The impact of surface and retardation losses on valence electron energy-loss spectroscopy

The inelastic scattering of fast electrons transmitting thin foils of silicon (Si), silicon nitride (Si3N4), gallium arsenide (GaAs), gallium nitride (GaN) and cadmium selenide (CdSe) was analyzed using dielectric theory. In particular, the impact of surface and bulk retardation losses on valence electron energy-loss spectroscopy (VEELS) was studied as a function of the foil thickness. It is shown that for the materials analyzed, surface and retardation losses can cause a systematic, thickness-dependent modulation of the dielectric volume losses, which can hamper the determination of the bulk dielectric data as well as the identification of band-gap and interband transition energies by VEELS. For Si and GaAs, where the dielectric function is strongly peaked with high absolute values, retardation losses lead to additional intensity maxima in the spectrum. For thin films of these materials (below ∼100 nm), the additional intensity maxima are related to retardation effects due to the finite size of the sample leading to the excitation of guided light modes. For thicker films, exceeding about 200 nm, the intensity maxima are caused by bulk retardation losses, i.e., Cerenkov losses. Although thickness-dependent modulations were observed for Si3N4, GaN and CdSe, the form of the dielectric functions and their lower maxima, means that for TEM samples <100 nm thick, the band-gap energies of these materials can be accurately identified by VEELS. Guidelines are given that allow for forecasting the impact of surface and retardation losses on VEELS.