Optical guided modes coupled with Čerenkov radiation excited in Si slab using angular-resolved electron energy-loss spectrum

Retardation effects in the valence electron energy-loss spectrum (EELS) of a Si slab are analyzed by angular-resolved EELS. The dispersion curves of the valence spectra excited in a slab are directly observed from a specimen area with several different thicknesses and are interpreted by performing a calculation of the dispersion relation using Kröger's formula. The dispersion curves observed below about 3 eV are attributed to guided modes coupled with Čerenkov radiation (ČR). The coupling between guided modes and ČR is found to be dependent on the sample thickness (t). For the sample with t > 150 nm, the intensity of the guided modes increased linearly with thickness, revealing the coupling with ČR. For t < 150 nm, however, the intensity of the guided modes rapidly decreased due to a diminished coupling with ČR, resulting from the thickness-dependent dispersion curves of the guided modes.