1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
EE5342 – Semiconductor Device Modeling and Characterization Lecture 12 February 26, 2010
Professor Ronald L. Carter

2. ln ia ln(IKF) ln[(IS*IKF) 1/2] ln(ISR) ln(IS) va= Vext VKF
Vext - vd = ia*Rs
low level injection
ln ia
ln(IKF)
Effect of Rs
ln[(IS*IKF) 1/2]
Effect of high level injection
ln(ISR)
Data
ln(IS)
va= Vext
recomb. current
VKF
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3. Static Model Equations for I-V Parameter Extraction
In the region where:
id ~ ISeff[exp {vd/(NeffVt)} – 1]
{did/dvd}/iD = d[ln(id)]/dvd = 1/(NeffVt), so
{dvd/d[ln(id)]}/Vt = (id,vd), and
exp{ln(id) – vd/(NeffVt)} = (id,vd).
Note: iD, Vt, etc., are normalized to 1A, 1V, resp.
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4. Static Model Equations for C-V Parameter Extraction
The Capacitance-Voltage model eqn. is:
Cj = CJO[1 - vd/VJ]-M
{dvd/d[ln(Cj)]} = -(1/M)(1 - vd/VJ)
Experimentally plot y = {dvd/d[ln(Cj)]} vs. vd
The slope estimates -1/M, the vd-axis intercept estimates VJ.
On the Cj vs. vd plot, the Cj-axis intercept is CJO
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5. PiN Diode PiN: Na >> Nint (= N-) & Nint << Nd
Wi = Intrinsic region (metall.) width
Em,P-T = Peak field mag. when xn = Wi
Vbi = fi = Vtln(NaNd/ni2)
Vbi,int = fi,int = Vtln(NaNint/ni2)
VHL = Vtln(Nd/Nint), the offset at N+N-
Vbi = Vbi,int + VHL
VPT = applied voltage when xn = Wi
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6. PiN Diode Depletion Fields
Normalized Position, x’ = x/Wi
Normalized Field, E/Em,P-T
dx’p
dx’n
x’n
-x’p
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7. PiN Diode Depletion Conditions

8. CV data and N(x) calculation

9. Bipolar junction transistor (BJT)E B C
VEB
VCB
Charge neutral Region
Depletion Region
The BJT is a “Si sandwich” Pnp (P=p+,p=p-) or Npn (N=n+, n=n-)
BJT action: npn Forward Active when VBE > 0 and VBC < 0
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10. BJT coordinate systemsz
x”c x” WB
WB+WC
-WE xB x
x’E x’
Charge neutral Region
Depletion Region
Base
Collector
Emitter
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11. BJT boundary and injection cond (npn)
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12. BJT boundary and injection cond (npn)
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13. IC npn BJT (*Fig 9.2a)
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14. npn BJT bands in FA region
q(VbiE-VBE )
q(VbiC-VBC )
qVBE
qVBC
injection
high field
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15. Coordinate system - prototype npn BJT (Fig 9.8*)
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16. Notation for npn & pnp BJTs
NE, NB, NC E, B, and C doping (maj)
xE, xB, xC E, B, and C CNR widths
DE, DB, DC Dminority for E, B, and C
LE, LB, LC Lminority for E, B, and C (L2min = Dmin tmin)
The minority carrier lifetimes in the E, B, and C regions are tE0, tB0, & tC0
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17. Notation for npn 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
The excess carrier concentrations dpE(x’), dnB(x), dpC(x’’) are the positional mathematical functions in the E, B, and C
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18. Notation for pnp 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
dnE(x’), dpB(x), dnC(x’’): positional ma- thematical function for the excess minority carriers in the E, B, and C
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19. npn BJT boundary conditions
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20. Emitter solution in npn BJT

21. Base solution in npn BJT

22. Collector solution in npn BJT

23. Hyperbolic sine function

24. npn BJT regions of operation
VBC
Reverse Active
Saturation
VBE
Forward Active
Cutoff
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25. npn FA BJT minority carrier distribution (Fig 9.4*)
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26. npn RA BJT minority carrier distribution (Fig 9.11a*)
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27. npn cutoff BJT min carrier distribution (Fig 9.10a*)
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28. npn sat BJT minority carrier distribution (Fig 9.10b*)
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29. Defining currents in FA mode npn BJT (Fig 9.13*)
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30. References
1 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.
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