Open AccessElastic electron scattering using the finite element method
Author(s) -
Denis Aubry,
Ann Lenaig Hamon,
Guillaume Puel
Publication year - 2010
Publication title -
european journal of computational mechanics
Language(s) - English
Resource type - Journals
eISSN - 2642-2085
pISSN - 2642-2050
DOI - 10.13052/ejcm.19.117-128
Subject(s) - helmholtz equation , finite element method , physics , plane wave , electron , scattering , helmholtz free energy , mathematical analysis , inverse , inverse problem , function (biology) , inverse scattering problem , wave function , plane (geometry) , classical mechanics , computational physics , mathematics , optics , quantum mechanics , geometry , boundary value problem , thermodynamics , evolutionary biology , biology
We address here the case of electron-matter elastic interaction as it occurs in Transmission Electron Microscopy (TEM) experiments. In the forward problem, we show that it is possible to derive the scattered electron wave function as the solution of a Helmholtz equation. This equation depends on the spatial potential associated with the analyzed sample, and can be relevantly solved using the Finite Element Method (FEM). Then we present an inverse formulation dealing with the determination of the sample’s potential when the total wave function is measured at the exit plane of the sample.