Modeling of Electron State in Quantum Dot Structures

摘要

Mathematical computer modeling of the state of electrons in a cubic quantum dot with a shell is considered in order to use the research results to optimize the parameters of third generation solar panels and methodical support of virtual simulation laboratory work in physics courses, physical foundations of modern information technologies and physics programs. The solution of the Schrödinger equation for S-electrons in the 3D case is obtained. To solve the Schrödinger equation, we use the Fourier method of separation of variables, as well as the numerical method of successive approximations (iterations) to determine the eigenvalues of the electron energy. Boundary conditions are used, in this case the wave function must be continuous and smooth at the core-shell boundary of the cubic quantum dot. The dependence of discrete energy levels on the parameters of the nucleus and shell of a cubic quantum dot is studied. Scilab, MathCad software packages, numerical methods for solving partial differential derivatives, and discrete structured grids are used for mathematical computer modeling and plotting the corresponding wave function and probability density of an electron in a given region of a cubic quantum dot. The research results are used to provide methodological support for laboratory workshops for undergraduates majoring in “Computer Science” and “Electric Power Engineering, Electrical Engineering and Electromechanics” in the disciplines “Physics”, “Physical foundations of modern information technology” and “Physical and mathematical support of master’s programs”.