- Jan Rusz: Vibrational Spectroscopy at Nanometer and Atomic Scale
- 17. 2. 2021, 14:10
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Abstract:
Scanning transmission electron microscopy (STEM) offers a wealth of techniques for studying material properties, such as material composition, distribution of elements, crystal structure, valence electron excitations or chemical environment of constituting elements. What is unique about STEM is the spatial resolution combined with bulk sensitivity. The electron beam, which passes through the sample, can be focused to sub-Ångström spot sizes, allowing to study the properties down to atomic lateral resolution. Recently, the wide range of techniques available in STEM has been extended to the domain of ultra-low energy losses (in the context of transmission electron microscopy), by developing a new generation of efficient monochromators [1] enabling to reach energy resolution of sub-5meV.
The vibrational spectroscopy in STEM is developing very rapidly and recently it has culminated with reports of atomic scale contrast [2,3,4] and, particularly, detection of vibrational signatures of a single-atom impurity [5] and planar defects [6].
Spectacular progresses in vibrational spectroscopy experiments calls for computational methods, which aid the interpretation of the measured data. Spatially resolved vibrational spectroscopy is most easily complemented by calculating projected phonon densities of states, which can be calculated for any subset of atoms in a vibrating lattice [5]. Alternatively, a full quantum mechanical calculation of transition matrix elements for phonon excitations can be performed, in combination with multislice propagation of the electron beam through the lattice [7]. Finally, quantum-excitation of phonons (QEP) method has been used for explaining atomic level contrast in vibrational STEM [2].
We have introduced an alternative model for simulations of vibrational spectroscopy [8], which inherits the efficiency of so called frozen phonon multislice method, commonly used to simulate a diffuse background in diffraction patterns due to scattering of electrons on atoms in motion. In this method an electron beam is elastically propagated through a series of snapshots of vibrating structure model of the
system. This is most commonly implemented by assuming independent atomic displacements according to Einstein model. Here we utilize so called colored thermostats within molecular dynamics, which allow to selectively excite only phonons from a chosen frequency range. Using such non-equilibrium molecular dynamics we can generate snapshots of vibrating lattice in an energy-resolved way. The method allows for flexible simulations, fully considering correlated motion of atoms (phonons), arbitrary electron beam shape and its dynamical propagation through the material, arbitrary orientation of the beam vs sample and orientation of the detector. Among further advantages of our method is that it doesn't require an explicit knowledge of phonon modes, making it well suitable for treating large structure models, including defects. We have used this model to simulate nanometer-scale and atomic scale variations of vibrational spectra, both in terms of intensity and spectral shape.
References:
[1] O. L. Krivanek et al., Nature 514, 209 (2014).
[2] F. S. Hage et al.,Phys. Rev. Lett. 122, 016103 (2019).
[3] K. Venkatraman et al., Nature Physics, 1 (2019).
[4] R. Senga et al., Nature 573, 247 (2019).
[5] F. S. Hage et al. Science 367, 1124 (2020).
[6] X. Yan et al., Nature 589, 65 (2021).
[7] C. Dwyer, Phys. Rev. B 89, 054103 (2014).
[8] P. M. Zeiger and J. Rusz, Phys. Rev. Lett. 124, 025501 (2020).