Understanding phonon selection and interference in momentum-resolved electron energy loss spectroscopy

Abstract: As momentum-resolved Electron Energy Loss Spectroscopy (q-EELS) becomes more widely used for phonon measurements, better understanding of the intricacies of the acquired signal becomes necessary. Selection rules limit the allowed scattering directions, which may prohibit the appearance of specific phonon branches, and features may appear with no clear explanation. To explore both, we perform frequency-resolved q-EELS simulations via the multislice method and compare results to Spectral Energy Density (SED) and Lattice Dynamics (LD) calculations. We discuss common misconceptions of phonon behavior and characterization generally and in the context of measured or simulated q-EELS signals. We highlight the presence of an ``interferometric Brillouin zone'' (closely related to the Dynamic Structure Factor), resulting from the simultaneous sampling of the lattice across each basis index. We also demonstrate the scattering selection rules on well-studied systems and explore the acquisition of a polarization-selective signal based on this phenomena. Finally, we identify thickness-dependent sensitivity effects, where the upper surface of a film is sampled at a disproportionate level. We show that this can yield sensitivity to through-plane vibrational modes, which may be measured experimentally assuming sufficient sensitivity can be achieved. Our work should serve as a road map to guide momentum-resolved vibrational EELS measurements in the future, particularly as ever-increasing energy and momentum resolution becomes available.