semiconductor device modeling and characterization – ee5342 lecture 25 – spring 2011
DESCRIPTION
Semiconductor Device Modeling and Characterization – EE5342 Lecture 25 – Spring 2011. Professor Ronald L. Carter [email protected] http://www.uta.edu/ronc/. The npn Gummel-Poon Static Model. C. R C. I CC - I EC = IS ( exp(v BE /NFV t - exp(v BC /NRV t )/Q B. I BR. B. R BB. I LC. - PowerPoint PPT PresentationTRANSCRIPT
Semiconductor Device Modeling and
Characterization – EE5342 Lecture 25 – Spring 2011
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
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The npn Gummel-Poon Static ModelC
E
B
B’
ILC
ILEIBF
IBRICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB
RC
RE
RBB
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Gummel Poon npnModel Equations
IBF = ISexpf(vBE/NFVt)/BF
ILE = ISEexpf(vBE/NEVt)
IBR = ISexpf(vBC/NRVt)/BR
ILC = ISCexpf(vBC/NCVt)
QB = (1 + vBC/VAF + vBE/VAR )
{½ + ¼ + (BFIBF/IKF + BRIBR/IKR)}
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BJT CharacterizationReverse Gummel
+
-
iE
RC
iB
RE
RB
vBCxvBC
vBE
++
-
-
vBEx= 0 = vBE + iBRB - iERE
vBCx = vBC +iBRB +(iB+iE)RC
iB = IBR + ILC =
(IS/BR)expf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
iE = RIBR/QB =
ISexpf(vBC/NRVt)
(1-vBC/VAF-vBE/VAR )
{IKR terms}-1
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1.E-10
1.E-08
1.E-06
1.E-04
1.E-02
0.1 0.3 0.5 0.7 0.9
Sample rg data forparameter extraction
• IS=10f• Nr=1• Br=2• Isc=10p • Nc=2• Ikr=.1m• Vaf=100• Rc=5• Rb=100
iE, iB vs. vBCext
iB data
iE data
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1.E-10
1.E-08
1.E-06
1.E-04
1.E-02
0.1 0.3 0.5 0.7 0.9
Region a - IKRIS, RB, RC, NR, VAF
Region b - IS, NR, VAF, RB, RC
Region c - IS/BR, NR, RB, RC
Region d - IS/BR, NRRegion e - ISC, NC
Reverse GummelData Sensitivities
iE(A),iB(A) vs. vBC(V)
iE
vBCx = 0
iB
a
b
c
d
e
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Region (b) rgData SensitivitiesRegion b - IS, NR, VAF, RB, RCiE = RIBR/QB = ISexp(vBC/NRVt)
(1-vBC/VAF-vBE/VAR ){IKR terms}-1
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Region (a) rgData Sensitivities
Region a - IKRIS, RB, RC, NR, VAFiE=RIBR/QB~[ISIKR]1/2exp(vBC/2NRVt)
(1-vBC/VAF-vBE/VAR )
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Region (e) rgData SensitivitiesRegion e - ISC, NCiB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
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Region (d) rgData SensitivitiesRegion d - BR, IS, NRiB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
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Region (c) rgData SensitivitiesRegion c - BR, IS, NR, RB, RCiB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
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0.9
1.1
1.3
1.5
1.7
1.9
2.1
0.1 0.3 0.5 0.7 0.9
Simple extraction of NR, NC from rg data
Data set used Nr = 1Nc = 2
Flat Neff region from iE data = 1.00 for 0.195 < vBC < 0.375
Max Neff value from iB data is 1.914 for 0.195 < vBC < 0.205
NEeff vs. vBCext
iB
data
iE data
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1.E-16
1.E-14
1.E-12
1.E-10
0.2 0.4 0.6
Simple extractionof IS, ISC from data
Data set used • IS = 10fA• ISC = 10pAMin ISeff for iE data =
9.96E-15 for vBC = 0.200
Max ISeff value for iB data is 8.44E-12 for vBC = 0.200ISeff vs. vBCext
iB data
iE data
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0.0
0.5
1.0
1.5
2.0
1.E-10 1.E-06 1.E-02
Simple extractionof BR from data
• Data set used Br = 2
• Extraction gives max iE/iB = 1.7 for 0.48 V < vBC < 0.55V 1.13A < iE < 14.4A
• Minimum value of Neff =1 for same range
iE/iB vs. iE
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Gummel PoonBase ResistanceIf 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)RB
1
IRBi144
1i
IRB24
z 2B
B
2
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RB and RE from FG data
RE slope and , RERB intercept has
ii
vs. ,i
VNFi
v of plot a Thus,
REii
RERBi
VNFi
v
REii
RERBi
v
VNFi
1ii
ISE1VNF
REiRERBivexp
BFIS
i
B
C
BB
X,BE
B
C
B
t
B
X,BE
B
C
B
X,BE
t
B
B
B
t
CBX,BEB
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RB and RE from FG data
• In this case, the data were generated with
• RB = 98.76 , compare to
77.4 - 32.3• RE = 1.432 ,
compare to 32.3
y = 32.3x + 77.4
120
130
140
150
1.4 1.6 1.8 2.0
B
C
BB
X,BE
ii
vs. ,i
VNFi
v
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References1 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).