1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
Semiconductor Device Modeling and Characterization – EE5342 Lecture 24 – Spring 2011
Professor Ronald L. Carter

2. 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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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)
QB = (1 + vBC/VAF + vBE/VAR ) 
{½ + [¼ + (BFIBF/IKF + BRIBR/IKR)]1/2 }
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4. 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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5. 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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6. 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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7. 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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8. 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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9. 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
If iC > IKF, then
iC ~ [IS*IKF]1/2 exp(vBE/2NFVt) 
(1-vBC/VAF-vBE/VAR )
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10. 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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11. 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 + -
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12. 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
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13. Reverse Gummel Data Sensitivitiesc
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
vBCx = 0 a d e iB b iE
iE(A),iB(A) vs. vBC(V)
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14. 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
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15. Region (a) rg Data Sensitivities
Region a - IKRIS, RB, RC, NR, VAF
iE=bRIBR/QB~[ISIKR]1/2exp(vBC/2NRVt)
(1-vBC/VAF-vBE/VAR )
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16. Region (e) rg Data Sensitivities
Region e - ISC, NC
iB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
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17. Region (d) rg Data Sensitivities
Region d - BR, IS, NR
iB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
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18. 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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19. 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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