1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
Semiconductor Device Modeling and Characterization EE5342, Lecture 8-Spring 2002
Professor Ronald L. Carter
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2. Effect of carrier recombination in DR
The S-R-H rate (tno = tpo = to) is
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3. Effect of carrier rec. in DR (cont.)
For low Va ~ 10 Vt
In DR, n and p are still > ni
The net recombination rate, U, is still finite so there is net carrier recomb.
reduces the carriers available for the ideal diode current
adds an additional current component
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4. Effect of carrier rec. in DR (cont.)
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5. High level injection effects
Law of the junction remains in the same form, [pnnn]xn=ni2exp(Va/Vt), etc.
However, now dpn = dnn become >> nno = Nd, etc.
Consequently, the l.o.t.j. reaches the limiting form dpndnn = ni2exp(Va/Vt)
Giving, dpn(xn) = niexp(Va/(2Vt)), or dnp(-xp) = niexp(Va/(2Vt)),
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6. High level inj effects (cont.)
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7. Summary of Va > 0 current density eqns.
Ideal diode, Jsexpd(Va/(hVt))
ideality factor, h
Recombination, Js,recexp(Va/(2hVt))
appears in parallel with ideal term
High-level injection, (Js*JKF)1/2exp(Va/(2hVt))
SPICE model by modulating ideal Js term
Va = Vext - J*A*Rs = Vext - Idiode*Rs
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8. Plot of typical Va > 0 current density eqns.
Vext-Vd=JARs
ln J
low level injection
ln(JKF)
Effect of Rs
ln[(Js*JKF) 1/2]
Effect of high level injection
ln(Jsrec)
data
ln(Js)
Vext
recomb. current
VKF
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9. Reverse bias (Va<0) => carrier gen in DR
Va < 0 gives the net rec rate, U = -ni/2t0, t0 = mean min carr g/r l.t.
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10. Reverse bias (Va< 0), carr gen in DR (cont.)
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11. Reverse bias junction breakdown
Avalanche breakdown
Electric field accelerates electrons to sufficient energy to initiate multiplication of impact ionization of valence bonding electrons
field dependence shown on next slide
Heavily doped narrow junction will allow tunneling - see Neamen*, p. 274
Zener breakdown
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12. Ecrit for reverse breakdown (M&K**)
Taken from p. 198, M&K**
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13. Reverse bias junction breakdown
Assume -Va = VR >> Vbi, so Vbi-Va-->VR
Since Emax~ 2VR/W = (2qN-VR/(e))1/2, and VR = BV when Emax = Ecrit (N- is doping of lightly doped side ~ Neff)
BV = e (Ecrit )2/(2qN-)
Remember, this is a 1-dim calculation
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14. Junction curvature effect on breakdown
The field due to a sphere, R, with charge, Q is Er = Q/(4per2) for (r > R)
V(R) = Q/(4peR), (V at the surface)
So, for constant potential, V, the field, Er(R) = V/R (E field at surface increases for smaller spheres)
Note: corners of a jctn of depth xj are like 1/8 spheres of radius ~ xj
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15. BV for reverse breakdown (M&K**)
Taken from Figure 4.13, p. 198, M&K**
Breakdown voltage of a one-sided, plan, silicon step junction showing the effect of junction curvature.4,5
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16. Example calculations
Assume throughout that p+n jctn with Na = 3e19cm-3 and Nd = 1e17cm-3
From graph of Pierret mobility model, mp = 331 cm2/V-sec and Dp = Vtmp = ?
Why mp and Dp?
Neff = ?
Vbi = ?
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17. L08 07Feb02

18. Parameters for examples
Get tmin from the model used in Project tmin = (45 msec) (7.7E-18cm3)Ni+(4.5E-36cm6)Ni2
For Nd = 1E17cm3, tp = 25 msec
Why Nd and tp ?
Lp = ?
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19. Hole lifetimes, taken from Shur***, p. 101.
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20. Example
Js,long, = ?
If xnc, = 2 micron, Js,short, = ?
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21. Example (cont.)
Estimate VKF
Estimate IKF
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22. Example (cont.) Estimate Js,rec Estimate Rs if xnc is 100 micron
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23. Example (cont.) Estimate Jgen for 10 V reverse bias Estimate BV
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24. Diode equivalent circuit (small sig)ID
h is the practical “ideality factor” IQ VD VQ
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25. Small-signal eq circuit
Cdiff and Cdepl are both charged by
Va = VQ Va
Cdiff
rdiff
Cdepl
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26. Diode Switching Consider the charging and discharging of a Pn diode
(Na > Nd)
Wd << Lp
For t < 0, apply the Thevenin pair VF and RF, so that in steady state
IF = (VF - Va)/RF, VF >> Va , so current source
For t > 0, apply VR and RR
IR = (VR + Va)/RR, VR >> Va, so current source
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27. Diode switching (cont.)
VF,VR >> Va
F: t < 0 Sw RF
R: t > 0 VF + RR D + VR
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28. Diode charge for t < 0 pn
pno x xn
xnc
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29. Diode charge for t >>> 0 (long times)pn
pno xn
xnc x
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30. Equation summary
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31. Snapshot for t barely > 0pn
Total charge removed, Qdis=IRt
pno x xn
xnc
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32. I(t) for diode switchingID IF ts
ts+trr t
- 0.1 IR
-IR
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33. References
* Semiconductor Physics and Devices, 2nd ed., by Neamen, Irwin, Boston, 1997.
**Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, John Wiley, New York, 1986.
***Physics of Semiconductor Devices, Shur, Prentice-Hall, 1990.
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