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EE 5340 Semiconductor Device Theory Lecture 17 - Fall 2009

EE 5340 Semiconductor Device Theory Lecture 17 - Fall 2009. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc. Soln. to the Poisson Eqn. in the D.R. E x. x n. -x p. x. -x pc. x nc. -E max. Band diagram for P + -n jctn at V a > 0. E c. q(V bi -V a ). q(V a ).

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EE 5340 Semiconductor Device Theory Lecture 17 - Fall 2009

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  1. EE 5340Semiconductor Device TheoryLecture 17 - Fall 2009 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

  2. Soln. to the Poisson Eqn. in the D.R. Ex xn -xp x -xpc xnc -Emax

  3. Band diagram for P+-n jctn at Va> 0 Ec q(Vbi-Va) q(Va) qfp < 0 EFi Ec EFN EFP Ev EFi qfn > 0 *Na > Nd => |fp|> fn Ev p-type for x<0 n-type for x>0 x -xpc xn 0 -xp xnc

  4. Evaluating the diode current density due to diffusion in the CNR

  5. General time-constant

  6. General time-constant (cont.)

  7. General time-constant (cont.)

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

  9. Diode Diffusion and Recombination Currents

  10. 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)),

  11. High level injeffects (cont.)

  12. 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

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

  14. For Va < 0 carrier generation/ recombination in DR • The S-R-H rate (tno = tpo = to) is

  15. Reverse bias (Va<0)=> carrier gen/rec in DR • Consequently U = -ni/2t0 • t0 = mean min. carr. g/r lifetime

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

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

  18. 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

  19. 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

  20. 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

  21. 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

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

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

  24. 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

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

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

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

  28. Equationsummary

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

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

  31. 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

  32. Ideal diode equationfor 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]

  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.

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