EE 5340 Semiconductor Device Theory Lecture 16 - Fall 2009 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc L 16 Oct 15

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 This material will not be published.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. 86-24 to 86-27, Los Angeles, CA, 1986. L 16 Oct 15

Evaluating the diode current density 9/28/2009 UTA Confidential

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 L 16 Oct 15

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 L 16 Oct 15

Cap. of a (1-sided) short diode (cont.) L 16 Oct 15

General time- constant L 16 Oct 15

General time- constant (cont.) L 16 Oct 15

General time- constant (cont.) L 16 Oct 15

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). L 16 Oct 15

Effect of carrier recombination in DR The S-R-H rate (tno = tpo = to) is L 16 Oct 15

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 L 16 Oct 15

Effect of carrier rec. in DR (cont.) L 16 Oct 15

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)), L 16 Oct 15

High level inj effects (cont.) L 16 Oct 15

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 L 16 Oct 15

Plot of typical Va > 0 current density equations ln(J) data Effect of Rs Vext VKF L 16 Oct 15

For Va < 0 carrier recombination in DR The S-R-H rate (tno = tpo = to) is L 16 Oct 15

Reverse bias (Va<0) => carrier gen in DR Consequently U = -ni/2t0 t0 = mean min. carr. g/r lifetime L 16 Oct 15

Reverse bias (Va< 0), carr gen in DR (cont.) L 16 Oct 15

Ecrit for reverse breakdown (M&K**) Taken from p. 198, M&K** L 16 Oct 15

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 L 16 Oct 15

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 L 16 Oct 15

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 L 16 Oct 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 L 16 Oct 15

Diode equivalent circuit (small sig) ID h is the practical “ideality factor” IQ VD VQ L 16 Oct 15

Small-signal eq circuit Cdiff and Cdepl are both charged by Va = VQ Va Cdiff rdiff Cdepl L 16 Oct 15

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 L 16 Oct 15

Diode switching (cont.) VF,VR >> Va F: t < 0 Sw RF R: t > 0 VF + RR D + VR L 16 Oct 15

Diode charge for t < 0 pn pno x xn xnc L 16 Oct 15

Diode charge for t >>> 0 (long times) pn pno x xn xnc L 16 Oct 15

Equation summary L 16 Oct 15

Snapshot for t barely > 0 pn Total charge removed, Qdis=IRt pno x xn xnc L 16 Oct 15

I(t) for diode switching ID IF ts ts+trr t - 0.1 IR -IR L 16 Oct 15

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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 L 16 Oct 15

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] L 16 Oct 15

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. L 16 Oct 15