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Semiconductor
Device Modeling
& Characterization
Lecture 16
Professor Ronald L. Carter
[email protected]
Spring 2001
L16 March 8
1
Note Corrections
Made on L 12
• ISE changed to ISR
• NE changed to NR
L16 March 8
2
Gummel-Poon Static
npn Circuit Model
C
RC
B
RBB
B’
ILC
IBR
ILE
IBF
ICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB
RE
L16 March 8
E
3
Gummel-Poon Static
Model Parameters
name parameter
IS
BF
NF
VAF
ISE
NE
BR
NR
VAR
ISC
NC
EG
XTI
units default
transport saturation current
A
ideal maximum forward beta
forward current emission coefficient forward Early voltage
V
B-E leakage saturation current
A
B-E leakage emission coefficient
ideal maximum reverse beta
reverse current emission coefficient reverse Early voltage
V
B-C leakage saturation current
A
B-C leakage emission coefficient
energy gap for temperature
eV
effect on IS
temperature exponent for effect on IS
L16 March 8
area
1.0e-16
100
1.0
infinite
0
1.5
1
1
infinite
0
2
1.11
*
-
3
*
*
4
Gummel-Poon Static
Model Parameters
name parameter
units default
area
IKF
A
infinite
*
A
infinite
*
W
A
0
infinite
*
*
W
RB
*
W
W
°C
0
0
27
*
*
corner for forward beta
high current roll-off
IKR corner for reverse beta
high current roll-off
RB
zero bias base resistance
IRB current where base resistance
falls halfway to its min value
RBM minimum base resistance
at high currents
RE
emitter resistance
RC
collector resistance
TNOM parameter - meas. temperature
L16 March 8
5
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)
QB = (1 + vBC/VAF + vBE/VAR ) 
{ + [ + (BFIBF/IKF + BRIBR/IKR)]1/2 }
L16 March 8
6
Gummel Poon
Base Resistance
If IRB = 0, RBB = RBM+(RB-RBM)/QB
If IRB > 0
RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z))
z=
[1+144iB/(p2IRB)]1/2-1
(24/p2)(iB/IRB)1/2
Regarding (i) RBB and (x) RTh on slide 22,
RB = RBM + DR/(1+iB/IRB)aRB , DR = RB - RBM
L16 March 8
7
Distributed base
resistance function
RBBTh = RBM +
DR/(1+iB/IRB)aRB
(DR = RB - RBM )
L16 March 8
Normalized base resistance 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.
8
VAR Parameter
Extraction (rEarly)
L16 March 8
9
BJT Characterization
Forward Gummel
vBCx= 0 = vBC + iBRB - iCRC
iC
vBEx = vBE +iBRB +(iB+iC)RE
iB = IBF + ILE =
ISexpf(vBE/NFVt)/BF
+ ISEexpf(vBE/NEVt)
iC = bFIBF/QB =
ISexpf(vBE/NFVt)/QB
L16 March 8
iB
+
vBEx
-
RB
RC
vBC +
+
vBE
RE
10
IKF, RB, RE Param.
Extraction
BJT I (A) vs. Vbe (V) for the G-P model Forward
Gummel configuration (Vbcx=0)
1.E-02
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-09
1.E-10
Ic
1.E-11
Ib
1.E-12
1.E-13
1.E-14
0.1
L16 March 8
0.3
0.5
0.7
0.9
11
IS, N Parameter
Extraction
BJT I (A) vs. Vbe (V) for the G-P model Forward
Gummel configuration (Vbcx=0)
1.E-02
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-09
1.E-10
Ic
1.E-11
Ib
1.E-12
1.E-13
1.E-14
0.1
L16 March 8
0.3
0.5
0.7
0.9
12
ISE, NE Parameter
Extraction
BJT I (A) vs. Vbe (V) for the G-P model Forward
Gummel configuration (Vbcx=0)
1.E-02
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-09
1.E-10
Ic
1.E-11
Ib
1.E-12
1.E-13
1.E-14
0.1
L16 March 8
0.3
0.5
0.7
0.9
13
BJT Characterization
Reverse Gummel
vBEx= 0 = vBE + iBRB - iERE
vBCx = vBC +iBRB +(iB+iE)RC
iB = IBR + ILC =
ISexpf(vBC/NRVt)/BR
+ ISCexpf(vBC/NCVt)
iE = bRIBR/QB =
ISexpf(vBC/NRVt)/QB
L16 March 8
vBCx
+
RC
iB
RB
iE
vBC +
+
vBE
RE
14