The Electron Spectrum of Quantum Wires in n-Si of Arbitrarily Doping Profile

Electron spectrum in doped $n$-Si quantum wires is calculated by the Thomas – Fermi (TF) method under finite temperatures. The many-body exchange corrections are taken into account. The doping profile is arbitrary. At the first stage the electron potential energy is calculated from a simple two-dimensional equation. The effective iteration scheme is proposed there. Then the energy sub-levels and wave functions are simulated from the Schrödinger equation. The expansion by the eigenfunctions of the linear harmonic oscillator is used. The quantum mechanical perturbation theory yields goods results for the lower energy sub-levels.