1. Semiconductor Device Modeling & Characterization Lecture 18
Professor Ronald L. Carter
Spring 2001
L18 March 15

2. Gummel-Poon Static npn Circuit Model
Intrinsic
Transistor B
RBB
ILC
IBR
ICC - IEC =
IS(exp(vBE/NFVt) -
exp(vBC/NRVt)/QB B’
ILE
IBF RE E
L18 March 15

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
L18 March 15

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 + -
L18 March 15

5. 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)
L18 March 15

6. Region (a) rg Data Sensitivities
Region a - IKRIS, RB, RC, NR, VAF
iE=bRIBR/QB~[ISIKR]1/2exp(vBC/NRVt)
(1-vBC/VAF-vBE/VAR )
L18 March 15

7. 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
L18 March 15

8. Region (c) rg Data Sensitivities
Region c - BR, IS, NR, RB, RC
iB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
L18 March 15

9. Region (d) rg Data Sensitivities
Region d - BR, IS, NR
iB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
L18 March 15

10. Region (e) rg Data Sensitivities
Region e - ISC, NC
iB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
L18 March 15

11. 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
L18 March 15

12. Extraction of RE from refly data
RE  vCE/iB
Slope gives RE  7.1 Ohm
Model data assumed RE = 1 Ohm
L18 March 15

13. Extraction of RBM from refly data
RBM  (vBE - vCE)/iB
Slope gives RBM  108 Ohm
Model data assumed
RB = RBM = 100 Ohm
L18 March 15

14. 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
L18 March 15

15. 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)]
L18 March 15

16. Simple extraction of NF, NE from fg dataiB
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
iC data
NEeff vs. vBEext
L18 March 15

17. 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
L18 March 15

18. 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
L18 March 15