1. EE 5340 Semiconductor Device Theory Lecture 16 - Fall 2009
Professor Ronald L. Carter
L 16 Oct 15

2. Supplemental Material Relevant to the Project
At the beginning of the class, supplemental material relevant to the project will be given.
This material will not be published. You will need to take notes
This material will be of significant assistance in completing the project.
The first supplemental material will address the papers written by Law, et al., and Swirhun, et al., in IEDM 86, pp to 86-27, Los Angeles, CA, 1986.
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3. Evaluating the diode current density
9/28/2009
UTA Confidential

4. Charge distr in a (1- sided) short diode
dpn
Assume Nd << Na
The sinh (see L15) excess minority carrier distribution becomes linear for Wn << Lp
dpn(xn)=pn0expd(Va/Vt)
Total chg = Q’p = Q’p = qdpn(xn)Wn/2
Wn = xnc- xn
dpn(xn)
Q’p x xn
xnc
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5. Charge distr in a 1- sided short diode
dpn
Assume Quasi-static charge distributions
Q’p = +qdpn(xn,Va)Wn/2
dQ’p =q(W/2) x {dpn(xn,Va+dV) dpn(xn,Va)}
Wn = xnc - xn (Va)
dpn(xn,Va+dV)
dpn(xn,Va)
dQ’p
Q’p x xn
xnc
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6. Cap. of a (1-sided) short diode (cont.)
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7. General time- constant
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8. General time- constant (cont.)
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9. General time- constant (cont.)
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10. Effect of non- zero E in the CNR
This is usually not a factor in a short diode, but when E is finite -> resistor
In a long diode, there is an additional ohmic resistance (usually called the parasitic diode series resistance, Rs)
Rs = L/(nqmnA) for a p+n long diode.
L=Wn-Lp (so the current is diode-like for Lp and the resistive otherwise).
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11. Effect of carrier recombination in DR
The S-R-H rate (tno = tpo = to) is
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12. 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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13. Effect of carrier rec. in DR (cont.)
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14. 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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15. High level inj effects (cont.)
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16. 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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17. Plot of typical Va > 0 current density equations
ln(J)
data
Effect of Rs
Vext
VKF
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18. For Va < 0 carrier recombination in DR
The S-R-H rate (tno = tpo = to) is
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19. Reverse bias (Va<0) => carrier gen in DR
Consequently U = -ni/2t0
t0 = mean min. carr. g/r lifetime
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20. Reverse bias (Va< 0), carr gen in DR (cont.)
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21. Ecrit for reverse breakdown (M&K**)
Taken from p. 198, M&K**
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22. 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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23. 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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24. 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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25. 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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26. Diode equivalent circuit (small sig)ID
h is the practical “ideality factor” IQ VD VQ
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27. Small-signal eq circuit
Cdiff and Cdepl are both charged by
Va = VQ Va
Cdiff
rdiff
Cdepl
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28. Diode Switching Consider the charging and discharging of a Pn diode
(Na > Nd)
Wn << 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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29. Diode switching (cont.)
VF,VR >> Va
F: t < 0 Sw RF
R: t > 0 VF + RR D + VR
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30. Diode charge for t < 0 pn
pno x xn
xnc
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31. Diode charge for t >>> 0 (long times)pn
pno x xn
xnc
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32. Equation summary
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33. Snapshot for t barely > 0pn
Total charge removed, Qdis=IRt
pno x xn
xnc
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34. I(t) for diode switchingID IF ts
ts+trr t
- 0.1 IR
-IR
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35. L 16 Oct 15

36. L 16 Oct 15

37. Ideal diode equation for EgN = EgN
Js = Js,p + Js,n = hole curr + ele curr
Js,p = qni2Dp coth(Wn/Lp)/(NdLp), [cath.] = qni2Dp/(NdWn), Wn << Lp, “short” = qni2Dp/(NdLp), Wn >> Lp, “long”
Js,n = qni2Dn coth(Wp/Ln)/(NaLn), [anode] = qni2Dn/(NaWp), Wp << Ln, “short” = qni2Dn/(NaLn), Wp >> Ln, “long”
Js,n<<Js,p when Na>>Nd , Wn & Wp cnr wdth
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38. Ideal diode equation for heterojunction
Js = Js,p + Js,n = hole curr + ele curr
Js,p = qniN2Dp/[NdLptanh(WN/Lp)], [cath.] = qniN2Dp/[NdWN], WN << Lp, “short” = qniN2Dp/(NdLp), WN >> Lp, “long”
Js,n = qniP2Dn/[NaLntanh(WP/Ln)], [anode] = qniP2Dn/(NaWp), Wp << Ln, “short” = qniP2Dn/(NaLn), Wp >> Ln, “long”
Js,p/Js,n ~ niN2/niP2 ~ exp[[EgP-EgN]/kT]
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39. 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.
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