1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
EE5342 – Semiconductor Device Modeling and Characterization Lecture 15 March 08, 2010
Professor Ronald L. Carter

2. Gummel-Poon Static npn Circuit Model
Intrinsic
Transistor RC B
RBB
ILC
IBR
ICC - IEC = {IS/QB}*
{exp(vBE/NFVt)-exp(vBC/NRVt)} B’
ILE
IBF RE E
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3. Gummel-Poon Model General Form
QXXXXXXX NC NB NE <NS> MNAME <AREA> <OFF> <IC=VBE, VCE> <TEMP=T>
Netlist Examples
Q Q2N3904 IC=0.6, 5.0
Q QNPN .67
NC, NB and NE are the collector, base and emitter nodes
NS is the optional substrate node; if unspecified, the ground is used. MNAME is the model name,
AREA is the area factor, and
TEMP is the temperature at which this device operates, and overrides the specification in the Analog Options dialog.
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4. Gummel-Poon Static Model
Gummel Poon Model Parameters (NPN/PNP)
Adaptation of the integral charge control model of Gummel and Poon.
Extends the original model to include effects at high bias levels.
Simplifies to Ebers-Moll model when certain parameters not specified.
Defined by parameters
IS, BF, NF, ISE, IKF, NE determine forward characteristics
IS, BR, NR, ISC, IKR, NC determine reverse characteristics
VAF and VAR determine output conductance for for and rev
RB(depends on iB), RC, and RE are also included
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5. Gummel-Poon Static Par.
NAME PARAMETER UNIT DEFAULT
IS transport saturation current A 1.0e-16
BF ideal maximum forward beta - 100
NF forward current emission coef
VAF forward Early voltage V infinite
ISE B-E leakage saturation current A 0
NE B-E leakage emission coefficient - 1.5
BR ideal maximum reverse beta - 1
NR reverse current emission coeff. - 1
VAR reverse Early voltage V infinite
ISC B-C leakage saturation current A 0
NC B-C leakage emission coefficient - 2
EG energy gap (IS dep on T) eV 1.11
XTI temperature exponent for IS - 3
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6. Gummel-Poon Static Model Parameters
NAME PARAMETER UNIT DEFAULT
IKF corner for forward beta A infinite
high current roll-off
IKR corner for reverse beta A infinite
RB zero bias base resistance W 0
IRB current where base resistance A infinite
falls halfway to its min value
RBM minimum base resistance W RB
at high currents
RE emitter resistance W 0
RC collector resistance W 0
TNOM parameter - meas. temperature °C 27
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7. 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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8. 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 = {½ +[¼ +(BF IBF/IKF + BR IBR/IKR)]1/2 } (1 - vBC/VAF - vBE/VAR )-1
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9. Gummel Poon Base Resistance
If IRB = 0, RBB = RBM+(RB-RBM)/QB
If IRB > 0
RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z))
[1+144iB/(p2IRB)]1/2-1
z =
(24/p2)(iB/IRB)1/2
Regarding (i) RBB and (x) RTh on slide 23,
RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB
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10. Gummel Poon Base Resistance
If IRB = 0, RBB = RBM+(RB-RBM)/QB
If IRB > 0
RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z))
[1+144iB/(p2IRB)]1/2-1
z =
(24/p2)(iB/IRB)1/2
Regarding (i) RBB and (x) RTh on previous slide,
RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB
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11. 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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12. Ideal F-G Data iC and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec

13. 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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14. Ideal R-G Data iE and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec

15. Distributed resis- tance in a planar BJT
emitter
base
collector
reg 4
reg 3
reg 2
reg 1
coll base & emitter contact regions
The base current must flow lateral to the wafer surface
Assume E & C cur-rents perpendicular
Each region of the base adds a term of lateral res.
 vBE diminishes as current flows
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16. Simulation of 2- dim. current flow=
 DV 
Both sources have same current iB1 = iB.
The effective value of the 2-dim. base resistance is
Rbb’(iB) = DV/iB = RBBTh
Distributed device is repr. by Q1, Q2, … Qn
Area of Q is same as the total area of the distributed device.
Both devices have the same vCE = VCC
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17. Analytical solution for distributed Rbb
Analytical solution and SPICE simulation both fit
RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB
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18. Distributed base resistance function
Normalized base resis-tance vs. current. (i) RBB/RBmax, (ii) RBBSPICE/RBmax, after fitting RBB and RBBSPICE to RBBTh (x) RBBTh/RBmax.
FromAn Accurate Mathematical Model for the Intrinsic Base Resistance of Bipolar Transistors, by Ciubotaru and Carter, Sol.-St.Electr. 41, pp , 1997.
RBBTh = RBM +
DR/(1+iB/IRB)aRB
(DR = RB - RBM )
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19. 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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20. 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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21. 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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22. 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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23. 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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24. 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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25. 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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26. 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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27. 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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28. 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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29. 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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30. 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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31. 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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32. 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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33. 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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34. 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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35. 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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36. 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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37. 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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38. 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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39. 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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40. 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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