Green's function for electron scattering and its applications in low-voltage point-projection microscopy and optical potential

Abstract

The Green's function is a powerful mathematical tool in developing the theory of condensed-matter physics. It is usually easy to write the equation in the form of G(r, r′), but the critical challenge is to find its analytical or numerical solution. In this paper, the Green's function for electron scattering is reviewed, and its general solution is given. The theory is extended into the regimes that are suitable for numerical calculations in different scattering geometries, such as the images in the low-voltage lensless point-projection microscopy. An iterative calculation technique is introduced for computing the Green's function using the Born series, and the result is applied to calculate the optical potential introduced in electron diffraction for recovering the multiple diffuse scattering effects. With the Green's function presented here and the theory reported previously by Wang (1996, Phil. Mag. B. 74, 733), quantitative analysis of electron diffuse scattering due to short-range order of point defects and thermal diffuse scattering is likely to be feasible.