Thomas-Fermi method for computing the electron spectrum and wave functions of highly doped quantum wires in n-Si

Abstract

The application of the Thomas-Fermi method to calculate the electron spectrum in quantum wells formed by highly doped n-Si quantum wires is presented under finite temperatures where the many-body effects, like exchange, are taken into account. The electron potential energy is calculated initially from a single equation. Then the electron energy sub-levels and the wave functions within the potential well are simulated from the Schrödinger equation. For axially symmetric wave functions the shooting method has been used. Two methods have been applied to solve the Schrödinger equation in the case of the anisotropic effective electron mass, the variation method and the iteration procedure for the eigenvectors of the Hamiltonian matrix.