1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
Semiconductor Device Modeling and Characterization – EE5342 Lecture 23 – Spring 2011
Professor Ronald L. Carter

2. Linking current E-M circuit model
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3. E-M model equations
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4. The npn Gummel-Poon Static ModelRC
ICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB B
RBB
ILC
IBR B’
ILE
IBF RE E
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5. 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)
QB = (1 + vBC/VAF + vBE/VAR ) 
{½ + [¼ + (BFIBF/IKF + BRIBR/IKR)]1/2 }
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6. Common emitter current gain, bF
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7. Recombination/Gen Currents (FA)
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8. 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expf(vBE/NFVt)/BF
+ ISEexpf(vBE/NEVt)
iC = bFIBF/QB =
ISexpf(vBE/NFVt)/QB
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9. Ideal F-G Data iC and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec
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10. BJT Characterization Reverse GummeliE RC iB RE RB
vBCx
vBC
vBE + -
vBEx= 0 = vBE + iBRB - iERE
vBCx = vBC +iBRB +(iB+iE)RC
iB = IBR + ILC =
ISexpf(vBC/NRVt)/BR
+ ISCexpf(vBC/NCVt)
iE = bRIBR/QB =
ISexpf(vBC/NRVt)/QB
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11. Ideal R-G Data iE and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec
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12. 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
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13. 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)
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14. 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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15. VAF Parameter Extraction (fEarly)
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 iC iB
vCE
vBE
0.2 < vCE < 5.0
0.7 < vBE < 0.9
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16. 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)
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17. Forward Early VAf extraction
VAFeff = iC/[iC/vBC]vBE
VAF was set at 100V for this data
When vBC = 0
vBE = 0.75VAF=101.2
vBE = 0.85VAF=101.0
vBE = 0.75 V
vBE = 0.85 V
VAFeff(V) vs. vCE (V)
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18. BJT Characterization Forward Gummel
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 iC RC iB RE RB
vBEx
vBC
vBE + -
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19. 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
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20. 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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21. Forward Gummel Data Sensitivities
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
vBCx = 0 c iC b d iB e
iC(A),iB(A) vs. vBE(V)
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22. 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
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23. Region (e) fg Data Sensitivities
Region e - ISE, NE
iB = IBF + ILE = (IS/BF)expf(vBE/NFVt)
+ ISEexpf(vBE/NEVt)
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24. 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
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25. Simple extraction of NF, NE from fg 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 iB
data
iC data
NEeff vs. vBEext
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26. Region (d) fg Data Sensitivities
Region d - IS/BF, NF
iB = IBF + ILE = (IS/BF)expf(vBE/NFVt)
+ ISEexpf(vBE/NEVt)
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27. 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
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28. References
1 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).
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