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Understanding Carrier Recombination and High-Level Injection Effects in Diode Modeling

This lecture details the effects of carrier recombination in semiconductor diodes, focusing on the Shockley-Read-Hall (S-R-H) recombination rate and its impact on diode current under varying injection levels. It discusses high-level injection dynamics, junction breakdown mechanisms including avalanche and Zener effects, and the influence of reverse bias on carrier generation. Practical examples and equations related to current density, diode switching, and equivalent circuits are provided to illustrate these concepts. The lecture is essential for understanding semiconductor device behavior.

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Understanding Carrier Recombination and High-Level Injection Effects in Diode Modeling

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  1. Semiconductor Device Modeling and CharacterizationEE5342, Lecture 8-Spring 2003 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

  2. Effect of carrierrecombination in DR • The S-R-H rate (tno = tpo = to) is

  3. Effect of carrierrec. 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

  4. Effect of carrierrec. in DR (cont.)

  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)),

  6. High level injeffects (cont.)

  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

  8. ln(J) Plot of typical Va > 0 current density equations data Effect of Rs Vext VKF

  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.

  10. Reverse bias (Va< 0),carr gen in DR (cont.)

  11. Reverse biasjunction 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

  12. Ecrit for reverse breakdown (M&K**) Taken from p. 198, M&K**

  13. Reverse biasjunction 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

  14. Junction curvatureeffect 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

  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

  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 = ?

  17. Parameters forexamples • Get tmin from the model used in Project 2 tmin = (45 msec) 1+(7.7E-18cm3)Ni+(4.5E-36cm6)Ni2 • For Nd = 1E17cm3, tp = 25 msec • Why Nd and tp ? • Lp = ?

  18. Hole lifetimes, taken from Shur***, p. 101.

  19. Example • Js,long, = ? • If xnc, = 2 micron, Js,short, = ?

  20. Example(cont.) • Estimate VKF • Estimate IKF

  21. Example(cont.) • Estimate Js,rec • Estimate Rs if xnc is 100 micron

  22. Example(cont.) • Estimate Jgen for 10 V reverse bias • Estimate BV

  23. Diode equivalentcircuit (small sig) ID h is the practical “ideality factor” IQ VD VQ

  24. Small-signal eqcircuit Cdiff and Cdepl are both charged by Va = VQ Va rdiff Cdepl Cdiff

  25. 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

  26. Diode switching(cont.) VF,VR >> Va F: t < 0 Sw RF R: t > 0 VF + RR D VR +

  27. Diode chargefor t < 0 pn pno x xn xnc

  28. Diode charge fort >>> 0 (long times) pn pno x xn xnc

  29. Equationsummary

  30. Snapshot for tbarely > 0 pn Total charge removed, Qdis=IRt pno x xn xnc

  31. I(t) for diodeswitching ID IF ts ts+trr t - 0.1 IR -IR

  32. 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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