Abstract
Recent developments in experiments with vibrational electron energy loss spectroscopy (EELS) have revealed spectral shape variations at spatial resolutions down to sub-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. In Zeiger and Rusz, Phys. Rev. Lett. 124, 025501 (2020) we have presented a frequency resolved frozen phonon multislice method for simulations of vibrational EELS. Detailed simulations for a plane wave electron beam scattering on a vibrating hexagonal boron nitride are presented in a companion manuscript (Zeiger and Rusz, arXiv:2104.03197). 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 size electron beam, we observe the same, although with better contrast. In addition, we observe atomic level contrast and sub-atomic scale spectral shape modifications, which are particularly strong for small detector collection angles.
Highlights
Heat management is a major design limitation of integrated circuits today [1,2] and Moore’s law is at the same time reaching its limits [3]
Advances in the field of phononic and thermoelectric materials allow for the control of phonons over large frequency regions and make it thereby possible to control the flow of heat [4]
We show that the frequency-resolved frozen phonon multislice (FRFPMS) method resolves both angle-resolved spectral shape variations on a nanometer scale as well as atomic scale spectral changes analogous to those reported in previous experimental works
Summary
Heat management is a major design limitation of integrated circuits today [1,2] and Moore’s law is at the same time reaching its limits [3]. (Scanning) transmission electron microscopy [(S)TEM] routinely allows to reach subangstrom spatial resolution [5,6,7,8,9,10] and thanks to recent advances in monochromators it offers an energy resolution of electron energy loss spectroscopy (EELS) down to 4.2 meV [11,12] Unprecedented experiments such as mapping of bulk and surface modes of nanocubes [13], investigations of the nature of polariton modes in van der Waals crystals [14], temperature measurement at the nanoscale [15,16], identification and mapping of isotopically labeled molecules [17], positionand momentum-resolved mapping of phonon modes [18,19,20], atomic resolution phonon spectroscopy [21,22], functional
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