Dynamics of Electrons in Gradient Nanostructures (Exactly Solvable Model)

TL;DR

This paper introduces an exactly solvable multi-parameter model for electron dynamics in gradient nanostructures, revealing how potential gradients influence electron transport and spectra, with implications for tunneling and optical analogies.

Contribution

The paper presents a novel, flexible model for potential profiles with continuous gradients, enabling analytical study of electron transport in complex nanostructures.

Findings

Gradient and curvature significantly affect electron spectra and tunneling.

Resonant contrast in over-barrier reflectivity exceeds that of rectangular barriers.

Reflectionless tunneling occurs in concave gradient potentials.

Abstract

A flexible multi-parameter exactly solvable model of potential profile, containing an arbitrary number of continuous smoothly shaped barriers and wells, both equal or unequal, characterized by finite values and continuous profiles of the potential and of its gradient, is presented. We demonstrate an influence of both gradient and curvature of these potentials on the electron transport and spectra of symmetric and asymmetric double-well (DW) potentials. The use of this model is simplified due to one to one correspondence between the algorithms of calculation of the transmittance of convex barriers and energy spectra of concave wells. We have shown that the resonant contrast between maximum and minimum in over-barrier reflectivity of curvilinear barrier exceeds significantly the analogous effect for rectangular barrier with the same height and width. Reflectionless tunneling of electrons below the bottom of gradient nanostructures forming concave potential barriers is considered. The analogy between dynamics of electrons in gradient fields and gradient optics of heterogeneous photonic barriers is illustrated.