Effective-Mass Theoretical Approach to Optical and Microwave Phenomena in Semiconductors I. Zeeman Effect of Acceptors in Si and Ge

The binding energies and the approximate eigenfunctions of shallow acceptor ground states in Si and Ge have been calculated based on the effective mass theory-variation method with the use of the revised valence band parameters. Results show an improvement over previous calculations of Kohn-Schechter and Schechter. The admixtures of the d-like part of the envelope functions obtained are generally small compared with the s -like part, which gives a test of the truncation of a spherical harmonics expansion of the envelope. The calculated wave functions are used to treat the Zeeman perturbation and other static perturbations acting on the ground state \(\varGamma_{8}\) quartet. Formulas for the two Zeeman splitting parameters entering the effective spin Hamiltonian defined by Bleaney are thus derived and numerically evaluated. The d -like envelope contributions to the splitting parameters are shown to be comparable with, or even larger than, the band edge g -factor. The theoretical values of the parameters for shallow acceptors in Si are compared with the observed ones showing an agreement within uncertainties of the chemical shift. For acceptors in Ge, the theoretical values are not conclusive because of the uncertainty of Luttinger's parameter κ.