L16 07Mar02 1

Semiconductor Device Modeling and CharacterizationEE5342, Lecture 16 -Sp 2002

Professor Ronald L. Carterronc@uta.edu

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

L16 07Mar02 2

Gummel-Poon Staticnpn Circuit Model

C

E

B

B’

ILC

ILE IBF

IBR ICC - IEC =

IS(exp(vBE/NFVt) -

exp(vBC/NRVt)/QB

RC

RE

RBB

IntrinsicTransistor

L16 07Mar02 3

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

L16 07Mar02 4

+

-+

-

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 5iC(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=0.75VAR=101.2

vBE=0.85VAR=101.0

vBE = 0.85 V

vBE = 0.75 V

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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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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)

(1-vBC/VAF-vBE/VAR )

{IKF terms}-1

+

-

iC RC

iB

RE

RB

vBEx

vBC

vBE

+

+

-

-

L16 07Mar02 11

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, theniC 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 0.9

iC(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 = 0.180ISeff 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

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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

vBCx

vBC

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

L16 07Mar02 23

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

L16 07Mar02 24

Definitions ofNeff and ISeff• In a region where iC or iB is approxi-

mately a single exponential term, theniC or iB ~ ISeffexp (vBCext /(NReffVt)

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

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

L16 07Mar02 25

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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Region (d) rgData SensitivitiesRegion d - BR, IS, NRiB = IBR + ILC = IS/BRexpf(vBC/NRVt)

+ ISCexpf(vBC/NCVt)

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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

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Region (b) rgData SensitivitiesRegion b - IS, NR, VAF, RB, RCiE = RIBR/QB = ISexp(vBC/NRVt)

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

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Region (e) rgData SensitivitiesRegion e - ISC, NCiB = IBR + ILC = IS/BRexpf(vBC/NRVt)

+ ISCexpf(vBC/NCVt)

L16 07Mar02 30

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

L16 07Mar02 31

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 < 0.205NEeff vs. vBCext

iB

data

iE data

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Region (c) rgData SensitivitiesRegion c - BR, IS, NR, RB, RCiB = IBR + ILC = IS/BRexpf(vBC/NRVt)

+ ISCexpf(vBC/NCVt)

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Region (a) rgData SensitivitiesRegion a - IKRIS, RB, RC, NR, VAFiE=RIBR/QB~[ISIKR]1/2exp(vBC/NRVt)

(1-vBC/VAF-vBE/VAR )

L16 07Mar02 34

vBE

RE-flyback dataextraction of RE

RE vCE/iB(from IC-CAP Modeling

Reference, p. 6-37)

RBM (vBE - vCE)/iB(adapted by RLC from

IC-CAP Modeling Reference, p. 6-39)

Qintr

o.c.

RBB

RE

vCE

B’E’

iB

L16 07Mar02 35

Extraction of REfrom refly data

RE vCE/iB

• Slope gives RE 7.1 Ohm

• Model data assumed

RE = 1 Ohm

y=7.1373x+0.0517

0.04

0.05

0.06

0.07

0.08

0.000 0.001 0.002 0.003vCE(V) vs. iB(A)

L16 07Mar02 36

Extraction of RBMfrom refly data

RBM (vBE - vCE)/iB

• Slope gives RBM 108

Ohm

• Model data assumed

RB = RBM = 100 Ohm

y=107.72x+0.6714

0.70

0.80

0.90

1.00

0.000 0.001 0.002 0.003vBC(V) vs. iB(A)