Théorie de diffusion électronique tridimensionnelle par matrices de transfert et fonctions de Green appliquée à la simulation du microscope à projection de Fresnel

Abstract

We developed a method to compute the electronic three-dimensional cattering, in order to simulate the Fresnel Projection Microscope. The framework of our model is the general transfer matrix methodology. The inherent instabilities were controlled with the layer addition algorithm and an accuracy estimator. This estimator provides an estimation of the relative error on the result - before the scattering computation itself. The propagation
equations take account of the electronic absorption (represented by an imaginary component in the potential energy) and the magnetic fields. With the basis used for the wavefunction representation, the problem is split into n independent parts in the case of a central n-fold symmetry axis. The outgoing states, obtained within the transfer- matrix methodology, are propagated over macroscopic distances in the Green function formalism. We simulated efficiently field emission from nanotips and confirmed their usefulness for projection microscopy. Our simulations
provide opening angles and total energy distributions in agreement with experimental results. We illustrated the Fraunhofer and Fresnel diffraction in the observation of a carbon fiber and investigated the influence of its general properties. We then used an atomic description of the matter to show how its specific properties can shape the diffraction figures. Simulations with magnetic fields confirm the existence of diffraction fringes that are oriented parallel to the field lines and tend to get closer with increasing field strength.

Date of Award	18 Dec 1998
Original language	French
Awarding Institution	University of Namur
Sponsors	Fonds de la Recherche Scientifique F.R.S.-FNRS
Supervisor	Jean-Pol VIGNERON (Supervisor), Amand Lucas (Jury), Michel Devel (Jury), Joseph DELHALLE (Jury) & [No Value] Vu thien binh (Jury)