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Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002

Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. Ideal Junction Theory. Assumptions E x = 0 in the chg neutral reg. (CNR) MB statistics are applicable Neglect gen/rec in depl reg (DR)

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Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002

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  1. Semiconductor Device Modeling and CharacterizationEE5342, Lecture 7-Spring 2002 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

  2. Ideal JunctionTheory Assumptions • Ex = 0 in the chg neutral reg. (CNR) • MB statistics are applicable • Neglect gen/rec in depl reg (DR) • Low level injections apply so that dnp < ppo for -xpc < x < -xp, and dpn < nno for xn < x < xnc • Steady State conditions

  3. Ideal JunctionTheory (cont.) Apply the Continuity Eqn in CNR

  4. Ideal JunctionTheory (cont.)

  5. Ideal JunctionTheory (cont.)

  6. Excess minoritycarrier distr fctn

  7. Forward Bias Energy Bands q(Vbi-Va) Imref, EFn Ec EF qVa EF EFi Imref, EFp Ev x -xpc -xp xn xnc 0

  8. CarrierInjection ln(carrier conc) ln Na ln Nd ln ni ~Va/Vt ~Va/Vt ln ni2/Nd ln ni2/Na x xnc -xpc -xp xn 0

  9. Minority carriercurrents

  10. Evaluating thediode current

  11. Special cases forthe diode current

  12. 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]

  13. 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

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

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

  16. 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

  17. 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

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

  19. General time-constant

  20. General time-constant (cont.)

  21. General time-constant (cont.)

  22. 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).

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

  24. 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

  25. 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. ***Physics of Semiconductor Devices, Shur, Prentice-Hall, 1990.

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