A general expression for the energy-loss probability in scanning trans
mission electron microscopy valid for complex microstructures is prese
nted in the framework of classical dielectric theory. Calculations are
carried out for small particles half embedded in a planar interface.
We used experimental data for the dielectric functions that characteri
ze the media and we take into account the coupling among different mul
tipolar terms. Resonances, present neither in the planar-interface nor
in the isolated-sphere energy-loss spectra, are found. The results ag
ree with many experimental results reported in the literature of the l
ast few years. A different behavior between conducting and insulator s
upports is found. The effect of an oxide coating around the spherical
particle is also discussed.