1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
Semiconductor Device Modeling and Characterization EE5342, Lecture 15 -Sp 2002
Professor Ronald L. Carter
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2. Charge components in the BJT
From Getreau, Modeling the
Bipolar Transistor,
Tektronix, Inc.
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3. Gummel-Poon Static npn Circuit ModelB
RBB
ILC
IBR
ICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB B’
ILE
IBF RE E
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4. Gummel-Poon Static npn Circuit ModelB
RBB
ILC
IBR
ICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB B’
ILE
IBF RE E
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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 coefficient - 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 ) 
{ + [ + (BFIBF/IKF + BRIBR/IKR)]1/2 }
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8. 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 22,
RB = RBM + DR/(1+iB/IRB)aRB , DR = RB - RBM
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9. 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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10. Ideal F-G Data iC and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec
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11. 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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12. Ideal R-G Data iE and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec
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13. 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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14. 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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15. Analytical solution for distributed Rbb
Analytical solution and SPICE simulation both fit
RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB
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16. 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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17. 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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18. Gummel-Poon Static npn Circuit ModelB
RBB
ILC
IBR
ICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB B’
ILE
IBF RE E
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19. 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
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20. 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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21. 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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22. 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
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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. 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
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25. 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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26. 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
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27. 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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28. 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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29. 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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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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