Calculation of electron transport in branched semiconductor nanostructures using quantum network model

TL;DR

This paper presents a comprehensive quantum network model for calculating electron transport in branched semiconductor nanostructures, incorporating advanced scattering matrix techniques and tunnel effects, demonstrated on GaAs-based networks.

Contribution

It introduces a novel computational scheme combining S-matrix methods, boundary conditions, and network formulas for electron transport analysis in nanostructures.

Findings

Effective calculation of S-matrices for network junctions using boundary conditions.

Network combining formula enables analysis of complex branched structures.

Electrical properties vary with temperature in GaAs nanostructure models.

Abstract

Electron transport in branched semiconductor nanostructures provides many possibilities for creating fundamentally new devices. We solve the problem of its calculation using a quantum network model. The proposed scheme consists of three computational parts: S-matrix of the network junction, S-matrix of the network in terms of its junctions' S-matrices, electric currents through the network based on its S-matrix. To calculate the S-matrix of the network junction, we propose scattering boundary conditions in a clear integro-differential form. As an alternative, we also consider the Dirichlet-to-Neumann and Neumann-to-Dirichlet map methods. To calculate the S-matrix of the network in terms of its junctions' S-matrices, we obtain a network combining formula. We find electrical currents through the network in the framework of the Landauer$-$B\"uttiker formalism. Everywhere for calculations, we use extended scattering matrices, which allows taking into account correctly the contribution of tunnel effects between junctions. We demonstrate the proposed calculation scheme by modeling nanostructure based on two-dimensional electron gas. For this purpose we offer a model of a network formed by smooth junctions with one, two and three adjacent branches. We calculate the electrical properties of such a network (by the example of GaAs), formed by four junctions, depending on the temperature.