L23 April 13 1

EE5342 – Semiconductor Device Modeling and CharacterizationLecture 23 - Spring 2004

Professor Ronald L. Carterronc@uta.edu

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

L23 April 13 2

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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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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Forward ActiveHybrid-pi Circuit model

Fig 9.33*

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

If IRB > 0

RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z))

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

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

1

IRBi144

1i

IRB24

z 2B

B

2

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h11_vs_ib

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h11_vs_frequency

L23 April 13 8

h11_vs_1/ib

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Gummel-Poon Staticnpn Circuit Model

C

IntrinsicTransistor

E

B

B’

ILC

ILEIBF

IBR

RC

RE

RBB

C’

E’ )ee(QIS

II

t

'C'B

t

'E'B

VNR

v

VNF

v

B

ECCC

L23 April 13 10

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)}

L23 April 13 11

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

vBE = vBEx –iBRBB -(iB+iC)RE

+

-

iC RC

iB

RE

RBB

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 = 100

iC, 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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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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Forward Gummelextr. of IS and IS/BF

IS/BF extr

ISextr – should to Neff at same point

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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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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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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

L23 April 13 19

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)

(1-vBC/VAF-vBE/VAR )

{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

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0.9

1.1

1.3

1.5

1.7

1.9

2.1

0.1 0.3 0.5 0.7 0.9

Simple extraction of NR, NC from rg data

Data set used Nr = 1Nc = 2

Flat Neff region from iE data = 1.00 for 0.195 < vBC < 0.375

Max Neff value from iB data is 1.914 for 0.195 < vBC < 0.205

NEeff vs. vBCext

iB

data

iE data

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1.E-16

1.E-14

1.E-12

1.E-10

0.2 0.4 0.6

Simple extractionof IS, ISC from data

Data set used • IS = 10fA• ISC = 10pAMin ISeff for iE data =

9.96E-15 for vBC = 0.200

Max ISeff value for iB data is 8.44E-12 for vBC = 0.200ISeff vs. vBCext

iB data

iE data

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0.0

0.5

1.0

1.5

2.0

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

Simple extractionof BR from data

• Data set used Br = 2

• Extraction gives max iE/iB = 1.7 for 0.48 V < vBC < 0.55V 1.13A < iE < 14.4A

• Minimum value of Neff =1 for same range

iE/iB vs. iE