The Fractional-Dimensional Space Approach: Excitons and Shallow Impurities in Semiconductor Low-Dimensional Systems

Abstract

The fractional-dimensional space approach is applied in the study of excitons and shallow impurities in semiconductor low-dimensional systems. In this scheme, a real anisotropic semiconductor heterostructure in a three-dimensional environment is treated as isotropic in an effective fractional-dimensional space, and the value of the fractional dimension is associated to the degree of anisotropy of the actual three-dimensional semiconductor system. When a magnetic field is applied along the growth direction of the semiconductor heterostructure, it introduces an additional degree of confinement and anisotropy besides the one imposed by the heterostructure barrier potential. The fractional dimension is then related to the anisotropy introduced both by the heterostructure barrier potential and magnetic field. In this work, we present results for excitons in GaAs–(Ga,Al)As quantum wells and symmetric-coupled double quantum wells, and shallow-impurity states in GaAs–(Ga,Al)As quantum wells and superlattices under growth-direction applied magnetic fields. Results are shown to be in good agreement with available experimental measurements and previous variational calculations.