Effect of nonparabolicity on the energy levels of hydrogenic donors in $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}-{\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ quantum-well structures

Binding energies of the ground state and of a few low-lying excited states of a hydrogenic donor in a quantum-well structure consisting of a single layer of GaAs sandwiched between two-semi-infinite layers of ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ are calculated, including the effect of nonparabolicity of the conduction band and following a variational approach. The effect of nonparabolicity of the conduction band is included by using an expression for the energy-dependent effective mass based on the $\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{p}}$ approximation. The variations of the binding energies of these states as a function of the size of the GaAs quantum well for different values of the potential barrier (or equivalently for different values of Al concentration $x$) are calculated. These results are compared with those obtained with the use of a parabolic conduction band.