Donor transition energy in GaAs superlattices in a magnetic field along the growth axis

The transition energies between the ground state (1s-like) and two excited states (2${\mathit{p}}^{\pm }$-like) are calculated for shallow donor impurities in GaAs superlattices in the presence of a magnetic field along the growth axis. Results are obtained as a function of the magnetic field and the well width for various widths and heights of the barriers of the superlattices. The dependence of the transition energies on the position of the donors and the effect of band nonparabolicity are also investigated. The calculation is based on a variational approach in which Gaussian-type trial wave functions with two variational parameters are used. Polaron correction to these energies is studied within second-order perturbation theory in which only the three-dimensional-bulk phonon modes of GaAs are included. We found that the polaron effect and band nonparabolicity have to be included in order to correctly describe the experimental transition energies.