Open AccessThomas-Fermi method for computing the electron spectrum and wave functions of highly doped quantum wires in n-Si
Author(s) -
V. Grimalsky,
O. Oubram,
S. Koshevaya,
Christian Castrejon-Martinez
Publication year - 2015
Publication title -
facta universitatis. series electronics and energetics/facta universitatis. series: electronics and energetics
Language(s) - English
Resource type - Journals
eISSN - 2217-5997
pISSN - 0353-3670
DOI - 10.2298/fuee1501103g
Subject(s) - eigenvalues and eigenvectors , wave function , schrödinger equation , electron , physics , hamiltonian (control theory) , quantum mechanics , effective mass (spring–mass system) , quantum well , fermi gamma ray space telescope , hamiltonian matrix , quantum , fermi energy , condensed matter physics , mathematics , symmetric matrix , mathematical optimization , laser
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 Schr?dinger equation. For axially symmetric wave functions the shooting method has been used. Two methods have been applied to solve the Schr?dinger equation in the case of the anisotropic effective electron mass, the variation method and the iteration procedure for the eigenvectors of the Hamiltonian matrix.