semiconductor device modeling and characterization ee5342, lecture 16 -sp 2002

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

L16 07Mar02 5

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

L16 07Mar02 6

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

L16 07Mar02 7

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

L16 07Mar02 8

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

L16 07Mar02 9

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

L16 07Mar02 10

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

L16 07Mar02 12

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)]

L16 07Mar02 13

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

L16 07Mar02 14

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

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

L16 07Mar02 15

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

+ ISEexpf(vBE/NEVt)

L16 07Mar02 16

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

L16 07Mar02 17

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

L16 07Mar02 18

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

+ ISEexpf(vBE/NEVt)

L16 07Mar02 19

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

L16 07Mar02 20

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

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

L16 07Mar02 21

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

+ ISEexpf(vBE/NEVt)

L16 07Mar02 22

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

L16 07Mar02 26

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

+ ISCexpf(vBC/NCVt)

L16 07Mar02 27

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

L16 07Mar02 28

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

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

L16 07Mar02 29

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

L16 07Mar02 32

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

+ ISCexpf(vBC/NCVt)

L16 07Mar02 33

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)