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L19 25Mar03 1
Semiconductor Device Modeling and CharacterizationEE5342, Lecture 19Spring 2003
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
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emitter
base
collector
reg 4reg 3reg 2reg 1
coll. base & emitter contact regions
Distributed resis-tance in a planar BJT
• The base current must flow lateral to the wafer surface
• Assume E & C cur-rents perpendicular
• Each region of the base adds a term of lateral res.
vBE diminishes as current flows
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Simulation of 2-dim. current flow
• Distributed device is repr. by Q1, Q2, … Qn
• Area of Q is same as the total area of the distributed device.
• Both devices have the same vCE = VCC
• Both sources have same current
iB1 = iB.• The effective value of
the 2-dim. base resistance isRbb’(iB) = V/iB = RBBTh
VCC
QnRR
Q2iBiB1
Q Q1R
=
V
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Analytical solutionfor distributed Rbb
• Analytical solution and SPICE simulation both fit
RBB = Rbmin + Rbmax/(1 + iB/IRB)RB
xi
Lr
dx
xdv
NEV
vLJ
NFV
vLJ
dxxdi
BBiBE
t
BESE
t
BES
B
expexp
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Distributed baseresistance function
Normalized base resis-tance vs. current. (i) RBB/RBmax, (ii) RBBSPICE/RBmax, after fitting RBB and RBBSPICE to RBBTh (x) RBBTh/RBmax.
FromAn Accurate Mathematical Model for the Intrinsic Base Resistance of Bipolar Transistors, by Ciubotaru and Carter, Sol.-St.Electr. 41, pp. 655-658, 1997.
RBBTh = RBM +
R/(1+iB/IRB)RB
(R = RB - RBM )
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If IRB = 0, RBB = RBM+(RB-RBM)/QB
If IRB > 0RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z))
[+iB/(IRB)]1/2-
Gummel PoonBase Resistance
(/)(iB/IRB)1/2z =
Regarding (i) RBB and (x) RTh on previous slide,
RBB = Rbmin + Rbmax/(1 + iB/IRB)RB
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Gummel-Poon Staticnpn Circuit Model
C
E
B
B’
ILC
ILEIBF
IBR ICC - IEC = {IS/QB}*
{exp(vBE/NFVt)-exp(vBC/NRVt)}
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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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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+
-+
-
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 5
iC(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 = 0.75VAF=101.2
vBE = 0.85VAF=101.0
vBE = 0.85 V
vBE = 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, then
iC 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 0.9iC(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 = 0.180
ISeff 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
If iC > IKF, then
iC ~ [IS*IKF]1/2 exp(vBE/2NFVt)
(1-vBC/VAF-vBE/VAR )
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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
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