THE EFFECT OF HERMANSON’S SPATIAL DIELECTRIC FUNCTION ON THE DENSITY OF IMPURITY STATES IN A GALLIUM ARSENIDE QUANTUM DOT (GaAs QD) OF RECTANGULAR CROSS-SECTION

Abstract

In this work, a theoretical study of the effect of Hermansons dielectric function (screening) on the density of impurity states (DOIS) of a donor impurity located in the center of a Gallium Arsenide (GaAs) Quantum Well Dot (QWD) of rectangular cross-section has been done. The density of impurity states (DOIS) of an unscreened (hydrogenic) donor impurity was calculated and compared with that of the screened (non-hydrogenic) donor impurity for the same system. The calculations were carried out using a trial wave function in the effective mass approximation. Calculations of the binding energies for the hydrogenic and non hydrogenic donor impurity as a function of the axial (growth) length of the QWD was done and the results used to compute the density of impurity states. The results show that impurity binding energies increase with decreasing quantum well axial length until about 20 nm for a constant QWD cross-section. The binding energies for the non-hydrogenic donor impurity were found to be higher than in the hydrogenic type. These results are in agreement with previous results obtained for donor impurities in quantum well wires and quantum well dots of similar geometry .The results for the density of impurity states clearly show an important feature that is a peak at lower binding energies coming from the contribution of impurities near the axial edge of the quantum well dot. It was also observed that the DOIS obtained for the non-hydrogenic donor impurities is markedly enhanced over that for purely hydrogenic donor impurities. In fact, the enhanced DOIS of the non-hydrogenic donor impurities is observed throughout the range of binding energy values considered. The findings of this research are in agreement with the results obtained by F. J. Ribeiro and A. Latge ‘In their work on the density of impurity states in spherical and cubic quantum dots, the DOIS exhibited a similar trend with a sharp peak of density of states at low binding energy followed by an almost exponential decrease with increasing binding energy. In our case, we have applied a spatial dielectric function and found that it enhances the DOIS. It is therefore, important that the effect of spatial dielectric function should be considered when designing optoelectronic devices.