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has been cited by the following article:

• TITLE: Simulations of the Electron Spectrum of Quantum Wires in n-Si of Arbitrarily Doping Profile by Thomas-Fermi Method

  AUTHORS: Volodymyr Grimalsky, Svetlana Koshevaya, Jesus Escobedo-Alatorre, Igor Moroz

  KEYWORDS: Cylindrical Quantum Well, High Arbitrary Doping, Thomas-Fermi Method, Electron Spectrum, Possible Degeneration of Levels

  JOURNAL NAME: Journal of Electromagnetic Analysis and Applications, Vol.10 No.8, August 31, 2018

  ABSTRACT: 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 that is valid for multidimensional problems. Then the energy levels and wave functions of this quantum well are simulated from the Schrödinger equations. The expansion by the full set of eigenfunctions of the linear harmonic oscillator is used. The quantum mechanical perturbation theory can be utilized to compute the energy levels. Generally, the perturbation theory for degenerate energy levels should be used.