Theory of energy loss in scanning transmission electron microscopy of supported small particles

A general expression for the energy loss probability in scanning transmission electron microscopy (STEM) is derived. The method uses a Green's function for the incident and scattered electrons and then folds the specimen into a local response function. Our expression is appropriate to any target geometry and dielectric response. As an application, the energy loss spectrum of a STEM electron moving close to an Al sphere half-embedded in an Al planar surface is calculated. The coupling between different l modes, neglected in earlier theoretical approaches, is taken into account.