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Transport of energetic electrons in solids

Maurizio Dapor
In modern physics we are interested in systems with many degrees of freedom. Let us consider, for example, the number of atoms in a solid, the number of electrons in an atom, or the number of electrons of a beam interacting with the many atoms and electrons of a solid. In many situations, these systems can be described by the calculations of de finite integrals of very high dimension. An example is the evaluation of the classical partition function for a gas of many atoms at a temperature T. The Monte Carlo method gives us a very accurate way to calculate high dimensional de nfiite integrals: it evaluates the integrand at a random sampling of abscissa. The Monte Carlo method is also used for evaluating the many physical quantities necessary to the study of the interactions of particle-beams with solid targets. The simulation of the involved physical processes, by random sampling, allows to solve many particle transport problems. Letting the particles carry out an arti cial, random walk - taking into account the e ffect of the single collisions - it is possible to accurately evaluate the di ffusion process. This book is devoted to the electron-beam interactions with the solid targets. As a researcher in this fi eld, I am persuaded that a book on kV electron transport in solids can be very useful. It is difficult, for the newcomer, to fi nd this topic exhaustively treated; and it is not easy for the beginner to sort out the importance of the great number of published papers. The Monte Carlo simulation is the most powerful theoretical method for evaluating the physical quantities related to the interaction of electrons with a solid target. A Monte Carlo simulation can be considered as an idealized experiment. The simulation does not investigate the fundamental principles of the interaction. It is necessary to know them - in particular the energy loss and angular deflection phenomena - to produce a good simulation. This book is complementary with respect to many other texts dedicated to similar subjects (including my book entitled Electron-Beam Interactions with Solids, published by Springer-Verlag in 2003) for the following two aspects. 1. I have, on the one hand, systematically minimized the mathematical contents of the more difficult theoretical parts. Since the essential concept to digest is the meaning of the various cross sections, the mathematical details, for the sake of clarity, have been deliberately avoided. I have reduced the theoretical part to the presentation of the energy loss and the angular deflections, providing simple recipes to calculate the stopping power, the diff erential inverse inelastic mean free path, and the diff erential elastic scattering cross section. This allowed me to avoid to describe in depth quantum theory. Mathematical contents and details can be found in the Appendices, in my previous book, and in many other books dedicated to modern physics and quantum mechanics. 2. In the derivation and use of the simpler theoretical transport models, I have, on the other hand, included many details. I think, indeed, there is a need of a basic physical picture in order to provide the beginner with a solid background about electron transport in solids. This can be only achieved by a step-by-step derivation of the analytical formulas. Comparing available experimental data with simulation results is a fundamental step in evaluating the quality of the Monte Carlo codes. Selected applications of the Monte Carlo method to kV electron transport in solids are presented in the second part of this book. The book compares computational simulations and experimental data in order to off er a more global vision.
Date of publication: 
Published in: 
Springer, Berlin 2014