Eur. Phys. J. B 72, 77-88 (2009)
https://doi.org/10.1140/epjb/e2009-00319-8

Dynamics of electrons in gradient nanostructures (exactly solvable model)

¹ Joint Institute of High Temperatures, Russian Acad. of Sciences, Izorskaya 13/19, 125412 Moscow, Russia
² Institute of Photonics and Electronics, Czech Acad. of Sciences, v.v.i. Chaberska 57, 182 51 Praha, Czech Republic
³ Laboratoire des Solides Irradies, CEA – DSM, CNRS, École Polytechnique, 91128, Palaiseau, France

Corresponding author: ^a guillaume.petite@polytechnique.edu

Received: 25 November 2008
Revised: 19 June 2009
Published online: 26 September 2009

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.