Modeling energy-loss spectra due to phonon excitation

Abstract

We discuss a fundamental theory of how to calculate the phonon-loss sector of the energy-loss spectrum for electrons scattering from crystalline solids. A correlated model for the atomic motion is used for calculating the vibrational modes. Spectra are calculated for crystalline silicon illuminated by a plane wave and by an atomic-scale focused coherent probe, in which case the spectra depend on probe position. These spectra are also affected by the size of the spectrometer aperture. The correlated model is contrasted with the Einstein model in which atoms in the specimen are assumed to vibrate independently. We also discuss how both the correlated and Einstein models relate to a classical view of the energy-loss process.