L21 April 7 1

EE5342 – Semiconductor Device Modeling and CharacterizationLecture 21 - Spring 2005

Professor Ronald L. Carterronc@uta.edu

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

L21 April 7 2

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

L21 April 7 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 = {½ +¼ +(BF IBF/IKF + BR IBR/IKR)1/2} (1 - vBC/VAF - vBE/VAR )-1

L21 April 7 4

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

L21 April 7 5

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 = abs{iE/[iE/vBE]vBC}

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

vBC = 0.85 V

vBC = 0.75 V

L21 April 7 6

198

200

202

204

0 1 2 3 4

VAReff(V) vs. vEC (V)

Reverse EarlyVAR extraction

VAReff =

|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

L21 April 7 7

+

-+

-

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|

L21 April 7 8

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 =

abs{iC/[iC/vBC]vBE}

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

vBE = 0.85 V

vBE = 0.75 V

L21 April 7 9

99

101

103

105

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

Forward EarlyVAf extraction

VAFeff =

|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

L21 April 7 10

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

L21 April 7 11

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

L21 April 7 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

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

L21 April 7 13

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

L21 April 7 14

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

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

L21 April 7 15

Region (a) rgData Sensitivities

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

(1-vBC/VAF-vBE/VAR )

L21 April 7 16

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

+ ISCexpf(vBC/NCVt)

L21 April 7 17

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

+ ISCexpf(vBC/NCVt)

L21 April 7 18

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

+ ISCexpf(vBC/NCVt)

L21 April 7 19

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

L21 April 7 20

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

L21 April 7 21

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

L21 April 7 22

Forward ActiveHybrid-pi Circuit model

Fig 9.33*

L21 April 7 23

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

L21 April 7 24

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

BB

X,BE

B

C

B

X,BE

t

B

B

B

t

CBX,BEB

L21 April 7 25

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

L21 April 7 26

h11_vs_ib

L21 April 7 27

h11_vs_frequency

L21 April 7 28

h11_vs_1/ib