1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
EE5342 – Semiconductor Device Modeling and Characterization Lecture 20 - Spring 2004
Professor Ronald L. Carter
L20 April 01

2. Charge components in the BJT
From Getreau, Modeling the
Bipolar Transistor,
Tektronix, Inc.
L20 April 01

3. Gummel-Poon Static npn Circuit Model
Intrinsic
Transistor C’ B
RBB
ILC
IBR B’
ILE
IBF E’ RE E
L20 April 01

4. 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 }
L20 April 01

5. 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))
Regarding (i) RBB and (x) RTh on previous slide,
RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB
L20 April 01

6. 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
L20 April 01

7. 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)
L20 April 01

8. 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)
L20 April 01

9. 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
L20 April 01

10. 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)
L20 April 01

11. 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)
L20 April 01

12. BJT Characterization Forward GummeliC RC iB RE
RBB
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) 
(1-vBC/VAF-vBE/VAR )
{IKF terms }-1
vBE = vBEx –iBRBB -(iB+iC)RE
L20 April 01

13. 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, iB vs. vBEext
iC data
iB data
L20 April 01

14. 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)]
L20 April 01

15. Forward Gummel Data Sensitivities
iC(A),iB(A) vs. vBEx(V)
vBE = vBEx - iBRB - (iB+iC)RE
Region a – (IKFIS)1/2, RB, RE, NF, VAR, (slight RC)
Region b - IS, NF, VAR, slight (RB, RE)
Region c - IS/BF, NF, RB, RE, (no IKF, slight RC)
Region d - IS/BF, NF, (slight RB, RE)
Region e - ISE, NE iC
vBCx = 0 iB a b c d e
L20 April 01

16. 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
In this region expect to be able to estimate Neff ~ N at some point, and ISeff ~ IS at the same point.
For vBEx small, VAR effects can be negl.
L20 April 01

17. 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 )
L20 April 01

18. Region (e) fg Data Sensitivities
Region e - ISE, NE
iB = IBF + ILE = (IS/BF)expf(vBE/NFVt)
+ ISEexpf(vBE/NEVt)
In this region, ILE > IBF, so expect to be able to estimate Neff ~ NE at some point, and ISeff ~ ISE at the same point.
There are no VAR effects.
L20 April 01

19. Region (d) fg Data Sensitivities
Region d - IS/BF, NF
iB = IBF + ILE = (IS/BF)expf(vBE/NFVt)
+ ISEexpf(vBE/NEVt)
In this region, ILE < IBF expect to be able to estimate Neff ~ N at some point, and ISeff ~ IS at the same point.
There are no VAR effects but at high vBE, there are RBB and RE effects (RC much less).
L20 April 01

20. Region (c) fg Data Sensitivities
Region c - IS/BF, NF, RB, RE, (no IKF), (RC)
iB = IBF + ILE = (IS/BF)expf(vBE/NFVt)
+ ISEexpf(vBE/NEVt)
In this region, assuming iB ~ IBF, can take derivatives like ∂iB/∂iB  1 to form functions of RBB and RE for estimation.
There are no VAR or IKF effects but at high vBE, there are slight RC effects).
L20 April 01

21. 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
L20 April 01

22. 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
L20 April 01

23. 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
L20 April 01

24. 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
L20 April 01

25. 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 + -
L20 April 01

26. 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
L20 April 01

27. 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)
L20 April 01

28. 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)
L20 April 01

29. 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
L20 April 01

30. 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 )
L20 April 01

31. Region (e) rg Data Sensitivities
Region e - ISC, NC
iB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
L20 April 01

32. Region (d) rg Data Sensitivities
Region d - BR, IS, NR
iB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
L20 April 01

33. Region (c) rg Data Sensitivities
Region c - BR, IS, NR, RB, RC
iB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
L20 April 01

34. 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
L20 April 01

35. 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
L20 April 01

36. 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
L20 April 01

37. 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
L20 April 01

38. Extraction of RE from refly data
RE  vCE/iB
Slope gives RE  7.1 Ohm
Model data assumed RE = 1 Ohm
L20 April 01

39. Extraction of RBM from refly data
RBM  (vBE - vCE)/iB
Slope gives RBM  108 W
Model data assumed
RB = RBM = 100 Ohm
L20 April 01

40. BJT Project 2 Project 2 is in the “Example” files under bjt models.
Look at the file bjtPr2.mdl in the
/examples/model_files/bjt directory on gamma.
The assignment is to extract (using only procedures you develop) the static parameters for the npn bjt.
L20 April 01

41. References
* Modeling the Bipolar Transistor, by Ian Getreau, Tektronix, Inc., (out of print).
** IC-CAP Modeling Reference - Measurement, Modeling and Simulation of Electronic Components and Circuits, Agilent Technologies, May 2000.
L20 April 01