Inelastic scattering probabilities in scanning transmission electron microscopy

In this paper, we derive a general expression for the excitation probability corresponding to the collection of inelastically scattered electrons in a scanning transmission electronic microscopy configuration. We prove that, if all inelastically scattered electrons are collected, then the fraction of electrons that will be determined to have given rise to excitation in a localized target at impact parameter b may be calculated by simply convoluting over b (1) the probability P c(b) that a classical electron with the same velocity well create the excitation at given b, with (2) the probability of finding the electron in the microprobe at that impact parameter. We also show that, even in the opposite extreme, when a small solid angle of axial collection is employed, the energy-loss spectrum will still approximate to the classical expression provided that it is normalized to the same zero-loss intensity and if the Fourier-transformed profile function does not become too small for some ranges of its argument. A realistic microprobe distribution is used to compute the angular distribution of electrons that have created a surface plasmon or a surface optical phonon at a surface parallel to the electron trajectory. The results demonstrate the usefulness of the classical theory for axial detector positions as well as the possibility of enhanced spatial resolution for off-axis detector positions.