Landau-like states in the magneto-optical spectrum of a shallow donor impurity: Theory versus experiment

A calculation of the energy levels and the wave functions for a shallow donor impurity in an applied magnetic field is put forward. The behavior of the donor electron in directions perpendicular to the field is described by a basis set of Landau wave functions, and a variational procedure is used to generate approximate forms for the wave function along the field axis. Theoretical values for the ionization energies of the impurity are calculated and a comparison with both existing and new experimental data, also reported here, is made for impurities in bulk GaAs. The model is used to obtain hydrogenlike states of the impurity as well as the so-called ``metastable'' or ``autoionizing'' Landau-like states. A comparison with a ``hydrogenic'' method of calculation is used to highlight the validity of the model. Also, transition probabilities from the ground to excited donor states are deduced. The results obtained are used to identify the various peaks observed in experimental spectra. Differences between theory and experiment are attributed to the occurrence of Fano resonances. A discussion of the behavior of the impurity in an applied magnetic field calls into question the expected ordering of the energy levels of such a system. \textcopyright{} 1996 The American Physical Society.