Modeling Vibrational Electron Energy Loss Spectroscopy with the Frequency-Resolved Frozen Phonon Multislice Method

Abstract: Aberration correctors, improved monochromators, and better detectors have enabled exciting research with nanometer- and Ångstrom-scale resolution in the Scanning Transmission Electron Microscope (STEM). However the interaction of high-energy electrons with the many-body system of the sample is quite complex and hinders interpretation of experiments. Therefore measurements often need to be informed by extensive modeling of the beam-sample interaction.In this thesis, we report the development of a model for the computer simulation of vibrational Electron Energy Loss Spectroscopy (EELS) in the STEM, which we call the Frequency Resolved Frozen Phonon Multislice (FRFPMS) method. We motivate the development of the method by reviewing the field of vibrational EELS from the instrumental advances, which enabled it, over experimental progress to a detailed consideration of other theories of vibrational EELS. In the process, we identify the need for a method, which is able to take into account many of the complicating factors of the scattering process, such as multiple elastic interactions, and is computationally feasible today, even for extended structure models.After a brief overview of necessary computational methods, we showcase that the FRFPMS method satisfies this need by discussing several papers we have published on the method. We demonstrate that the FRFPMS method produces results, which agree very well with published experimental and also theoretical results, both for momentum-resolved as well as high spatial resolution vibrational EELS. Furthermore we compare the FRFPMS method with the Quantum Excitations of Phonons model and the first-order Born approximation for a simple model system. The FRFPMS method matches the predictions of the other theories provided that two small modifications are introduced, which modify the temperature and energy-loss dependent scaling as well as the large momentum-transfer behavior of the modelled cross section.We then apply such revised FRFPMS method to simulations of shifts of optical phonon frequencies in hBN as a function of isotopic composition. The FRFPMS results are in very good agreement with experiments performed by collaborators, demonstrating that vibrational EELS is capable of detecting such isotopic shift of phonon frequencies in a momentum-resolved fashion. In another application of our method we focus on  simulating atomically-resolved STEM-EELS experiments on SrTiO3, which allow to interpret a subtle asymmetry in experimental large detector off-axis vibrational STEM-EELS maps as result of sensitivity to the direction of the phonon eigenvector. This enables imaging of anisotropic displacements of atoms as a function of vibrational frequency.