SIMULATION OF SPHERICAL AND CYLINDRICAL QUANTUM POINTS

Abstract

The simplest models of 3D spatial quantum dots are considered: spherical and cylindrical. Mathematical, computer simulation of the state of electrons in quantum-size structures is used in the development of simulation laboratory work in the course "Physical Foundations of Modern Information Technologies" for masters of specialty "Computer Science and Information Technology Design". In computer simulation, Mathcad is used. It is of particular interest to consider the behavior of the electron in the case of spatial potential wells with finite-height walls. Quantum Dots (Quantum Dots CT) are used in the element base of nanoelectronics, primarily in the creation of fourth generation displays (AMOLED technology), which are replaced by liquid crystal displays. In addition, the creation of CT lasers is promising.

The properties of quantum dots (the discrete range of eigenvalues) depend on their shape, size and material (the magnitude of the effective mass of charge carriers). Boundary conditions also play an important role - the kind of potential that limits electron movement. The simplest CT model is a three-dimensional infinitely deep spatial potential well. But real quantum dots (both with and without shell) have potential finite-height walls, so modeling electronic structure and determining the wave function and probability density in this case is an urgent task.

The solution of the Schrödinger equation for the wave function of steady states of S-electrons in spherical and cylindrical coordinate systems is considered. The eigenvalues obtained in the first approximation, the type of wave function, and the probability of finding an electron in a given region of space are obtained.