Deep bound-hole states in semiconductors

Abstract

We treat in the spherical-band approximation the problem of a hole in the valence band of a cubic semiconductor bound to a short-range potential. We derive the set of band states in $k$ space which simultaneously diagonalize the energy and angular momentum operators and which provide a convenient basis for the solution of any bound-hole problem having spherical or approximately spherical symmetry. The bound-state wave functions are obtained in this basis (as well as in $r$ space) and are used to obtain the reduction of the shear deformation potential and of the isotropic $g$ factor for the bound relative to the band-edge states. These reduction factors lie between 1.0 and 0.2 and are found to be independent of the depth of the state and to be functions of only the light-hole-heavy-hole mass ratio of the valence bands.