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Semiconductor Device Modeling and CharacterizationEE5342, Lecture 16 -Sp 2002
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
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Gummel-Poon Staticnpn Circuit Model
C
E
B
B’
ILC
ILE IBF
IBR ICC - IEC =
IS(exp(vBE/NFVt) -
exp(vBC/NRVt)/QB
RC
RE
RBB
IntrinsicTransistor
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Gummel Poon npnModel 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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+
-+
-
VAF ParameterExtraction (fEarly)
iC
iB
vCEvBE
0.2 < vCE < 5.0
0.7 < vBE < 0.9
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
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0.000
0.001
0.002
0.003
0 1 2 3 4 5iC(A) vs. vCE (V)
Forward EarlyData 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
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99
101
103
105
0 1 2 3 4VAFeff(V) vs. vCE (V)
Forward EarlyVAf extractionVAFeff = iC/[iC/vBC]vBE
• VAF was set at 100V for this data
• When vBC = 0
vBE=0.75VAR=101.2
vBE=0.85VAR=101.0
vBE = 0.85 V
vBE = 0.75 V
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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
VAR ParameterExtraction (rEarly)
+
-+
-
iE
iB
vECvBC
0.2 < vEC < 5.0
0.7 < vBC < 0.9
Reverse Active Operation
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0.0000
0.0002
0.0004
0.0006
0 1 2 3 4 5
iE(A) vs. vEC (V)
Reverse EarlyData 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
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198
200
202
204
0 1 2 3 4
VAReff(V) vs. vEC (V)
Reverse EarlyVAR extractionVAReff = iE/[iE/vBE]vBC
• VAR was set at 200V for this data
• When vBE = 0
vBC=0.75VAR=200.5
vBC=0.85VAR=200.2
vBC = 0.85 V
vBC = 0.75 V
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BJT CharacterizationForward GummelvBCx= 0 = vBC + iBRB - iCRC
vBEx = vBE +iBRB +(iB+iC)RE
iB = IBF + ILE =
ISexp(vBE/NFVt)/BF
+ ISEexpf(vBE/NEVt)
iC = FIBF/QB =
ISexp(vBE/NFVt)
(1-vBC/VAF-vBE/VAR )
{IKF terms}-1
+
-
iC RC
iB
RE
RB
vBEx
vBC
vBE
+
+
-
-
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1.E-12
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 fg data forparameter extraction
• IS = 10f• NF = 1• BF = 100• Ise = 10E-14• Ne = 2• Ikf = .1m• Var = 200• Re = 1• Rb = 100iC, iB vs. vBEext
iB data
iC data
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Definitions ofNeff and ISeff• In a region where iC or iB is approxi-
mately a single exponential term, theniC or iB ~ ISeffexp (vBEext /(NFeffVt)
whereNeff = {dvBEext/d[ln(i)]}/Vt,
and ISeff = exp[ln(i) - vBEext/(NeffVt)]
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Region a - IKFIS, RB, RE, NF, VAR
Region b - IS, NF, VAR, RB, RE
Region c - IS/BF, NF, RB, RE
Region d - IS/BF, NFRegion e - ISE, NE
Forward GummelData Sensitivities
1.E-12
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
iC(A),iB(A) vs. vBE(V)
iC
vBCx = 0
iB
a
b
c
d
e
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Region (b) fgData SensitivitiesRegion b - IS, NF, VAR, RB, REiC = FIBF/QB = ISexp(vBE/NFVt)
(1-vBC/VAF-vBE/VAR ){IKF terms}-1
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Region (e) fgData SensitivitiesRegion e - ISE, NE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt)
+ ISEexpf(vBE/NEVt)
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Simple extractionof IS, ISE from data
1.E-16
1.E-14
1.E-12
1.E-10
0.1 0.3 0.5 0.7 0.9
Data set used • IS = 10f• ISE = 10E-14Flat ISeff for iC data =
9.99E-15 for 0.230 < vD < 0.255
Max ISeff value for iB data is 8.94E-14 for vD = 0.180ISeff vs. vBEext
iB data
iC data
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Simple extraction of NF, NE from fg data
Data set used NF=1NE=2
Flat Neff region from iC data = 1.00 for 0.195 < vD < 0.390
Max Neff value from iB data is 1.881 for 0.180 < vD < 0.181
0.9
1.1
1.3
1.5
1.7
1.9
2.1
0.1 0.3 0.5 0.7 0.9
NEeff vs. vBEext
iB
data
iC data
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Region (d) fgData SensitivitiesRegion d - IS/BF, NFiB = IBF + ILE = (IS/BF)expf(vBE/NFVt)
+ ISEexpf(vBE/NEVt)
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0
25
50
75
100
1.E-10 1.E-06 1.E-02
Simple extractionof BF from data
• Data set used BF = 100
• Extraction gives max iC/iB = 92 for 0.50 V < vD < 0.51 V 2.42A < iD < 3.53A
• Minimum value of Neff =1 for slightly lower vD and iD
iC/iB vs. iC
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Region (a) fgData SensitivitiesRegion a - IKFIS, RB, RE, NF, VARiC = FIBF/QB = ISexp(vBE/NFVt)
(1-vBC/VAF-vBE/VAR ){IKF terms}-1
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Region (c) fgData SensitivitiesRegion c - IS/BF, NF, RB, REiB = IBF + ILE = (IS/BF)expf(vBE/NFVt)
+ ISEexpf(vBE/NEVt)
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BJT CharacterizationReverse Gummel
+
-
iE
RC
iB
RE
RB
vBCx
vBC
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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Definitions ofNeff and ISeff• In a region where iC or iB is approxi-
mately a single exponential term, theniC or iB ~ ISeffexp (vBCext /(NReffVt)
whereNeff = {dvBCext/d[ln(i)]}/Vt,
and ISeff = exp[ln(i) - vBCext/(NeffVt)]
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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 (d) rgData SensitivitiesRegion d - BR, IS, NRiB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
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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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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 (e) rgData SensitivitiesRegion e - ISC, NCiB = IBR + ILC = IS/BRexpf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)
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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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0.9
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 < 0.205NEeff vs. vBCext
iB
data
iE data
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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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Region (a) rgData SensitivitiesRegion a - IKRIS, RB, RC, NR, VAFiE=RIBR/QB~[ISIKR]1/2exp(vBC/NRVt)
(1-vBC/VAF-vBE/VAR )
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vBE
RE-flyback dataextraction 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)
Qintr
o.c.
RBB
RE
vCE
B’E’
iB
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Extraction of REfrom refly data
RE vCE/iB
• Slope gives RE 7.1 Ohm
• Model data assumed
RE = 1 Ohm
y=7.1373x+0.0517
0.04
0.05
0.06
0.07
0.08
0.000 0.001 0.002 0.003vCE(V) vs. iB(A)
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Extraction of RBMfrom refly data
RBM (vBE - vCE)/iB
• Slope gives RBM 108
Ohm
• Model data assumed
RB = RBM = 100 Ohm
y=107.72x+0.6714
0.70
0.80
0.90
1.00
0.000 0.001 0.002 0.003vBC(V) vs. iB(A)