Modeling and Visualization of Electron Scattering on Quantum Rings

Abstract

The problem of scattering of quasi-dimensional electrons on a potential in the form of a quantum ring and a quantum dot is solved. The problem is addressed as a part of analysis of quantum interference effects in semiconductor nanostructures with nontrivial geometry as well as for the design of nanoelectronic devices based on them. In contrast to existing works, algorithms for solving both stationary and non-stationary Schrödinger equation with arbitrary scattering potential are developed here. Analytical and finite-difference methods are used, which makes it possible to obtain an arbitrarily accurate solution, with which the process of electron scattering on a quantum ring is modeled and visualized. This visualization allows us to discover how the shape of the quantum ring affects the angular distribution of the scattering amplitude as well as determine the presence of a self-interference of the scattered electron wave function.