Scattering states of coupled valence-band holes in point defect potential derived from variable phase theory

In this article we present a method to compute the scattering states of holes in spherical bands in the strong spin-orbit coupling regime. More precisely, we calculate scattering phase shifts and amplitudes of holes induced by defects in a semiconductor crystal. We follow a previous work done on this topic by Ralph [H. I. Ralph, Philips Res. Rept. 32 160 (1977)] to account for the p-wave nature and the coupling of valence band states. We extend Ralph's analysis to incorporate finite-range potentials in the scattering problem. We find that the variable phase method provides a very convenient framework for our purposes and show in detail how scattering amplitudes and phase shifts are obtained. The Green's matrix of the Schroedinger equation, the Lippmann-Schwinger equation and the Born approximation are also discussed. Examples are provided to illustrate our calculations with Yukawa type potentials.Comment: 16 pages and 9 figure

Auger Recombination in Semiconductor Quantum Wells

The principal mechanisms of Auger recombination of nonequilibrium carriers in semiconductor heterostructures with quantum wells are investigated. It is shown for the first time that there exist three fundamentally different Auger recombination mechanisms of (i) thresholdless, (ii) quasi-threshold, and (iii) threshold types. The rate of the thresholdless Auger process depends on temperature only slightly. The rate of the quasi-threshold Auger process depends on temperature exponentially. However, its threshold energy essentially varies with quantum well width and is close to zero for narrow quantum wells. It is shown that the thresholdless and the quasi-threshold Auger processes dominate in narrow quantum wells, while the threshold and the quasi-threshold processes prevail in wide quantum wells. The limiting case of a three-dimensional (3D)Auger process is reached for infinitely wide quantum wells. The critical quantum well width is found at which the quasi-threshold and threshold Auger processes merge into a single 3D Auger process. Also studied is phonon-assisted Auger recombination in quantum wells. It is shown that for narrow quantum wells the act of phonon emission becomes resonant, which in turn increases substantially the coefficient of phonon-assisted Auger recombination. Conditions are found under which the direct Auger process dominates over the phonon-assisted Auger recombination at various temperatures and quantum well widths.Comment: 38 pages, 7 figure