Rutherford backscattering analysis on thin crystals modelled using a Bloch-wave formulation

Abstract

The Lindhard model for the channeling of MeV ions in crystals is well established. Simulations usually use a Monte Carlo method, which utilises the classical ‘billiard ball’ theory of ions ‘bouncing’ between planes or tubes of charge in the crystal. We propose an alternative quantum mechanical approach, which is similar to that used for high-energy electron diffraction. The diffraction theory is based on a Bloch wave solution of the Schrödinger equation for an ion passing through the periodic crystal potential. The widely used universal screening function for ion–nucleus scattering is used to construct the crystal potential. Our formalism is used to simulate Rutherford backscattering (RBS) cross sections, measured as a function of beam tilt, for proton channeling in nickel. Sample temperature, dechanneling (absorption) and the convergence of the incident beam are taken into account in the calculations.