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 Indirect, like Si, so intermediate state Ec Ec ET Ef Efi Ev Ev k L14 06Oct2010

S-R-H trap characteristicsM&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” L14 06Oct2010

S-R-H trap char. (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 L14 06Oct2010

tpo = (Ntvthsp)-1, where sn,p~p(rBohr,n.p)2 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 L14 06Oct2010

S-R-H net recom- bination rate, U In the special case where tno = tpo = to = (Ntvthso)-1 the net rec. rate, U is L14 06Oct2010

S-R-H “U” function characteristics 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 L14 06Oct2010

S-R-H rec for excess 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) L14 06Oct2010

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. L14 06Oct2010

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. L14 06Oct2010

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. L14 06Oct2010

S-R-H rec for deficient 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 L14 06Oct2010

The Continuity Equation The chain rule for the total time derivative dn/dt (the net generation rate of electrons) gives L14 06Oct2010

The Continuity Equation (cont.) L14 06Oct2010

The Continuity Equation (cont.) L14 06Oct2010

The Continuity Equation (cont.) L14 06Oct2010

The Continuity Equation (cont.) L14 06Oct2010

The Continuity Equation (cont.) L14 06Oct2010

The Continuity Equation (cont.) L14 06Oct2010

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. L14 06Oct2010