Non-Equilibrium Electron Transport in Two-Dimensional Nano-Structures Modeled by Green's Functions and the Finite-Element Method

TL;DR

This paper presents a numerical scheme combining Green's functions and finite-element methods to model non-equilibrium electron transport in two-dimensional nano-structures, enabling analysis of current-voltage characteristics.

Contribution

It introduces a finite-element based approach with open boundary conditions for Green's functions, improving the simulation of electron transport in nano-structures.

Findings

Successfully calculates transmission probabilities for model potentials

Demonstrates non-linear I-V behavior in resonant tunneling structures

Validates the numerical scheme with test cases

Abstract

We use the effective-mass approximation and the density-functional theory with the local-density approximation for modeling two-dimensional nano-structures connected phase-coherently to two infinite leads. Using the non-equilibrium Green's function method the electron density and the current are calculated under a bias voltage. The problem of solving for the Green's functions numerically is formulated using the finite-element method (FEM). The Green's functions have non-reflecting open boundary conditions to take care of the infinite size of the system. We show how these boundary conditions are formulated in the FEM. The scheme is tested by calculating transmission probabilities for simple model potentials. The potential of the scheme is demonstrated by determining non-linear current-voltage behaviors of resonant tunneling structures.