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Semiconductor Device Modeling and Characterization EE5342, Lecture 5-Spring 2002

Semiconductor Device Modeling and Characterization EE5342, Lecture 5-Spring 2002. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. Minority hole lifetimes. Taken from Shur 3 , (p.101). Minority electron lifetimes. Taken from Shur 3 , (p.101). Parameter example.

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Semiconductor Device Modeling and Characterization EE5342, Lecture 5-Spring 2002

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  1. Semiconductor Device Modeling and CharacterizationEE5342, Lecture 5-Spring 2002 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

  2. Minority hole lifetimes. Taken from Shur3, (p.101).

  3. Minority electron lifetimes. Taken from Shur3, (p.101).

  4. Parameter example • tmin = (45 msec) 1+(7.7E-18cm3)Ni+(4.5E-36cm6)Ni2 • For Nd = 1E17cm3, tp = 25 msec • Why Nd and tp ?

  5. Direct rec forexcess min carr • Define low-level injection as dn = dp < no, for n-type, and dn = dp < po, for p-type • The recombination rates then are R’n = R’p = dn(t)/tn0, for p-type, and R’n = R’p = dp(t)/tp0, for n-type • Where tn0 and tp0 are the minority-carrier lifetimes

  6. S-R-H rec fordeficient min carr • If n < ni and p< pi, then the S-R-H net recomb rate becomes (p < po, n < no): U = R - G = - ni/(2t0cosh[(ET-Efi)/kT]) • And with the substitution that the gen lifetime, tg = 2t0cosh[(ET-Efi)/kT], and net gen rate U = R - G = - ni/tg • The intrinsic concentration drives the return to equilibrium

  7. The ContinuityEquation • The chain rule for the total time derivative dn/dt (the net generation rate of electrons) gives

  8. The ContinuityEquation (cont.)

  9. The ContinuityEquation (cont.)

  10. The ContinuityEquation (cont.)

  11. The ContinuityEquation (cont.)

  12. The ContinuityEquation (cont.)

  13. The ContinuityEquation (cont.)

  14. Poisson’sEquation • The electric field at (x,y,z) is related to the charge density r=q(Nd-Na-p-n) by the Poisson Equation:

  15. Poisson’sEquation • For n-type material, N = (Nd - Na) > 0, no = N, and (Nd-Na+p-n)=-dn +dp +ni2/N • For p-type material, N = (Nd - Na) < 0, po = -N, and (Nd-Na+p-n) = dp-dn-ni2/N • So neglecting ni2/N, [r=(Nd-Na+p-n)]

  16. Quasi-FermiEnergy

  17. Quasi-FermiEnergy (cont.)

  18. Quasi-FermiEnergy (cont.)

  19. p-type Ec Ec Ev EFn qfn= kT ln(Nd/ni) EFi Ev Energy bands forp- and n-type s/c n-type EFi qfp= kT ln(ni/Na) EFp

  20. JunctionC (cont.) r +Qn’=qNdxn +qNd dQn’=qNddxn -xp x -xpc xn xnc Charge neutrality => Qp’ + Qn’ = 0, => Naxp = Ndxn -qNa dQp’=-qNadxp Qp’=-qNaxp

  21. JunctionC (cont.) • The C-V relationship simplifies to

  22. JunctionC (cont.) • If one plots [C’j]-2vs. Va Slope = -[(C’j0)2Vbi]-1 vertical axis intercept = [C’j0]-2 horizontal axis intercept = Vbi C’j-2 C’j0-2 Va Vbi

  23. Arbitrary dopingprofile • If the net donor conc, N = N(x), then at xn, the extra charge put into the DR when Va->Va+dVa is dQ’=-qN(xn)dxn • The increase in field, dEx =-(qN/e)dxn, by Gauss’ Law (at xn, but also const). • So dVa=-(xn+xp)dEx= (W/e) dQ’ • Further, since N(xn)dxn = N(xp)dxp gives, the dC/dxn as ...

  24. Arbitrary dopingprofile (cont.)

  25. Arbitrary dopingprofile (cont.)

  26. Arbitrary dopingprofile (cont.)

  27. Example • An assymetrical p+ n junction has a lightly doped concentration of 1E16 and with p+ = 1E18. What is W(V=0)? Vbi=0.816 V, Neff=9.9E15, W=0.33mm • What is C’j? = 31.9 nFd/cm2 • What is LD? = 0.04 mm

  28. Law of the junction(follow the min. carr.)

  29. Law of the junction (cont.)

  30. Law of the junction (cont.)

  31. InjectionConditions

  32. 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

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

  34. Ideal JunctionTheory (cont.)

  35. Ideal JunctionTheory (cont.)

  36. Excess minoritycarrier distr fctn

  37. References • 1Device Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986. • 2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981. • 3 Physics of Semiconductor Devices, Shur, Prentice-Hall, 1990.

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