Parametrized equations for excitons in two-dimensional semiconductor quantum wells with arbitrary potential profiles

We derive parametrized equations using variational calculation for energy levels and the spatial extension of Wannier excitons in two-dimensional quantum wells with an arbitrary shape of the confining potential. The formulation is performed in the framework of the effective mass approximation, two-band model and taking into account both mass mismatch and dielectric mismatch. According to the new formulation, qualitative and general features of excitons are deduced. Illustrations are given for GaA1As-GaAs-GaA1As and CdMnTe-CdTe-CdMnTe systems for both rectangular and parabolic quantum wells as well as for the 2s exciton state. The comparison with existing data displays good agreement. An application of the model is given for an exciton in a parabolic quantum well under a constant electric field.