EXCITONIC AND SHALLOW-DONOR STATES IN SEMICONDUCTING QUANTUM-WELLS - A FRACTIONAL-DIMENSIONAL SPACE APPROACH

A systematic study of shallow-donor and excitonic states in semiconduc ting quantum wells within a fractional-dimensional space approach is p resented. In this scheme, the Schrodinger equation is solved in a noni nteger-dimensional space in which the interactions are assumed to occu r in an isotropic effective environment, and the fundamental quantity is the parameter D, which defines the fractional dimension associated with the effective medium and the degree of anisotropy of the interact ions. The fractional dimensionality of the isotropic effective space i s derived via an unambiguous procedure in which one may obtain the exa ct solution for the energies of the actual physical system under consi deration. Explicit calculations of the fractional-dimensional paramete r are made in the case of shallow donors and excitons in finite-barrie r GaAs-(Ga,Al)As quantum wells, with impurity and exciton binding ener gies found in good agreement with previous variational results and ava ilable experimental data.