Derivation method of the dielectric function of amorphous materials using angle-resolved electron energy loss spectroscopy for exciton size evaluation

Accurately deriving the momentum transfer dependence of the dielectric function ε(q, ω) using angle-resolved electron energy loss spectroscopy (AR-EELS) is necessary for evaluating the average electron-hole distance, i.e. the exciton size, in materials. Achieving accurate exciton size evaluations will promote the comprehension of optical functionality in materials such as photocatalysts. However, for amorphous materials, it is difficult to accurately derive ε(q, ω) because the elastic scattering intensity originating from the amorphous structure and the inelastic scattering intensity associated with elastic scattering overlap in the EELS spectrum. In this study, a method to remove these overlapping intensities from the EELS spectrum is proposed to accurately derive ε(q, ω) of an amorphous material. Amorphous SiO2 (am-SiO2) was subjected to AR-EELS measurements, and ε(q, ω) of am-SiO2 was derived after removing the intensity due to the amorphous structure using the proposed method. Thereafter, the exciton absorption intensity and the exciton size were evaluated. Applying the proposed method, the exciton absorption intensity was considerably suppressed in the q-region after 1.0 Å-1, where the elastic and inelastic scattering intensities originating from the amorphous structure are dominant. The exciton size evaluated was 2 nm ($ \pm $ 1 nm), consistent with the theoretically predicted size of ∼1 nm. Therefore, the proposed method is effective for deriving accurate ε(q, ω), facilitating exciton size evaluation for amorphous materials using AR-EELS.