L14 March 3 1
EE5342 – Semiconductor Device Modeling and CharacterizationLecture 14 - Spring 2005
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
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Re{Y} vs. frequency
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10
Y-parameter data
300 mV
700 mV
1000 mV
800 mV
900 mV
500 mV
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Im{Y} vs. frequency
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10
Y-parameter data
300 mV
700 mV
1000 mV800 mV
900 mV
500 mV
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Bipolar junctiontransistor (BJT)• The BJT is a “Si
sandwich” Pn (P=p+,=p-) or Np(N=n+, =n-)
• BJT action: npn Forward Active when VBE > 0 and VBC < 0
P n
E B C
VEB VCB
Charge neutral Region
Depletion Region
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BJT coordinatesystems
0
z
x”c x”
0 WB WB+WC-WE
0 xB x0x’Ex’
Charge neutral RegionDepletion Region
Base CollectorEmitter
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BJT boundary andinjection cond (npn)
0p
p , VVfexppp
0p
p , VVfexppp
C
C
2i
E
E
2i
x"xnC
Nn
0nCtBC0nC0"xnC
x'xnE
Nn
0nEtBE0nE0'xnE
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BJT boundary andinjection cond (npn)
. V
Vfexpnn
n , VVfexpnn
dependent-inter are BC Base the that Note
tBC0pBxBxpB
Nn
0pBtBE0pB0xpB B
2i
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IC npn BJT(*Fig 9.2a)
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npn BJT bandsin FA region
qVBC
qVBE
q(VbiE-VBE ) q(VbiC-VBC )
injection high field
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Coordinate system - prototype npn BJT (Fig 9.8*)
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Notation fornpn & pnp BJTs• NE, NB, NC E, B, and C doping (maj)• xE, xB, xCE, B, and C CNR widths• DE, DB, DC Dminority for E, B, and C• LE, LB, LC Lminority for E, B, and C(L2
min = Dmin min)
E0, B0, C0 minority carrier life- times for E, B, and C regions
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Notation fornpn BJTs only• pEO, nBO, pCO: E, B, and C thermal
equilibrium minority carrier conc • pE(x’), nB(x), pC(x’’): positional mathe-
matical function for the E, B, and C total minority carrier concentrations
pE(x’), nB(x), pC(x’’): positional ma- thematical function for the excess minority carriers in the E, B, and C
L14 March 3 13
Notation forpnp BJTs only• nEO, pBO, nCO: E, B, and C thermal
equilibrium minority carrier conc • nE(x’), pB(x), nC (x’’): positional mathe-
matical function for the E, B, and C total minority carrier concentrations
nE(x’), pB(x), nC(x’’): positional ma- thematical function for the excess minority carriers in the E, B, and C
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npn BJT boundary conditions
0xp ,1VVexpp0x"p :C
etc. ,Nnn ,1V
Vexpnxn
,1VVexpn0xn :B
1VVexpp0p ,0xx'p :E
CCt
BC0CC
B
2i
0Bt
BC0BBB
tBE
0BB
tBE
0EEEE
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Emitter solutionin npn BJT
EEE
E
t
BE
E
E
E
E
t
BE
E
Lxx
xxV
V
Lx
Lxx
VV
x
, '1exppx'p
sinh
'sinh1exppx'p
ppp , 0x'px'
'pD
E0E
E0
E
E0EE0
E2
E2
E
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Base solutionin npn BJT
BtBC
BtBE
B0
BBBt
BC
B
Bt
BE
B
BB0
B
B0BB0BB
B2B
2
xx
VVfx
x1VVfn
Lx when and Lx
VVf
Lxx
VVf
Lx
nxn
nnn , 0Dxn
xxn
expexp
sinhexp
sinhexpsinh
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Collector solutionin npn BJT
CCtBCC
C0C
CC
CC
tBC
C0C
C0CC0CC
C2
C2
Lx , VV , L"xpx"p
Lxsinh
L"xxsinh1V
Vexppx"p
ppp , 0Dx"p
x""xp
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Hyperbolic sinefunction
Lx
Lxsinh0L
x giving,Lx1L
x1Lx1L
x1Lxsinh L, x if so
...!2yy1e ,
eeee
Lxsinh
itlim
2yL/xL/xL/xL/x
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npn BJT regionsof operation
VBE
VBC
Forward Active
Reverse Active Saturation
Cutoff
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npn FA BJT minoritycarrier distribution (Fig 9.4*)
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npn RA BJT minoritycarrier distribution (Fig 9.11a*)
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npn cutoff BJT mincarrier distribution (Fig 9.10a*)
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npn sat BJT minoritycarrier distribution (Fig 9.10b*)
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Defining currents inFA mode npn BJT (Fig 9.13*)
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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.