Mathematical analysis of electron states in indium arsenide/gallium arsenide domain of quantum dots by the solution of the schrodinger equation

Abstract

Semiconductor quantum dots (QDs) have unique atom-like properties. Quantum dots have been extensively studied in recent years because of their potential for technological applications. Briefly stated a quantum dot (QD) is a portion of matter whose excitations are confined in all three spatial dimensions. This means that an electron that is in the interior of a QD will experience a potential barrier in all directions. The dimensions of QDs usually range from 1nm to 20 nm. They can be fabricated from many different kinds of semiconductor materials and in various geometrical shapes (cubes, spheres and cones for instance). All these opportunities can be utilized to achieve certain desirable properties of the QD. In this work, the electronic states of Indium Arsenide (InAs) quantum dot grown on a Gallium Arsenide (GaAs) substrate has been studied. The analytical expressions of electron wave function for cone-like quantum dot on the semiconductor surface has been obtained and the governing Eigen value equation has been solved. The dependence of ground state energy on radius and height of the conical shaped nano-dots is obtained. In addition, the energy of eigenvalues is computed for various length and thickness of the wetting layer (WL). The calculation is based on one band Schrödinger equation and the simulation is performed using MATLAB.