Exciton in Semiconductor Quantum Box: An Important Analytical Computational Step

Abstract

A theoretical model to determine the properties of an exciton confined in a semiconductor quantum box with rectangular potential is presented. We have used the two-band model and the effective mass approximation. The theoretical approach includes a considerable analytic phase and makes it possible to reduce the numerical calculations. According to the new formulation, the limit cases for an exciton in a bulk semiconductor and an exciton confined in a two-dimensional structure are deduced, and a good agreement is shown in comparison with known results in the literature. We calculated the binding energy, spatial extension, and effective Bohr radius of the exciton. The variation law of the confined exciton energy, as a function of the dimension of the semiconductor quantum box, is established. The illustrations are given for a rectangular confining potential with finite and infinite barriers.