The Effect of Hermanson’s Spatial Dielectric Function on the Density of Impurity States in a Gallium Arsenide Quantum Dot of Rectangular Cross-Section

Leonard Machuka

doi:10.11648/j.ijamtp.20180403.12

Abstract

We have carried out a theoretical study of the effect of Hermanson’s spatial dielectric function on the density of impurity states (DOIS) for a shallow hydrogenic donor impurity located in the center of a Gallium Arsenide (GaAs) Quantum Well Dot (QWD) of rectangular cross-section. 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. Our calculations were carried out using a trial wave function within the effective mass approximation. Our calculations have been carried out with finite barriers. In this study, we first calculated the ground state binding energies of both hydrogenic and non-hydrogenic donor impurity for different dot sizes. The donor binding energies in the two regimes are then used to compute the DOIS. The results show that for both hydrogenic and non-hydrogenic donor impurities, the DOIS sharply rises to a peak, and then decreases almost exponentially with increase in binding energy. The results also show that the DOIS obtained for the non-hydrogenic donor impurities is markedly enhanced over that for purely hydrogenic donor impurities in which a dielectric constant is employed in the potential. In fact, the enhanced DOIS is observed throughout the range of values for binding energy considered. To a good extend there is good agreement between our results and those reported in the literature. It is therefore, important that the effect of the spatial dielectric function should be considered when designing optoelectronic devices.

Highlights

The physics of shallow-donor impurity states in semiconductor quantum-dot structures is an interesting area of research owing to the ability to manipulate their electronic and optical properties [1,2]
We present a plot of the density of impurity states (DOIS) as a function of the binding energy for the non-hydrogenic donor impurity with the dielectric constant replaced by the spatial dielectric function given by equation (5)
The differences in DOIS more significantly show up below 25 meV and show more deviations as the binding energy decreases up to about the peak value. This behavior is consistent with previous research findings which have reported an important feature that is a peak in DOIS at lower binding energies that comes from the contribution of impurities near the axial edge of the quantum well dot

Summary

Introduction

The physics of shallow-donor impurity states in semiconductor quantum-dot structures is an interesting area of research owing to the ability to manipulate their electronic and optical properties [1,2]. Much research has been carried out on the superlattices of a GaAs layer sandwiched between Ga1-xAlxAs barriers because of its direct bandgap Owing to this, it emits and absorbs light efficiently making it applicable in a wide range of semiconductor devices e.g. solar cells, solid state laser photodetectors, etc [3]. It emits and absorbs light efficiently making it applicable in a wide range of semiconductor devices e.g. solar cells, solid state laser photodetectors, etc [3] When impurities such as hydrogenic and non-hydrogenic donors are introduced into semiconductors; they affect carrier transport and optical properties of such semiconductors. Oyoko [13] has carried out studies on the effect of uniaxial stress on the density of impurity states [DOIS] of shallow hydrogenic donor impurities in GaAs quantum wells.

74 Leonard Machuka and Hannigton Odhiamb Oyoko

Results and Discussions

Conclusion