Electron scattering states at solid surfaces calculated with realistic potentials

TL;DR

This paper presents a computational method for calculating electron scattering states at solid surfaces using realistic potentials, employing a multigrid algorithm and quantum transmitting boundary method for accuracy and efficiency.

Contribution

It introduces a novel approach combining reciprocal lattice representation and multigrid techniques to solve scattering states with realistic potentials at surfaces.

Findings

Efficient multigrid algorithm for solving scattering states

Accurate charge density calculations at surfaces

Analysis of boundary condition effects on solutions

Abstract

Scattering states with LEED asymptotics are calculated for a general non-muffin tin potential, as e.g. for a pseudopotential with a suitable barrier and image potential part. The latter applies especially to the case of low lying conduction bands. The wave function is described with a reciprocal lattice representation parallel to the surface and a discretization of the real space perpendicular to the surface. The Schroedinger equation leads to a system of linear one-dimensional equations. The asymptotic boundary value problem is confined via the quantum transmitting boundary method to a finite interval. The solutions are obtained basing on a multigrid technique which yields a fast and reliable algorithm. The influence of the boundary conditions, the accuracy and the rate of convergence with several solvers are discussed. The resulting charge densities are investigated.