Calculation of Electronic Properties of InAs/GaAs Cubic, Spherical and Pyramidal Quantum Dots with Finite Difference Method

Abstract

We have calculated the properties of electron states in an InAs/GaAs quantum dot system based on the effective mass approximation of a one-band Hamiltonian model. This semiconductor nanostructure system consisted of an InAs quantum dot embedded in a GaAs substrate. In this paper, the Schrödinger equation of an ideal cubic quantum dot with infinite barrier was solved using a finite difference approach. The sparse matrix of N3 x N3 for the Hamiltonian was diagonalized to calculate the lowest states of electrons in this nanostructure system. The calculation was performed for different dot size and the obtained energy levels are comparable to those calculated analytically. The finite difference method was relatively faster and applicable to quantum dots of any geometry or potential profile. This was proven by applying the developed computational procedure to quantum dots of cubic, spherical and pyramidal geometries for the InAs/GaAs nanostructure system.