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Simulations of the Electron Spectrum of Quantum Wires in <i>n</i>-Si of Arbitrarily Doping Profile by Thomas-Fermi Method
CIICAp, IICBA, Autonomous University of State Morelos (UAEM), Cuernavaca, Mexico
CIICAp, IICBA, Autonomous University of State Morelos (UAEM), Cuernavaca, Mexico
CIICAp, IICBA, Autonomous University of State Morelos (UAEM), Cuernavaca, Mexico
Faculty of Mathematics and Informatics, Rivne State Humanitarian University, Rivne, Ukraine
- 1 CIICAp, IICBA, Autonomous University of State Morelos (UAEM), Cuernavaca, Mexico
- 2 CIICAp, IICBA, Autonomous University of State Morelos (UAEM), Cuernavaca, Mexico
- 3 CIICAp, IICBA, Autonomous University of State Morelos (UAEM), Cuernavaca, Mexico
- 4 Faculty of Mathematics and Informatics, Rivne State Humanitarian University, Rivne, Ukraine
Journal of Electromagnetic Analysis and Applications·Volume 10 (2018)·Pages 143–156·Published 31 August 2018·DOI10.4236/jemaa.2018.108011
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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 Schr ö dinger 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.
KeywordsCylindrical Quantum WellHigh Arbitrary DopingThomas-Fermi MethodElectron SpectrumPossible Degeneration of Levels
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