EE 5340 Semiconductor Device Theory Lecture 16 – Spring 2011

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

2. Ideal diodeequation • Assumptions: • low-level injection • Maxwell Boltzman statistics • Depletion approximation • Neglect gen/rec effects in DR • Steady-state solution only • Current dens, Jx = Jsexpd(Va/Vt) • where expd(x) = [exp(x) -1]

3. Ideal diodeequation (cont.) • Js = Js,p + Js,n = hole curr + elecurr Js,p = qni2Dpcoth(Wn/Lp)/(NdLp) = qni2Dp/(NdWn), Wn<< Lp, “short” = qni2Dp/(NdLp), Wn>> Lp, “long” Js,n = qni2Dncoth(Wp/Ln)/(NaLn) = qni2Dn/(NaWp), Wp<< Ln, “short” = qni2Dn/(NaLn), Wp>> Ln, “long” Js,n<< Js,p when Na >> Nd

4. Diffnt’l, one-sided diode conductance ID Static (steady-state) diode I-V characteristic IQ Va VQ

5. Diffnt’l, one-sided diode cond. (cont.)

6. 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

7. 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 xnc xn

8. Cap. of a (1-sided) short diode (cont.)

9. Evaluating the diode current density

10. General time-constant

11. General time-constant (cont.)

12. General time-constant (cont.)

13. 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).

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

15. 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

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

17. 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)),

18. High level injeffects (cont.)

19. 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

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

21. 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.