1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
Semiconductor Device Modeling and Characterization EE5342, Lecture 16 -Sp 2002
Professor Ronald L. Carter
L16 07Mar02

2. Gummel-Poon Static npn Circuit Model
Intrinsic
Transistor B
RBB
ILC
IBR
ICC - IEC =
IS(exp(vBE/NFVt) -
exp(vBC/NRVt)/QB B’
ILE
IBF RE E
L16 07Mar02

3. Gummel Poon npn Model 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 Parameter Extraction (fEarly)
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
Forward Active
Operation iC iB
vCE
vBE
0.2 < vCE < 5.0
0.7 < vBE < 0.9
L16 07Mar02

5. Forward Early Data 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
iC(A) vs. vCE (V)
L16 07Mar02

6. Forward Early VAf extraction
VAFeff = iC/[iC/vBC]vBE
VAF was set at 100V for this data
When vBC = 0
vBE=0.75VAR=101.2
vBE=0.85VAR=101.0
vBE = 0.75 V
vBE = 0.85 V
VAFeff(V) vs. vCE (V)
L16 07Mar02

7. VAR Parameter Extraction (rEarly)
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 iE iB
vEC
vBC
0.2 < vEC < 5.0
0.7 < vBC < 0.9
Reverse Active
Operation
L16 07Mar02

8. Reverse Early Data 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
iE(A) vs. vEC (V)
L16 07Mar02

9. Reverse Early VAR extraction
VAReff = iE/[iE/vBE]vBC
VAR was set at 200V for this data
When vBE = 0
vBC=0.75VAR=200.5
vBC=0.85VAR=200.2
vBC = 0.75 V
vBC = 0.85 V
VAReff(V) vs. vEC (V)
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10. BJT Characterization Forward GummeliC RC iB RE RB
vBEx
vBC
vBE + -
vBCx= 0 = vBC + iBRB - iCRC
vBEx = vBE +iBRB +(iB+iC)RE
iB = IBF + ILE =
ISexp(vBE/NFVt)/BF
+ ISEexpf(vBE/NEVt)
iC = bFIBF/QB =
ISexp(vBE/NFVt) 
(1-vBC/VAF-vBE/VAR )
{IKF terms }-1
L16 07Mar02

11. Sample fg data for parameter extraction
IS = 10f
NF = 1
BF = 100
Ise = 10E-14
Ne = 2
Ikf = .1m
Var = 200
Re = 1
Rb = 100
iC data
iB data
iC, iB vs. vBEext
L16 07Mar02

12. Definitions of Neff and ISeff
In a region where iC or iB is approxi-mately a single exponential term, then
iC or iB ~ ISeffexp (vBEext /(NFeffVt)
where
Neff = {dvBEext/d[ln(i)]}/Vt,
and
ISeff = exp[ln(i) - vBEext/(NeffVt)]
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13. Forward Gummel Data Sensitivities
vBCx = 0
Region a - IKFIS, RB, RE, NF, VAR
Region b - IS, NF, VAR, RB, RE
Region c - IS/BF, NF, RB, RE
Region d - IS/BF, NF
Region e - ISE, NE c iC b d iB e
iC(A),iB(A) vs. vBE(V)
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14. Region (b) fg Data Sensitivities
Region b - IS, NF, VAR, RB, RE
iC = bFIBF/QB = ISexp(vBE/NFVt) 
(1-vBC/VAF-vBE/VAR ){IKF terms }-1
L16 07Mar02

15. Region (e) fg Data Sensitivities
Region e - ISE, NE
iB = IBF + ILE = (IS/BF)expf(vBE/NFVt)
+ ISEexpf(vBE/NEVt)
L16 07Mar02

16. Simple extraction of IS, ISE from data
Data set used
IS = 10f
ISE = 10E-14
Flat ISeff for iC data = 9.99E-15 for < vD < 0.255
Max ISeff value for iB data is 8.94E-14 for vD = 0.180
iC data
iB data
ISeff vs. vBEext
L16 07Mar02

17. Simple extraction of NF, NE from fg dataiB
data
Data set used
NF=1
NE=2
Flat Neff region from iC data = 1.00 for < vD < 0.390
Max Neff value from iB data is for < vD < 0.181
iC data
NEeff vs. vBEext
L16 07Mar02

18. Region (d) fg Data Sensitivities
Region d - IS/BF, NF
iB = IBF + ILE = (IS/BF)expf(vBE/NFVt)
+ ISEexpf(vBE/NEVt)
L16 07Mar02

19. Simple extraction of BF from data
Data set used BF = 100
Extraction gives max iC/iB = 92 for 0.50 V < vD < 0.51 V 2.42A < iD < 3.53A
Minimum value of Neff =1 for slightly lower vD and iD
iC/iB vs. iC
L16 07Mar02

20. Region (a) fg Data Sensitivities
Region a - IKFIS, RB, RE, NF, VAR
iC = bFIBF/QB = ISexp(vBE/NFVt) 
(1-vBC/VAF-vBE/VAR ){IKF terms }-1
L16 07Mar02

21. Region (c) fg Data Sensitivities
Region c - IS/BF, NF, RB, RE
iB = IBF + ILE = (IS/BF)expf(vBE/NFVt)
+ ISEexpf(vBE/NEVt)
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22. BJT Characterization Reverse Gummel
vBEx= 0 = vBE + iBRB - iERE
vBCx = vBC +iBRB +(iB+iE)RC
iB = IBR + ILC =
(IS/BR)expf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
iE = bRIBR/QB =
ISexpf(vBC/NRVt)
(1-vBC/VAF-vBE/VAR )
{IKR terms }-1 iE RC iB RE RB
vBCx
vBC
vBE + -
L16 07Mar02

23. Sample rg data for parameter extraction
IS=10f
Nr=1
Br=2
Isc=10p
Nc=2
Ikr=.1m
Vaf=100
Rc=5
Rb=100
iB data
iE data
iE, iB vs. vBCext
L16 07Mar02

24. Definitions of Neff and ISeff
In a region where iC or iB is approxi-mately a single exponential term, then
iC or iB ~ ISeffexp (vBCext /(NReffVt)
where
Neff = {dvBCext/d[ln(i)]}/Vt,
and
ISeff = exp[ln(i) - vBCext/(NeffVt)]
L16 07Mar02

25. Reverse Gummel Data Sensitivitiesc
vBCx = 0
Region a - IKRIS, RB, RC, NR, VAF
Region b - IS, NR, VAF, RB, RC
Region c - IS/BR, NR, RB, RC
Region d - IS/BR, NR
Region e - ISC, NC a d e iB b iE
iE(A),iB(A) vs. vBC(V)
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26. Region (d) rg Data Sensitivities
Region d - BR, IS, NR
iB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
L16 07Mar02

27. Simple extraction of BR from data
Data set used Br = 2
Extraction gives max iE/iB = 1.7 for 0.48 V < vBC < 0.55V 1.13A < iE < 14.4A
Minimum value of Neff =1 for same range
iE/iB vs. iE
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28. Region (b) rg Data Sensitivities
Region b - IS, NR, VAF, RB, RC
iE = bRIBR/QB = ISexp(vBC/NRVt)
(1-vBC/VAF-vBE/VAR ){IKR terms }-1
L16 07Mar02

29. Region (e) rg Data Sensitivities
Region e - ISC, NC
iB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
L16 07Mar02

30. Simple extraction of IS, ISC from data
Data set used
IS = 10fA
ISC = 10pA
Min ISeff for iE data = 9.96E-15 for vBC = 0.200
Max ISeff value for iB data is 8.44E-12 for vBC = 0.200
iB data
iE data
ISeff vs. vBCext
L16 07Mar02

31. Simple extraction of NR, NC from rg data
Data set used
Nr = 1
Nc = 2
Flat Neff region from iE data = 1.00 for < vBC < 0.375
Max Neff value from iB data is for < vBC < 0.205 iB
data
iE data
NEeff vs. vBCext
L16 07Mar02

32. Region (c) rg Data Sensitivities
Region c - BR, IS, NR, RB, RC
iB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
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33. Region (a) rg Data Sensitivities
Region a - IKRIS, RB, RC, NR, VAF
iE=bRIBR/QB~[ISIKR]1/2exp(vBC/NRVt)
(1-vBC/VAF-vBE/VAR )
L16 07Mar02

34. RE-flyback data extraction 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)
o.c.
Qintr
vCE
RBB B’
vBE E’ iB RE
L16 07Mar02

35. Extraction of RE from refly data
RE  vCE/iB
Slope gives RE  7.1 Ohm
Model data assumed RE = 1 Ohm
L16 07Mar02

36. Extraction of RBM from refly data
RBM  (vBE - vCE)/iB
Slope gives RBM  108 Ohm
Model data assumed
RB = RBM = 100 Ohm
L16 07Mar02