semiconductor device modeling and characterization – ee5342 lecture 22 – spring 2011 professor...
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Semiconductor Device Modeling and
Characterization – EE5342 Lecture 22 – 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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E-M model equations
BB
BC2i
CSRSESFBB
BE2i
S
t
BCCSR
t
BEESE
t
BEESF
t
BCCSC
xNDAqn
IIIxN
DAqn
I gives iprelationsh yreciprocit The
VV
fIV
VfII
V
VfI
VV
fII
expexp
expexp
4
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Common emitter current gain, F
lim. , V2
Vexp
Dn2
xxn ,
xDN
xDN
L2
x
lim. , V2
Vexp
Dn2
xxn ,
L2
xxDN
xDN
limited. or limited is BJT a Usually,
V2
Vexp
Dn2
xxn
L2
xxDN
xDN
1 so ,
1 ; III with ,
II
Tt
BE
0BBO
BBEi
EBE
BEB2B
2B
t
BE
0BBO
BBEi2B
2B
EBE
BEB
T
1
t
BE
0BBO
BBEi2B
2B
EBE
BEB
0
00CBE
B
C0
5
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Recombination/GenCurrents (FA)
CB
CBBCeff,
1gen
BCeff,
BCbiCBC
gen
BCiGC
1rec
BEt
BE
rec
iBERE
NNNN
N and
rate, ionrecombinat the is and DR CB
the is qN
VV2W where ,
2Wqn
J
.rate ionrecombinat the is and DR
EB the is W where ,V2
Vexp
2
nqWJ
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npn Base-width mod.(Early Effect) Fig 9.15*
xn
qDJ nn
BC
B
BBC
BB
BC
BBjC
BC
j
Vx
xJ
VJ
xJ
xJ
Vx
AqNCV
Q
pn
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Base-width modulation(Early Effect, cont.)
Fig 9.16*
ACEB
jC
CE
B
jC
B
BC
B
BCB
VVI
Q
C
VI
AqN
C
xJ
Vx
AxJ
VI
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Charge componentsin the BJT **From Getreau, Modeling the
Bipolar Transistor, Tektronix, Inc.
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Gummel-Poon Staticnpn Circuit Model
C
E
B
B’
ILC
ILEIBF
IBRICC - IEC = {IS/QB}*
{exp(vBE/NFVt)-exp(vBC/NRVt)}
RC
RE
RBB
IntrinsicTransistor
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Gummel-PoonModelGeneral FormQXXXXXXX NC NB NE <NS> MNAME <AREA> <OFF> <IC=VBE, VCE> <TEMP=T>Netlist Examples
Q5 11 26 4 Q2N3904 IC=0.6, 5.0Q3 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-PoonStatic ModelGummel 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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NAME PARAMETER UNIT DEFAULTIS transport saturation current A 1.0e-16BF ideal maximum forward beta - 100NF forward current emission coef. - 1.0VAF forward Early voltage V infiniteISE B-E leakage saturation current A 0NE B-E leakage emission coefficient - 1.5BR ideal maximum reverse beta - 1NR reverse current emission coeff. - 1VAR reverse Early voltage V infiniteISC B-C leakage saturation current A 0NC B-C leakage emission coefficient - 2EG energy gap (IS dep on T) eV 1.11XTI temperature exponent for IS - 3
Gummel-Poon Static Par.
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Gummel-Poon StaticModel ParametersNAME PARAMETER UNIT DEFAULTIKF corner for forward beta A infinite
high current roll-offIKR corner for reverse beta A infinite
high current roll-offRB zero bias base resistance W 0IRB current where base resistance A
infinitefalls halfway to its min value
RBM minimum base resistance W RBat high currents
RE emitter resistance W 0RC collector resistance W 0TNOM parameter - meas. temperature °C
27
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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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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 = {½ +¼ +(BF IBF/IKF + BR IBR/IKR)1/2} (1 - vBC/VAF - vBE/VAR )-1
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Gummel PoonBase ResistanceIf IRB = 0, RBB = RBM+(RB-RBM)/QB
If IRB > 0RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z))
[+iB/(IRB)]1/2- (/)(iB/IRB)1/2
z =
Regarding (i) RBB and (x) RTh on slide 23,
RBB = Rbmin + Rbmax/(1 + iB/IRB)RB
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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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Making a diode from the GP BJT modelC
E
B
B’
ILC
ILEIBF
IBRICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB
RC
RE
RBB
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Making a completediode 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
• 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 CharacterizationForward GummelvBCx= 0 = vBC + iBRB - iCRC
vBEx = vBE +iBRB +(iB+iC)RE
iB = IBF + ILE =
ISexpf(vBE/NFVt)/BF
+ ISEexpf(vBE/NEVt)
iC = FIBF/QB =
ISexpf(vBE/NFVt)/QB
+
-
iC RC
iB
RE
RB
vBEx
vBC
vBE
++
-
-
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Ideal F-G DataiC and iB (A)
vs. vBE (V)
N = 1 1/slope = 59.5 mV/dec
N = 2 1/slope = 119 mV/dec
BJ T I (A) vs. Vbe (V) for the G-P model Forward Gummel configuration (Vbcx=0)
1.E-16
1.E-15
1.E-14
1.E-13
1.E-12
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
0.0 0.2 0.4 0.6 0.8
I c
I b
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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 =
ISexpf(vBC/NRVt)/BR
+ ISCexpf(vBC/NCVt)
iE = RIBR/QB =
ISexpf(vBC/NRVt)/QB
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Ideal R-G DataiE and iB (A)
vs. vBE (V)
N = 1 1/slope = 59.5 mV/dec
N = 2 1/slope = 119 mV/dec
BJ T I (A) vs. Vbe (V) for the G-P model Forward Gummel configuration (Vbcx=0)
1.E-16
1.E-15
1.E-14
1.E-13
1.E-12
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
0.0 0.2 0.4 0.6 0.8
I c
I b
Ie
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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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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).