensitivitiesRegion b - IS, NF, VAR, RB, REiC = FIBF/QB = ISexp(vBE/NFVt)

(1-vBC/VAF-vBE/VAR ){IKF terms}-1

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Region (e) fgData SensitivitiesRegion e - ISE, NE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt)

+ ISEexpf(vBE/NEVt)

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Simple extractionof IS, ISE from data

1.E-16

1.E-14

1.E-12

1.E-10

0.1 0.3 0.5 0.7 0.9

Data set used • IS = 10f• ISE = 10E-14Flat ISeff for iC data =

9.99E-15 for 0.230 < vD < 0.255

Max ISeff value for iB data is 8.94E-14 for vD = 0.180

ISeff vs. vBEext

iB data

iC data

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Simple extraction of NF, NE from fg data

Data set used NF=1NE=2

Flat Neff region from iC data = 1.00 for 0.195 < vD < 0.390

Max Neff value from iB data is 1.881 for 0.180 < vD < 0.181

0.9

1.1

1.3

1.5

1.7

1.9

2.1

0.1 0.3 0.5 0.7 0.9

NEeff vs. vBEext

iB

data

iC data

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Region (d) fgData SensitivitiesRegion d - IS/BF, NFiB = IBF + ILE = (IS/BF)expf(vBE/NFVt)

+ ISEexpf(vBE/NEVt)

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0

25

50

75

100

1.E-10 1.E-06 1.E-02

Simple extractionof BF from data

• Data set used BF = 100

• Extraction gives max iC/iB = 92 for 0.50 V < vD < 0.51 V 2.42A < iD < 3.53A

• Minimum value of Neff =1 for slightly lower vD and iD

iC/iB vs. iC

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Region (a) fgData SensitivitiesRegion a - IKFIS, RB, RE, NF, VARiC = FIBF/QB = ISexp(vBE/NFVt)

(1-vBC/VAF-vBE/VAR ){IKF terms}-1

If iC > IKF, then

iC ~ [IS*IKF]1/2 exp(vBE/2NFVt)


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Region (c) fgData SensitivitiesRegion c - IS/BF, NF, RB, REiB = IBF + ILE = (IS/BF)expf(vBE/NFVt)

+ ISEexpf(vBE/NEVt)

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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 =

(IS/BR)expf(vBC/NRVt)

+ ISCexpf(vBC/NCVt)

iE = RIBR/QB =

ISexpf(vBC/NRVt)


{IKR terms}-1

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1.E-10

1.E-08

1.E-06

1.E-04

1.E-02

0.1 0.3 0.5 0.7 0.9

Sample rg data forparameter extraction

• IS=10f• Nr=1• Br=2• Isc=10p • Nc=2• Ikr=.1m• Vaf=100• Rc=5• Rb=100

iE, iB vs. vBCext

iB data

iE data

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1.E-10

1.E-08

1.E-06

1.E-04

1.E-02

0.1 0.3 0.5 0.7 0.9

Region a - IKRIS, RB, RC, NR, VAF

Region b - IS, NR, VAF, RB, RC

Region c - IS/BR, NR, RB, RC

Region d - IS/BR, NRRegion e - ISC, NC

Reverse GummelData Sensitivities

iE(A),iB(A) vs. vBC(V)

iE

vBCx = 0

iB

a

b

c

d

e

Semiconductor Device Modeling and Characterization EE5342, Lecture 19 Spring 2003

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