1. EE 5340 Semiconductor Device Theory Lecture 17 - Fall 2003
Professor Ronald L. Carter
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2. 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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3. Plot of typical Va > 0 current density equations
ln(J)
data
Effect of Rs
Vext
VKF
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4. For Va < 0 carrier recombination in DR
The S-R-H rate (tno = tpo = to) is
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5. Reverse bias (Va<0) => carrier gen in DR
Consequently U = -ni/2t0
t0 = mean min. carr. g/r lifetime
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6. Reverse bias (Va< 0), carr gen in DR (cont.)
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7. Ecrit for reverse breakdown (M&K**)
Taken from p. 198, M&K**
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8. 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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9. 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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10. 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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11. 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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12. Diode equivalent circuit (small sig)ID
h is the practical “ideality factor” IQ VD VQ
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13. Small-signal eq circuit
Cdiff and Cdepl are both charged by
Va = VQ Va
Cdiff
rdiff
Cdepl
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14. 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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15. Diode switching (cont.)
VF,VR >> Va
F: t < 0 Sw RF
R: t > 0 VF + RR D + VR
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16. Diode charge for t < 0 pn
pno x xn
xnc
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17. Diode charge for t >>> 0 (long times)pn
pno x xn
xnc
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18. Equation summary
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19. Snapshot for t barely > 0pn
Total charge removed, Qdis=IRt
pno x xn
xnc
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20. I(t) for diode switchingID IF ts
ts+trr t
- 0.1 IR
-IR
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21. L 17 Oct 21

22. L 17 Oct 21

23. 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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24. 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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25. Bipolar junction transistor (BJT)
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 P n p E B C
VEB
VCB
Charge neutral Region
Depletion Region
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26. npn BJT topology x x’ p-Base n-Collector N-Emitter z WB WB+WC -WE x”c
Charge Neutral Region
Depletion Region x x’
p-Base
n-Collector
N-Emitter z WB
WB+WC
-WE
x”c x” xB
x’E IE IC IB
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27. BJT boundary and injection cond (npn)
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28. BJT boundary and injection cond (npn)
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29. IC npn BJT (*Fig 9.2a)
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30. 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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