Kinetics of Transmission Through and Reflection from Interfaces in Nanostructures

Abstract

An exact time-dependent solution for the wave function $\psi \left(\mathbf{r},t\right)$ of a particle moving in the presence of an asymmetric rectangular well/barrier potential varying in one dimension is obtained. Such a potential can model the spin-dependent potential profile of the magnetic multilayers used in spintronics devices. The solution describes the transmission through and reflection from this potential as a function of time. It is presented in terms of integrals of elementary functions and is a sum of the forward- and backward-moving components of the wave packet. The relative contribution of these components and their interference as well as of the potential asymmetry to the probability density ${\left|\psi \left(x,t\right)\right|}^2$ is considered and numerically visualized for narrow and broad energy (momentum) distributions of the initial Gaussian wave packet. It is shown that in the case of a broad initial wave packet, the quantum mechanical counterintuitive effect of the influence of the backward-moving components on the considered quantities becomes essential. The influence of the potential asymmetry in this case is also more pronounced.