We develop several methods for computer simulation of low energy electron scattering on three-dimensional nanostructures. We apply these formalisms to the simulation of the Fresnel projection microscope. One of these formalisms uses the Lippmann-Schwinger integral equation and another uses the technique of transfer matrices. These formalisms are based on cylindrical partial waves decomposition of the stationary diffusion state. This approach allows the decoupling of the scattering problem in the case of structures with axial or helical symmetry. We propose a new method for calculating the matrices ‘t’ and ‘s’. This method is based on solving the Lippmann-Schwinger equation on a single layer of the structure at a time. It is more stable and faster than the available methods. For structures infinite according to one dimension of the space, we introduce the new concept of effective scattering width instead of the scattering cross section. Among other things, our simulations concern the scattering by nanotubes and the B-DNA molecule. To this end, we determine effective atomic potentials based on the total and differential atomic cross sections. We also propose a new algorithm for reconstruction of the structure from the scattered intensity in the far field considered as an electronic hologram.
Diffusion élastique d’électrons lents par des structures hélicoïdales: application au microscope à projection de Fresnel
Moreau, F. (Author). 23 Aug 2012
Student thesis: Doc types › Doctor of Sciences