Electron scattering in microstructure processes

Abstract

The study of electron beam penetration in solids is fundamental to understanding the basic processes in a variety of applications, such as microscopy, electron probe microanalysis and microlithography. The physics of electron scattering in solids has been discussed in sect. 2, in order to obtain a useful theoretical description of the electron transport problem. Due to the complexity of the electron scattering process strong simplifications have been proposed. The single-scattering approach of Everhart and the diffusion sphere approach of Archard, described in sect. 3, have the merit of modelling, in a very simple way, two extreme cases, large-angle single scattering and diffusion: the real situation can be considered as being intermediate between the two. Presently, the most basic approach to the study the electron penetration in solids is the Monte Carlo method. MC calculations consider the behaviour of individual electrons. The trajectory of an electron through the solid is calculated step by step, assuming it is scattered through randomly determined angles, on the basis of the equations used to approximate the physical processes. The great success of Monte Carlo calculations relies upon three factors: a) its adaptability to systems having a variety of geometries, with reference to size, shape or internal structure; b) the number of different output data available from MC calculations, in the form of plots of electron trajectories, energy and angular distributions of forward and backward scattered electrons; c) the physical insight into the problem, allowed by the capability of treating the process directly in terms of its basic mechanisms. The accuracy of such calculations depends on the accuracy of the modelling of the scattering, MC results being, in any case, more accurate than analytical treatments.