Transcript Semiconductor Device Modeling and Characterization – EE5342 Lecture 22 – Spring 2011 Professor Ronald L.

Semiconductor Device Modeling
and Characterization – EE5342
Lecture 22 – Spring 2011
Professor Ronald L. Carter
[email protected]
http://www.uta.edu/ronc/
The npn Gummel-Poon Static Model
C
RC
B
RBB
B’
ILC
IBR
ILE
IBF
ICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB
RE
E
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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 ) 
{½ + [¼ + (BFIBF/IKF + BRIBR/IKR)]1/2 }
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E-M model equations
 VBC 
 VBE 
  FIES exp f

IC  ICS exp f
 Vt 
 Vt 
 VBE 
 VBC 
  R ICS exp f

IE  IES exp f
 Vt 
 Vt 
The reciprocit y relationsh ip gives IS
2
qni AEDB
NBxB
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 FIES  IS  R ICS
qni2ACDB

NBxB
4
Common emitter
current gain, bF
IC
0

b 0  , with IE  IB  IC ; b 0 
, so b 
IB
1  0
1
xB2
2L2B
1
 NBDE xB
nixBE xB
 VBE  

b  


exp
 
2nBODB  0
 2Vt  
 NEDBxE
Usually, a BJT is  limited or  T limited.
NBDE xB
xB2  nixBE xB
  VBE  
 2 ,  
exp
  ,   lim.
NEDBxE
2LB  2nBODB  0
 2Vt  
xB2
NBDE xB

2
NEDBxE
2LB
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 nixBE xB
  VBE  
,  
exp
  ,   T lim.
 2Vt  
 2nBODB  0
5
Recombination/Gen
Currents (FA)
JRE
qWBEni
 VBE 

exp
, where WBE is the EB
2rec
 2Vt 
1
DR and rec
is the recombinat ion rate.
JGC
qniWBC
2VbiC  VBC 

, where WBC 
is the
2 gen
qNeff,BC
1
CB DR and  gen
is the recombinat ion rate,
and Neff,BC
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NBNC

NB  NC
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npn Base-width mod.
(Early Effect)
Fig 9.15*
 n p
n
Jn  qDn
x
Qj
VBC
 CjC
xB
 qNBA
VBC
J
J

xB
xB
J
J xB

VBC xB VBC
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Base-width modulation
(Early Effect, cont.)
I
J xB

A
VCB
xB VBC
Fig 9.16*
J CjC

xB qNBA
CjC
I
I


VCE QB VCE  VA
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Charge components
in the BJT
**From Getreau, Modeling the
Bipolar Transistor, Tektronix, Inc.
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Gummel-Poon Static
npn Circuit Model
C
RC
B
RBB
B’
ILC
IBR
ILE
IBF
Intrinsic
Transistor
ICC - IEC = {IS/QB}*
{exp(vBE/NFVt)-exp(vBC/NRVt)}
RE
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E
10
Gummel-Poon
Model
General Form
QXXXXXXX NC NB NE <NS> MNAME <AREA> <OFF> <IC=VBE,
VCE> <TEMP=T>
Netlist Examples
Q5 11 26 4 Q2N3904 IC=0.6, 5.0
Q3 5 2 6 9 QNPN .67
NC, NB and NE are the collector, base and emitter nodes
NS is the optional substrate node; if unspecified, the ground is used.
MNAME is the model name,
AREA is the area factor, and
TEMP is the temperature at which this device operates, and overrides
the specification in the Analog Options dialog.
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Gummel-Poon
Static Model
Gummel Poon Model Parameters (NPN/PNP)
Adaptation of the integral charge control model of Gummel and Poon.
Extends the original model to include effects at high bias levels.
Simplifies to Ebers-Moll model when certain parameters not specified.
Defined by parameters
IS, BF, NF, ISE, IKF, NE determine forward characteristics
IS, BR, NR, ISC, IKR, NC determine reverse characteristics
VAF and VAR determine output conductance for for and rev
RB(depends on iB), RC, and RE are also included
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Gummel-Poon Static Par.
NAME PARAMETER
IS
transport saturation current
BF
ideal maximum forward beta
NF
forward current emission coef.
VAF forward Early voltage
ISE B-E leakage saturation current
NE
B-E leakage emission coefficient
BR
ideal maximum reverse beta
NR
reverse current emission coeff.
VAR reverse Early voltage
ISC B-C leakage saturation current
NC
B-C leakage emission coefficient
EG
energy gap (IS dep on T)
XTI temperature exponent for IS
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UNIT
A
V
A
V
A
eV
-
DEFAULT
1.0e-16
100
1.0
infinite
0
1.5
1
1
infinite
0
2
1.11
3
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Gummel-Poon Static
Model Parameters
NAME PARAMETER
UNIT
IKF
corner for forward beta
A
high current roll-off
IKR
corner for reverse beta
A
high current roll-off
RB
zero bias base resistance
W
IRB
current where base resistance A
falls halfway to its min value
RBM
minimum base resistance
W
at high currents
RE
emitter resistance
W
RC
collector resistance
W
TNOM parameter - meas. temperature °C
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DEFAULT
infinite
infinite
0
infinite
RB
0
0
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14
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 ) 
{½ + [¼ + (BFIBF/IKF + BRIBR/IKR)]1/2 }
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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 = {½ +[¼ +(BF IBF/IKF + BR IBR/IKR)]1/2 }
(1 - vBC/VAF - vBE/VAR )-1
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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 23,
RBB = Rbmin + Rbmax/(1 + iB/IRB)RB
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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 previous slide,
RBB = Rbmin + Rbmax/(1 + iB/IRB)RB
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Making a diode from the GP BJT model
C
RC
B
RBB
B’
ILC
IBR
ILE
IBF
ICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB
RE
E
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Making a complete
diode with G-P BJT
• RB = RC = 0
• Set RE to the desired
RS value
• Set ILE and NE to
ISR and NR so this is
the rec. current
• Set BR=BF>>1, ~1e8 so
IBR, IBF are neglibigle
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• Set ISC = 0 so ILC is =
0
• Set IS to IS for diode
so ICC-IEC is the
injection curr.
• Set VAR = VAF = 0
• IKF gives the desired
high level injection,
set IKR = 0
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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
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iB
+
vBEx
-
RB
RC
vBC +
+
vBE
RE
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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
Ideal F-G
Data
1.E-06
1.E-07
1.E-08
1.E-09
1.E-10
1.E-11
1.E-12
Ic
1.E-13
Ib
1.E-14
1.E-15
1.E-16
0.0
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0.2
0.4
0.6
0.8
iC and iB (A)
vs. vBE (V)
N = 1  1/slope
= 59.5
mV/dec
N = 2  1/slope
= 119 mV/dec
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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
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vBCx
+
RC
iB
RB
iE
vBC +
+
vBE
RE
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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
Ideal R-G
Data
1.E-06
1.E-07
1.E-08
1.E-09
1.E-10
1.E-11
1.E-12
Ic
Ie
1.E-13
Ib
1.E-14
1.E-15
1.E-16
0.0
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0.2
0.4
0.6
0.8
iE and iB (A)
vs. vBE (V)
N = 1  1/slope
= 59.5
mV/dec
N = 2  1/slope
= 119 mV/dec
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Distributed resistance in a planar BJT
coll.
base
& emitter contact regions
reg 1
reg 2
reg 3
reg 4
emitter
base
collector
• The base current
• Each region of the
must flow lateral to
base adds a term
the wafer surface
of lateral res.
• Assume E & C cur•  vBE diminishes as
rents perpendicular
current flows
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Simulation of 2dim. current flow
Q
VCC
 DV 
iB1 = iB
R
Q1
• 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
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R
Q2
R
Qn
• Both sources have
same current
iB1 = iB.
• The effective value of
the 2-dim. base
resistance is
Rbb’(iB) = DV/iB = RBBTh
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Analytical solution
for distributed Rbb
diB x 
 vBE
 JS L exp 
dx
 NFVt

 vBE
  JSE L exp 

 NEVt
dvBE x 
rBi
  iB x 
dx
L



• Analytical solution and SPICE
simulation both fit
RBB = Rbmin + Rbmax/(1 + iB/IRB)RB
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Distributed base
resistance function
RBBTh = RBM +
DR/(1+iB/IRB)RB
(DR = RB - RBM )
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.
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References
1
2
OrCAD PSpice A/D Manual, Version 9.1,
November, 1999, OrCAD, Inc.
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).
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