A fractional-dimensional space approach to the study of shallow-donor states in symmetric-coupled GaAs–Ga1−xAlxAs multiple quantum wells

Abstract

The fractional-dimensional space approach is extended to study shallow-donor states in symmetric-coupled GaAs–Ga1−xAlxAs multiple quantum wells. In this scheme, the real anisotropic “shallow donor+multiple quantum well” semiconductor system is mapped, for each shallow-donor state, into an effective fractional-dimensional isotropic environment, and the fractional dimension is essentially related to the anisotropy of the actual semiconductor system. Calculations within the fractional-dimensional space scheme were performed for the binding energies of 1s-like shallow-donor states in various positions in symmetric-coupled double and triple GaAs–Ga1−xAlxAs semiconductor quantum wells, and for varying well and barrier thicknesses. Fractional-dimensional theoretical results are shown to be in good agreement with previous variational theoretical calculations.