A theoretical investigation is presented of the properties of shallow donor impurities in a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As superlattice in the presence of a magnetic field directed along the growth axis. The energy levels of several of the lowest donor states have been obtained as functions of (1) the well width, (2) the donor position, and (3) the magnetic-field strength. The calculation is based on a variational approach in which we use a trial wave function with two variational parameters. This wave function shows exponential behavior in sufficiently small magnetic fields and Gaussian behavior in sufficiently large magnetic fields. The magnetopolaron effect on these donor energies is studied within second-order perturbation theory where a formal summation over all electron states is performed. The effect of band nonparabolicity is also included in order to correctly explain magneto-optical experimental results at high magnetic fields. Our results are in very good agreement with the available experimental data in the whole magnetic-field range and for weakly and strongly coupled superlattices.

• Received 21 March 1994

DOI:https://doi.org/10.1103/PhysRevB.50.15182