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

摘要

We use the effective-mass approximation and the density-functional theorywith the local-density approximation for modeling two-dimensionalnano-structures connected phase-coherently to two infinite leads. Using thenon-equilibrium Green's function method the electron density and the currentare calculated under a bias voltage. The problem of solving for the Green'sfunctions numerically is formulated using the finite-element method (FEM). TheGreen's functions have non-reflecting open boundary conditions to take care ofthe infinite size of the system. We show how these boundary conditions areformulated in the FEM. The scheme is tested by calculating transmissionprobabilities for simple model potentials. The potential of the scheme isdemonstrated by determining non-linear current-voltage behaviors of resonanttunneling structures.