Semiconductor Device Modeling and
Characterization – EE5342 Lecture 21 – Spring 2011
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
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Linking current E-M circuit model
ECCC
CTEC
I-I
II
CB
t
BC
R
S
R
EC
I
V
Vfexp
II
t
BE
F
S
F
CC
EB
V
Vfexp
II
I
B
E
C
2
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Non-ideal effects in BJTs• Recombination/Generation effects
• 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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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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Base region high-level injection (npn)
HLI in ennp :Note
Nennp when
n
NlnV2V when HLI aseB
npennp
edges DR @ Junction the of Law
tBE
tBE
tBE
V/V2i0BB
BV2/V
i0B0B
i
BtBE
0xBBV/V2
i0'xEE
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Effect of HLI in npnbase region (cont)
HLI).-E for changes J (notice markedly
change to factor JJ/J causing
, L/xsinh
V/VfexpnL/xtanh
V2/Vexpn
LqD
J
:as region) HLI the (in rewritten be must
, L/xsinhV/Vfexp
L/xtanh
V/Vfexp
LnqD
J
0x at current electron the lyConsequent
pE
pEnEnE
BB
tBCB0
BB
tBEi
B
BnE
BB
tBC
BB
tBE
B
B0BnE
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Effect of HLI in npnbase region (cont)
markedly. change
to /JJ factor the causing
, L/xtanh
V/VfexpnL/xsinh
V2/Vexpn
LqD
J
:as region) HLI the (in rewritten be must
, L/xtanhV/Vfexp
L/xsinh
V/Vfexp
LnqD
J
xx at current electron the eFurthermor
nEnCT
BB
tBCB0
BB
tBEi
B
BnC
BB
tBC
BB
tBE
B
B0BnC
B
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Emitter region high-level injection (npn)
HLI in ennp :Note
Nennp so
n
NlnV2V when HLI Emitter
npennp
edges DR @ Junction the of Law
tBE
tBE
tBE
V/V2i0EE
EV2/V
i0E0E
i
EtBE
0xBBV/V2
i0'xEE
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Effect of HLI innpn emitter region
HLI).-B for changes the to addition in
change to factor JJ/J causing
, V2
Vexp
L/xtanhL
nqDJ as
n/NlnVV (for rewritten be must
, 1V
Vexp
L/xtanhL
pqDJ
0x' at current hole the lyConsequent
pEnEnE
t
BE
EEE
iEpE
iEtBE
t
BE
EEE
E0EpE
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Bandgap narrowing effects Fig 9.20*
kT
Eexpnn
17e2
NmV10E
E0NEE
g2i
2iE
dg
gdgg
21
slope Replaces ni2
throughout
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Junction breakdown at BC junction• Reach-through or punch-through
when WCB and/or WEB become large enough to reduce xB to zero
• Avalanche breakdown when Emax at EB junction or CB junction reaches Ecrit.
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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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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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Charge componentsin the BJT **From Getreau, Modeling the
Bipolar Transistor, Tektronix, Inc.
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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).
Recommended