EE 5340 Semiconductor Device Theory Lecture 13 - Fall 2010 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

Reverse bias junction breakdown Avalanche breakdown Electric field accelerates electrons to sufficient energy to initiate multiplication of impact ionization of valence bonding electrons field dependence shown on next slide Heavily doped narrow junction will allow tunneling - see Neamen*, p. 274 Zener breakdown L 13 Oct 06

Reverse bias junction breakdown Assume -Va = VR >> Vbi, so Vbi-Va-->VR Since Emax~ 2VR/W = (2qN-VR/(e))1/2, and VR = BV when Emax = Ecrit (N- is doping of lightly doped side ~ Neff) BV = e (Ecrit )2/(2qN-) Remember, this is a 1-dim calculation L 13 Oct 06

Effect of V  0 L 13 Oct 06

Reverse bias junction breakdown L 13 Oct 06

Ecrit for reverse breakdown [M&K] Taken from p. 198, M&K** Casey 2model for Ecrit L 13 Oct 06

Table 4.1 (M&K* p. 186) Nomograph for silicon uniformly doped, one-sided, step junctions (300 K). (See Figure 4.15 to correct for junction curvature.) (Courtesy Bell Laboratories). L 13 Oct 06

Reverse bias junction breakdown Assume -Va = VR >> Vbi, so Vbi-Va-->VR Since Emax~ 2VR/W = (2qN-VR/(e))1/2, and VR = BV when Emax = Ecrit (N- is doping of lightly doped side ~ Neff) BV = e (Ecrit )2/(2qN-) Remember, this is a 1-dim calculation L 13 Oct 06

Junction curvature effect on breakdown The field due to a sphere, R, with charge, Q is Er = Q/(4per2) for (r > R) V(R) = Q/(4peR), (V at the surface) So, for constant potential, V, the field, Er(R) = V/R (E field at surface increases for smaller spheres) Note: corners of a jctn of depth xj are like 1/8 spheres of radius ~ xj L 13 Oct 06

Figure 4.15 (p. 208, M&K) Breakdown voltage of one-sided, planar, silicon step junction, showing the effect of junction curvature [6, 7]. L 13 Oct 06

Direct carrier gen/recomb k Ec Ev (Excitation can be by light) gen rec - + Ev Ec Ef Efi L 13 Oct 06

Direct gen/rec of excess carriers Generation rates, Gn0 = Gp0 Recombination rates, Rn0 = Rp0 In equilibrium: Gn0 = Gp0 = Rn0 = Rp0 In non-equilibrium condition: n = no + dn and p = po + dp, where nopo=ni2 and for dn and dp > 0, the recombination rates increase to R’n and R’p L 13 Oct 06

Direct rec for low-level injection 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 L 13 Oct 06

Shockley-Read- Hall Recomb Indirect, like Si, so intermediate state Ec Ec ET Ef Efi Ev Ev k L 13 Oct 06

S-R-H trap characteristics* 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” L 13 Oct 06

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 L 13 Oct 06

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 L 13 Oct 06

S-R-H net recom- bination rate, U In the special case where tno = tpo = to = (Ntvthso)-1 the net rec. rate, U is L 13 Oct 06

References [M&K] Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, Wiley, New York, 1986. [2] Devices for Integrated Circuits: Silicon and III-V Compound Semiconductors, by H. Craig Casey, Jr., John Wiley & Sons, New York, 1999. Bipolar Semiconductor Devices, by David J. Roulston, McGraw-Hill, Inc., New York, 1990. L 13 Oct 06

References [M&K] Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, Wiley, New York, 1986. [2] Devices for Integrated Circuits: Silicon and III-V Compound Semiconductors, by H. Craig Casey, Jr., John Wiley & Sons, New York, 1999. Bipolar Semiconductor Devices, by David J. Roulston, McGraw-Hill, Inc., New York, 1990. *Semiconductor Physics and Devices, by Donald A. Neamen, Irwin, Chicago, 1997 L 13 Oct 06