Simulations of spatially and angle-resolved vibrational electron energy loss spectroscopy for a system with a planar defect

Recent developments in experiments with vibrational electron energy loss spectroscopy (EELS) have revealed spectral shape variations at spatial resolutions down to the atomic scale. Interpretation in terms of local phonon density of states enables their qualitative understanding, yet a more detailed analysis is calling for advances in theoretical methods. Recently, we have presented a frequency resolved frozen phonon multislice method for simulations of vibrational EELS [P. M. Zeiger and J. Rusz, Phys. Rev. Lett. 124, 025501 (2020).]. Detailed simulations for a plane-wave electron beam scattering on vibrating hexagonal boron nitride are presented in a companion paper [P. M. Zeiger and J. Rusz, Phys. Rev. B 104, 104301 (2021)]. Here we present simulations of vibrational EELS assuming a convergent electron probe of nanometer size and atomic size on a hexagonal boron nitride structure model with a planar defect. With a nanometer beam we observe spectral shape modifications in the presence of the defect, which are correlated with local changes of the phonon density of states. With an atomic-sized electron beam, we observe the same, although with better contrast. In addition, we observe atomic-level contrast and atomic scale spectral shape modifications, which are particularly strong for small detector collection angles