Higher excited states of acceptors in cubic semiconductors

For the first time, higher excited states of shallow acceptors up to the 8S and 5P states are calculated, using a method based on the Baldereschi-Lipari theory including the cubic correction. The eigenvalues and eigenvectors of the effective-mass Hamiltonian for shallow acceptor states were obtained by the finite-element method. The resulting sparse matrix is diagonalized by a newly developed method based on Arnoldi’s algorithm. Except for the lowest n, each hydrogenlike state nL splits into two levels when spherical ‘‘spin-orbit’’ coupling increases from 0 to 1. This results in crossing and repulsion of levels with different n. The spectra are thus shown to have totally different structure in the real acceptor regime μ∼0.6 in contrast to exciton spectra for which μ∼0.1. The calculated spectra are in agreement with available experimental data, especially in the case of higher excited states for which central-cell correction is negligible. The spectra of the shallow acceptors in ZnTe, CdTe, and InP are calculated and compared with the experimental ones.