The Practical Application of Monte Carlo Models

Abstract The remainder of this book is devoted to the application of Monte Carlo models to a variety of problems in electron microscopy and microanalysis. The programs developed in Chaps. 3 and 4 provide only the framework that models the basic details of the electron interaction. We will now develop a variety of algorithms that, when implemented as PASCAL procedures and functions, can be used to transform these generic Monte Carlo models into programs customized to solve a particular problem. Before proceeding to these applications, however, there are a few practical considerations that are worth discussing. We have developed two types of Monte Carlo model, the single scattering model, which attempts to account for every elastic interaction suffered by the incident electron, and the plural scattering model, which considers only the resultant effect of scattering events occurring within some specified segment of the electron trajectory. These model share much of the same physics, and so, when properly used, can be expected to give comparable results. It is, however, necessary to decide what constitutes proper usage. An important general property of these models is what we shall call, by analogy with photographic film, their granularity. This concept expresses the idea that the Monte Carlo model is taking what is in reality a continuous sequence of scattering events and modeling it as a discrete series of independent events, just as a piece of film takes a picture and breaks it down into fragments the size of the grains making up the emulsion. The finer the grain size of the film, the higher the resolution of the image; and the finer the granularity (i.e., the step size) of the Monte Carlo simulation, the better the quality of the model generated. In the case of the single scattering model, the step size is of the order of the elastic mean free path and thus (depending on energy) is between a few nanometers and a few tens of nanometers, while for the plural scattering model, the step size is a fraction of the Bethe range and varies from tens of nanometers to fractions of a micrometer. In modeling some effect, it is therefore necessary to ensure that the granularity.