Excitons and shallow impurities in GaAs-Ga1-xAlxAs semiconductor heterostructures within a fractional-dimensional space approach: Magnetic-field effects

The fractional-dimensional space approach is extended to study exciton and shallow-donor states in symmetric-coupled GaAs-Ga1-xAlxAs multiple quantum wells. In this scheme, the real anisotropic "exciton (or shallow donor) plu s multiple quantum well'' semiconductor system is mapped, for each exciton (or donor) state, into an effective fractional-dimensional isotropic enviro nment, and the fractional dimension is essentially related to the anisotrop y of the actual semiconductor system. Moreover, the fractional-dimensional space approach was extended to include magnetic-field effects in the study of shallow-impurity states in GaAs-Ga1-xAlxAs quantum wells and superlattic es. In our study, the magnetic field was applied along the growth direction of the semiconductor heterostructure, and introduces an additional degree of confinement and anisotropy besides the one imposed by the heterostructur e barrier potential. The fractional dimension is then related to the anisot ropy introduced both by the heterostructure barrier potential and magnetic field. Calculations within the fractional-dimensional space scheme were per formed for the binding energies of 1s-like heavy-hole direct exciton and sh allow-donor states in symmetric-coupled semiconductor quantum wells, and fo r shallow-impurity states in semiconductor quantum wells and superlattices under growth-direction applied magnetic fields. Fractional-dimensional theo retical results are shown to be in good agreement with previous variational theoretical calculations and available experimental measurements.