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Application of coordinate transformation and finite differences method for electron and hole states calculations
Institution:1. College of Physics and Information Technology, Shaanxi Normal University, Xian 710062, Shaanxi, PR China;2. State Key Laboratory for Mechanical Behavior of Materials, Xian Jiaotong University, Xian 710049, Shaanxi, PR China;3. ICMMO/LEMHE, Université Paris-Sud 11, 91405 Orsay Cedex, France;1. Physics and Astronomy Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia;2. Laboratory of Nanosciences Research (LNR), E.A. n°4682, UFR Sciences, University of Reims, 21 rue Clément Ader, 51685 Reims cedex 02, France;3. Faculty of Electrical Engineering, Czestochowa University Technology, Armii Krajowej 17, Pl-42-201 Czestochowa, Poland;4. Lviv National University of Veterinary Medicine and Biotechnologies, Department of Inorganic and Organic Chemistry, 79010 Lviv, Ukraine;5. Chemical Department, Eastern European National University, Voli 13, Lutsk 43025, Ukraine;6. Department of Physics, Eastern European National University, Voli 13, Lutsk 43025, Ukraine;1. Department of Physics, Urmia Branch, Islamic Azad University, Urmia, Iran;2. Department of Solid State Physics, Yerevan State University, Al. Manookian 1, 0025 Yerevan, Armenia;1. Amirkhanov Institute of Physics Russian Academy of Sciences, Dagestan Science Centre, Makhachkala, Russia;2. Prokhorov General Physics Institute Russian Academy of Sciences, Moscow, Russia;3. Dagestan State University, Makhachkala, Russia;4. Institute of Geothermal Problems Russian Academy of Sciences, Dagestan Science Centre, Makhachkala, Russia;5. Instituto de Física, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/n, 24210-346 Niterói, RJ, Brazil
Abstract:In this work we are particularly interested for GaAs/Ga1−xAlxAs V-groove quantum wires. The paper presents an efficient and simple method for energy spectra and wave function calculations of electrons and holes in V-groove quantum wires. The method is based on the coordinate transformation of the V-groove quantum wire structure and the computational domain using a function proposed by Inoshita. Then, the Hamiltonian followed by implementation of the FDM (Finite Difference Method) in the new computational space leads to an eigenvalues problem resolved using specialized LAPACK’s routines. The influence of the parameters introduced in the mathematical function, is studied on the energy levels of electrons and holes as well as the oscillator strengths.
Keywords:V-groove quantum wire  Coordinate transformation  Finite difference method  Transition energy  Oscillator strengths
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