Effect of magnetic field on the energy levels of a hydrogenic impurity center in GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As quantum-well structures

We have calculated the binding energies of the ground (1s-like) and excited (2$p_{\pm }$-like) states of a hydrogenic donor associated with the first subband in a GaAs quantum well, sandwiched between two semi-infinite layers of ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As. Results have been obtained as a function of the potential-barrier height (or equivalently of Al concentration x) and the size of the quantum well in the presence of an arbitrary magnetic field. We have considered the two cases of donor at the center and at the edge of the well. The applied magnetic field is taken to be parallel to the axis of growth of the quantum-well structure. We have used a variational approach in which the trial wave functions are expanded in terms of appropriate Gaussian basis sets. For a given value of the magnetic field, the binding energies are found to be larger than their values in a zero magnetic field.