Infrared surface phonon nanospectroscopy of an interacting dielectric-particle–dielectric-substrate dimer using fast electrons

Refinements in energy monochromation and aberration correction in state-of-the-art scanning transmission electron microscopes has opened access to the far infrared regime for spectroscopic characterization at the nanoscale. At these low energies, the dielectric environment, such as a dielectric slab adjacent to the target specimen, may no longer play a passive role in the spectrum. Instead, the environment may itself host resonances that mix with those of the target and complicate interpretation of its spectral responses. This paper explores a theoretical description of the coupling between the collective vibrational surface modes of a dielectric particle and dielectric slab of varying thickness for the purpose of elucidating the interacting phononic excitations in dielectric materials typical of inelastic electron scattering measurements in the infrared. Dynamical coordinates and a governing Hamiltonian are rigorously defined in the quasistatic limit to account for phonon mode mixing and forcing by an aloof electron probe, which travels along a grazing trajectory, parallel to the dielectric slab. As the spectral window of interrogation by fast electron probes has been extended down to thermal energies with unprecedented meV energy resolution, theoretical models like that presented herein are crucial for accurate interpretation of experimental data.