Cubic contributions to the spherical model of shallow acceptor states

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Abstract
In a previous paper the effective-mass Hamiltonian for shallow acceptor states was separated into a spherical term and a cubic contribution. Neglecting the latter term, a spherical model was formulated which explained the main features of the experimental acceptor spectra. Here the effects of the cubic term are studied using perturbation theory, and all the details of the observed spectra are reproduced. As in the case of the spherical model, the eigenvalue problem is reduced to simple radial Hamiltonians which are explicitly given for the most important acceptor states. These Hamiltonians are solved numerically and the resulting eigenvalues are tabulated as functions of the relevant parameters. The predicted spectra are in good agreement with available experimental data for acceptors in Ge, InSb, and GaAs, but not for acceptors in Si, where the unusual strength of the cubic term makes the present analysis unsatisfactory.