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EE 5340 Semiconductor Device Theory Lecture 14 - Fall 2010

EE 5340 Semiconductor Device Theory Lecture 14 - Fall 2010. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc. Shockley-Read- Hall Recomb. E. Indirect, like Si, so intermediate state. E c. E c. E T. E f. E fi. E v. E v. k. S-R-H trap characteristics M&K.

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EE 5340 Semiconductor Device Theory Lecture 14 - Fall 2010

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  1. EE 5340Semiconductor Device TheoryLecture 14 - Fall 2010 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

  2. Shockley-Read-Hall Recomb E Indirect, like Si, so intermediate state Ec Ec ET Ef Efi Ev Ev k

  3. S-R-H trapcharacteristicsM&K • The Shockley-Read-Hall Theory requires an intermediate “trap” site in order to conserve both E and p • If trap neutral when orbited (filled) by an excess electron - “donor-like” • Gives up electron with energy Ec - ET • “Donor-like” trap which has given up the extra electron is +q and “empty”

  4. S-R-H trapchar. (cont.) • If trap neutral when orbited (filled) by an excess hole - “acceptor-like” • Gives up hole with energy ET - Ev • “Acceptor-like” trap which has given up the extra hole is -q and “empty” • Balance of 4 processes of electron capture/emission and hole capture/ emission gives the recomb rates

  5. S-R-H recombination • Recombination rate determined by: Nt (trap conc.), vth (thermal vel of the carriers), sn (capture cross sect for electrons), sp (capture cross sect for holes), with tno = (Ntvthsn)-1, and tpo = (Ntvthsp)-1, where sn,p~p(rBohr,n.p)2

  6. S-R-H net recom-bination rate, U • In the special case where tno = tpo = to = (Ntvthso)-1 the net rec. rate, U is

  7. S-R-H “U” functioncharacteristics • The numerator, (np-ni2) simplifies in the case of extrinsic material at low level injection (for equil., nopo = ni2) • For n-type (no > dn = dp > po = ni2/no): (np-ni2) = (no+dn)(po+dp)-ni2 = nopo - ni2 + nodp + dnpo + dndp ~ nodp (largest term) • Similarly, for p-type, (np-ni2) ~ podn

  8. S-R-H rec forexcess min carr • For n-type low-level injection and net excess minority carriers, (i.e., no > dn = dp > po = ni2/no), U = dp/tp, (prop to exc min carr) • For p-type low-level injection and net excess minority carriers, (i.e., po > dn = dp > no = ni2/po), U = dn/tn, (prop to exc min carr)

  9. Minority hole lifetimes Mark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “Self-Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility, IEEE ELECTRON DEVICE LETTERS, VOL. 12, NO. 8, AUGUST 1991 The parameters used in the fit are τo = 10 μs, Nref= 1×1017/cm2, and CA = 1.8×10-31cm6/s.

  10. Minority electron lifetimes Mark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “Self-Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility, IEEE ELECTRON DEVICE LETTERS, VOL. 12, NO. 8, AUGUST 1991 The parameters used in the fit are τo = 30 μs, Nref= 1×1017/cm2, and CA = 8.3×10-32 cm6/s.

  11. References for Part A Device Electronics for Integrated Circuits, 3rd ed., by Richard S. Muller, Theodore I. Kamins, and Mansun Chan, John Wiley and Sons, New York, 2003. Mark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “Self-Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility, IEEE ELECTRON DEVICE LETTERS, VOL. 12, NO. 8, AUGUST 1991. D.B.M. Klaassen; “A UNIFIED MOBILITY MODEL FOR DEVICE SIMULATION”, Electron Devices Meeting, 1990. Technical Digest., International 9-12 Dec. 1990 Page(s):357 – 360. David Roulston, Narain D. Arora, and Savvas G. Chamberlain “Modeling and Measurement of Minority-Carrier Lifetime versus Doping in Diffused Layers of n+-p Silicon Diodes”, IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-29, NO. 2, FEBRUARY 1982, pages 284-291. M. S. Tyagi and R. Van Overstraeten, “Minority Carrier Recombination in Heavily Doped Silicon”, Solid-State Electr. Vol. 26, pp. 577-597, 1983. Download a copy at Tyagi.pdf.

  12. 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

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

  14. The ContinuityEquation (cont.)

  15. The ContinuityEquation (cont.)

  16. The ContinuityEquation (cont.)

  17. The ContinuityEquation (cont.)

  18. The ContinuityEquation (cont.)

  19. The ContinuityEquation (cont.)

  20. References * Semiconductor Device Fundamentals, by Pierret, Addison-Wesley, 1996 [M&K] Device Electronics for Integrated Circuits, 3rd ed., by Richard S. Muller, Theodore I. Kamins, and Mansun Chan, John Wiley and Sons, New York, 2003. ISBN: 0-471-59398-2.

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