1. Semiconductor Device Modeling & Characterization Lecture 15
Professor Ronald L. Carter
Spring 2001
L15 March 6

2. npn BJT topology xE x’E x’C xC z xJE xJC n-emitter p-Base n-collectorIE IC IB xE
x’E
x’C xC z
xJE
xJC
n-emitter
p-Base
n-collector
Depletion Region
Charge Neutral Region
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3. Ebers-Moll npn injection current circuit model
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4. Ebers-Moll npn transport current circuit model
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5. Ebers-Moll npn linking current circuit model
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6. Non-ideal effects in BJTs
Base-width modulation (FA: xB changes with changes in VBC)
Current crowding in 2-dim base
High-level injection (minority carriers g.t. dopant - especially in the base).
Emitter Bandgap narrowing (NE ~ density of states at cond. band. edge)
Junction breakdown at BC junction
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7. Charge components in the BJT
From Getreau, Modeling the
Bipolar Transistor,
Tektronix, Inc.
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8. Gummel-Poon Static npn Circuit ModelB
RBB
ILC
IBR
ICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB B’
ILE
IBF RE E
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9. Gummel-Poon Model General Form
QXXXXXXX NC NB NE <NS> MNAME <AREA> <OFF> <IC=VBE, VCE> <TEMP=T>
Netlist Examples
Q Q2N3904 IC=0.6, 5.0
Q 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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10. 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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11. Gummel-Poon Static Model Parameters
name parameter units default area
IS transport saturation current A 1.0e-16 *
BF ideal maximum forward beta - 100
NF forward current emission coefficient - 1.0
VAF forward Early voltage V infinite
ISE B-E leakage saturation current A 0 *
NE B-E leakage emission coefficient - 1.5
BR ideal maximum reverse beta - 1
NR reverse current emission coefficient - 1
VAR reverse Early voltage V infinite
ISC B-C leakage saturation current A 0 *
NC B-C leakage emission coefficient - 2
EG energy gap for temperature eV 1.11
effect on IS
XTI temperature exponent for effect on IS - 3
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12. Gummel-Poon Static Model Parameters
name parameter units default area
IKF corner for forward beta A infinite *
high current roll-off
IKR corner for reverse beta A infinite *
RB zero bias base resistance W 0 *
IRB current where base resistance A infinite *
falls halfway to its min value
RBM minimum base resistance W RB *
at high currents
RE emitter resistance W 0 *
RC collector resistance W 0 *
TNOM parameter - meas. temperature °C 27
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13. 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 }
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14. 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))
[1+144iB/(p2IRB)]1/2-1
z =
(24/p2)(iB/IRB)1/2
Regarding (i) RBB and (x) RTh on slide 22,
RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB
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15. BJT Characterization Forward GummeliC RC iB RE RB
vBEx
vBC
vBE + -
vBCx= 0 = vBC + iBRB - iCRC
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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16. Ideal F-G Data iC and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec
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17. BJT Characterization Reverse GummeliE RC iB RE RB
vBCx
vBC
vBE + -
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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18. Ideal R-G Data iE and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec
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19. Distributed resis- tance in a planar BJT
emitter
base
collector
reg 4
reg 3
reg 2
reg 1
coll base & emitter contact regions
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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20. Simulation of 2- dim. current flow=
 DV 
Both sources have same current iB1 = iB.
The effective value of the 2-dim. base resistance is
Rbb’(iB) = DV/iB = RBBTh
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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21. Analytical solution for distributed Rbb
Analytical solution and SPICE simulation both fit
RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB
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22. Distributed base resistance 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 , 1997.
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