EE 5340 Semiconductor Device Theory Lecture 16 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

Ideal diode equation Assumptions: Current dens, Jx = Js expd(Va/Vt) low-level injection Maxwell Boltzman statistics Depletion approximation Neglect gen/rec effects in DR Steady-state solution only Current dens, Jx = Js expd(Va/Vt) where expd(x) = [exp(x) -1] ©rlc L16-22Mar2011

Ideal diode equation (cont.) Js = Js,p + Js,n = hole curr + ele curr Js,p = qni2Dp coth(Wn/Lp)/(NdLp) = qni2Dp/(NdWn), Wn << Lp, “short” = qni2Dp/(NdLp), Wn >> Lp, “long” Js,n = qni2Dn coth(Wp/Ln)/(NaLn) = qni2Dn/(NaWp), Wp << Ln, “short” = qni2Dn/(NaLn), Wp >> Ln, “long” Js,n << Js,p when Na >> Nd ©rlc L16-22Mar2011

Diffnt’l, one-sided diode conductance Static (steady-state) diode I-V characteristic IQ Va VQ ©rlc L16-22Mar2011

Diffnt’l, one-sided diode cond. (cont.) ©rlc L16-22Mar2011

Charge distr in a (1- sided) short diode dpn Assume Nd << Na The sinh (see L10) 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 ©rlc L16-22Mar2011

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 ©rlc L16-22Mar2011

Cap. of a (1-sided) short diode (cont.) ©rlc L16-22Mar2011

Evaluating the diode current density ©rlc L16-22Mar2011

General time- constant ©rlc L16-22Mar2011

General time- constant (cont.) ©rlc L16-22Mar2011

General time- constant (cont.) ©rlc L16-22Mar2011

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). ©rlc L16-22Mar2011

Effect of carrier recombination in DR The S-R-H rate (tno = tpo = to) is ©rlc L16-22Mar2011

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 ©rlc L16-22Mar2011

Effect of carrier rec. in DR (cont.) ©rlc L16-22Mar2011

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)), ©rlc L16-22Mar2011

High level inj effects (cont.) ©rlc L16-22Mar2011

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 ©rlc L16-22Mar2011

Plot of typical Va > 0 current density equations ln(J) data Effect of Rs Vext VKF ©rlc L16-22Mar2011

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. ©rlc L16-22Mar2011