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Semiconductor Device Modeling and Characterization – EE5342 Lecture 11 – Spring 2011

Semiconductor Device Modeling and Characterization – EE5342 Lecture 11 – Spring 2011. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. Minority carrier currents. Evaluating the diode current. Special cases for the diode current. Ideal diode equation. Assumptions:

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Semiconductor Device Modeling and Characterization – EE5342 Lecture 11 – Spring 2011

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  1. Semiconductor Device Modeling and Characterization – EE5342 Lecture 11 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

  2. Minority carriercurrents

  3. Evaluating thediode current

  4. Special cases forthe diode current

  5. Ideal diodeequation • Assumptions: • 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]

  6. Ideal diodeequation (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

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

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

  9. Charge distr in a (1-sided) short diode dpn • Assume Nd << Na • The sinh (see L12) 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

  10. Charge distr in a 1-sided short diode dpn • Assume Quasi-static charge distributions • Q’p = Q’p = qdpn(xn)Wn/2 • ddpn(xn) = (W/2)* {dpn(xn,Va+dV) - dpn(xn,Va)} dpn(xn,Va+dV) dpn(xn,Va) dQ’p Q’p x xnc xn

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

  12. General time-constant

  13. General time-constant (cont.)

  14. General time-constant (cont.)

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

  16. 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

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

  18. 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).

  19. 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)),

  20. High level injeffects (cont.)

  21. 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

  22. Diode Diffusion and Recombination Currents

  23. Diode Diffusion and Recombination Currents – One Sided Diode

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

  25. References *Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993. **MicroSim OnLine Manual, MicroSim Corporation, 1996.

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