Open Collections

Pushing the limits of electron energy loss spectroscopy: from phonons to core losses in real and momentum space

Banff International Research Station for Mathematical Innovation and Discovery

A new generation of beam monochromators has recently pushed the energy resolution of (scanning) transmission electron microscopes (S)TEMs deep into the sub 20meV range [1]. In addition to the obvious increase in resolution, the flexibility of these instruments is allowing the energy resolution, beam current and optics can be adjusted seamlessly within a greatly increased range, thus enabling tantalising new modes of operations. This contribution will illustrate some of the new possibilities offered by these instruments through a number of examples, putting a specific emphasis on the need for advanced theoretical calculations to rationalise the experimental results. The increase in resolution has made it possible to explore the phonon region of the electron energy loss spectrum (EELS). Although the physical origin of vibrational signals in the STEM is very similar to that giving rise to low-energy phonon vibrations in neutron or inelastic X-ray scattering, differences in experimental geometries and selection rules, among other factors, have made their interpretation challenging. A better understanding of this phonon response can be achieved by observing the dependence of the phonon peaks under different optical conditions and mapping their energy in momentum space. A theoretical formalism based on that used by inelastic X-ray and neutron scattering [2] can be applied to obtain a good agreement with experimental data, e.g. from two polymorphs of boron nitride, across different directions in the Brillouin zone [3]. However, while this approach is successful, more complex and computationally demanding models taking into account finite momentum resolution and final sample size are shown to be necessary if a truly quantitative match between experiment and theory is to be achieved [3]. Furthermore, the effect of atomic scale defects on the bonding of materials can now be fingerprinted through core and low loss spectroscopy with a greater precision and sensitivity than ever before. Here, 2-dimensional materials have provided an ideal â sandboxâ : low energy excitons can be clearly distinguished in MoS2, while the introduction of a single B or N atom in graphene results in subtle localised modifications of its electronic structure [5,6]. However, for a reliable prediction of the loss function of these materials, at finite momentum transfer within density functional theory (DFT), it is necessary to invoke corrections for local field effects, in addition to any excitonic modification to the optical absorption. Thus for a comprehensive understanding of the experimental results a theoretical treatment beyond classical dielectric theory is imperative. In conclusion, this contribution will aim to illustrate that while modern electron microscopes are now sufficiently advanced to push the validity of the approximations used in theoretical electronic structure calculations, there is evidently a growing need to increase the efficiency of more advanced computational schemes using the GW and BSE formalisms, among others, and to tackle increasingly large atomic models to provide realistic and quantitative simulations to validate the experiments. [1] O.L. Krivanek, T.C. Lovejoy, N. Dellby et al., Nature 514 (2014), pp. 209-212. [2] E. Burkel, J.Phys.: Cond. Mat. 13 (2001), 7627. [3] F.S. Hage, R. Nicholls, J. Yates et al., Submitted (2017). [4] H.C. Nerl, K.T. Winther, F.S. Hage et al., NPJ 2D Mat. Appl. 1 (2017), pp. 1-11. [5] T.P. Hardcastle, C.R. Seabourne, D.M. Kepaptsoglou et al., J.Phys.: Cond. Mat. 29 (2017), 225303. [6] F.S. Hage, T.P. Hardcastle, M.N. Gjerding et al., Submitted (2017).

Mathematics; Numerical analysis; Approximations and expansions; Control/optimization/operation research

video/mp4

Author affiliation: SuperSTEM Laboratory

2019-03-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68565

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/