Statistical multiple diffuse scattering in a distorted crystal system: An exact theory

Abstract

Abstract In electron scattering, diffuse scattering can be generated by atom vibrations, point vacancies and growth islands (or surface roughness). Most of the existing dynamical theories have been developed under the first-order diffuse scattering approximation; thus they are restricted to cases where the lattice distortion is small. In this paper, a formal dynamical theory is presented for calculating diffuse scattering with the inclusion of multiple diffuse scattering. By inclusion of a complex potential in dynamical calculation, a rigorous proof is given to show that the high-order diffuse scattering is fully recovered in the calculations using the equation derived under the distorted-wave Born approximation and, more importantly, the statistical time and structure averages over the distorted crystal lattices are evaluated analytically prior to numerical calculation. This conclusion establishes the basis for expanding the applications of the existing theories. The exact form of the optical potential i...