An Introduction to Monte Carlo Methods

Abstract The interaction of an electron beam with a solid is complex. Within a distance of a few tens to a few hundreds of angstroms of entering the target, the electron will interact with the sample in some way. The interaction could be the result of the attraction between the negatively charged electron and the positively charged atomic nucleus (and equally the repulsion between the negatively charged atomic electrons and negative charge on the incident electron), in which case the electron will be deflected through some angle relative to its previous direction of travel, but its energy will remain essentially unaltered. This is called an elastic scattering event. Alternatively, the incident electron could cause the ionization of the atom by removing an inner-shell electron from its orbit, so producing a characteristic x-ray or an ejected Auger electron; it could have a collision with a valence electron to produce a secondary electron; it could interact with the crystal lattice of the solid to generate phonons; or, in one of several other possible ways, it could give up some of its energy to the solid. These types of interactions in which the electron changes both its direction of travel and its energy are examples of inelastic scattering events. After traveling a further distance, the electron will then again be scattered, either elastically or inelastically as before, and this process will continue until either the electron gives up all of its energy to the solid and comes to thermal equilibrium with it or until it manages to escape from the solid in some way.