Resonant transport throught semiconductor nanostructures

TL;DR

This paper develops a theoretical framework for understanding quantum-coherent electron transport in semiconductor nanostructures, emphasizing resonant phenomena and the Fano line shape in conductance and capacitance.

Contribution

It introduces a scattering theory approach for nonspherical potentials and derives a general Fano resonance model for transport properties.

Findings

Resonant line shape described by a complex Fano function.

Identification of resonant and nonresonant contributions to conductance.

Mathematical foundations for scattering in nonspherical semiconductor potentials.

Abstract

Transport through semiconductor nanostructures is a quantum-coherent process. This paper focuses on systems in which the electron's dynamics is ballistic and the transport is dominated by the scattering from structure boundaries. Opposite to the well-known case of the nuclear reactions, the potentials defining semiconductor structures are nonspherically symmetric and the asymptotic motion of the electrons is determined by the different potential levels in the contacts. For this special type of potential the mathematical foundations for the scattering theoretical description of the transport phenomena are presented. The transport properties of the system are then derived from the scattering matrix using the Landauer-Buttiker formalism. A rigorous analysis of the analytical properties of the S matrix leads to the most general resonant line shape described by a Fano function with a complex asymmetry parameter. On this basis the resonant and nonresonant contributions to the conductance and capacitance of the system are identified.