1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
Semiconductor Device Modeling and Characterization EE5342, Lecture 20 Spring 2003
Professor Ronald L. Carter
L20 27Mar03

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
L20 27Mar03

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)
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
L20 27Mar03

4. 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 27Mar03

5. 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 27Mar03

6. Definitions of Neff and ISeff
In a region where iC or iB is approxi-mately a single exponential term, then
iE or iB ~ ISeffexp (vBCext /(NReffVt)
where
Neff = {dvBCext/d[ln(i)]}/Vt,
and
ISeff = exp[ln(i) - vBCext/(NeffVt)]
L20 27Mar03

7. 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 27Mar03

8. Region (d) rg Data Sensitivities
Region d - BR, IS, NR
iB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
L20 27Mar03

9. 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 27Mar03

10. 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 27Mar03

11. Region (e) rg Data Sensitivities
Region e - ISC, NC
iB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
L20 27Mar03

12. 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 27Mar03

13. 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 27Mar03

14. 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 27Mar03

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 )
L20 27Mar03

16. 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 27Mar03

17. Extraction of RE from refly data
RE  vCE/iB
Slope gives RE  7.1 Ohm
Model data assumed RE = 1 Ohm
L20 27Mar03

18. Extraction of RBM from refly data
RBM  (vBE - vCE)/iB
Slope gives RBM  108 Ohm
Model data assumed
RB = RBM = 100 Ohm
L20 27Mar03