Semiconductor Device Modeling and

Characterization – EE5342 Lecture 25 – Spring 2011

Professor Ronald L. Carterronc@uta.edu

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

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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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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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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 (a) rgData Sensitivities

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

(1-vBC/VAF-vBE/VAR )

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

+ ISCexpf(vBC/NCVt)

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

+ ISCexpf(vBC/NCVt)

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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

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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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RB and RE from FG data

RE slope and , RERB intercept has

ii

vs. ,i

VNFi

v of plot a Thus,

REii

RERBi

VNFi

v

REii

RERBi

v

VNFi

1ii

ISE1VNF

REiRERBivexp

BFIS

i

B

C

BB

X,BE

B

C

B

t

B

X,BE

B

C

B

X,BE

t

B

B

B

t

CBX,BEB

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RB and RE from FG data

• In this case, the data were generated with

• RB = 98.76 , compare to

77.4 - 32.3• RE = 1.432 ,

compare to 32.3

y = 32.3x + 77.4

120

130

140

150

1.4 1.6 1.8 2.0

B

C

BB

X,BE

ii

vs. ,i

VNFi

v

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h11_vs_ib

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h11_vs_frequency

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h11_vs_1/ib

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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).