Numerical simulation of coupling effect on electronic states in quantum wires

In this paper, the Schrödinger equation is solved for approximation of the ground state energies and associated wave functions of carriers confined in a rectangular semiconductor (SC) quantum wire embedded in a SiO2 matrix. The problem was treated with the effective one band Hamiltonian. The finite difference scheme was used for the discretization of 2D Schrödinger equation and LAPACK package to resolve the band matrix. The energy levels were determined and the coupling between quantum wires was investigated. The effect on energies and relative wave functions of quantum wires number, size and separation was studied. The results obtained show that the energy levels can be importantly modified and controlled by these parameters. The interaction is manifested by a reduction in energies and an increase in the peak value of the wave function of the higher energy wire. This study offers a fast and inexpensive way to check device designs and processes and can be used in diverse device applications.