Nonequilibrium electron transport in two-dimensional nanostructures modeled using Green's functions and the finite-element method

We use the effective-mass approximation and the density-functional theory with the local-density approximation for modeling two-dimensional nanostructures connected phase coherently to two infinite leads. Using the nonequilibrium 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 nonreflecting 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 nonlinear current-voltage behaviors of resonant tunneling structures.