Low-loss electron energy loss spectroscopy: An atomic-resolution complement to optical spectroscopies and application to graphene

Abstract

Photon-based spectroscopies have played a central role in exploring the electronic properties of crystalline solids and thin films. Though they remain a powerful tool for probing the electronic properties of nanostructures, they are limited by lack of spatial resolution. On the other hand, electron-based spectroscopies, e.g., electron-energy-loss spectroscopy (EELS) are now capable of sub-Angstrom spatial resolution. Core-loss EELS, a spatially-resolved analog of X-ray absorption, has been used extensively in the study of inhomogeneous complex systems. In this paper, we demonstrate that low-loss EELS in an aberration-corrected scanning transmission electron microscope, which probes low-energy excitations, combined with a theoretical framework for simulating and analyzing the spectra, is a powerful tool to probe low-energy electron excitations with atomic-scale resolution. The theoretical component of the method combines densityfunctional-theory (DFT) based calculations of the excitations with dynamical scattering theory for the electron beam. We apply the method to monolayer graphene in order to demonstrate that atomic-scale contrast is inherent in low-loss EELS even in a perfectly periodic structure. The method is a complement to optical spectroscopy as it probes transitions entailing momentum transfer. The theoretical analysis identifies the spatial and orbital origins of excitations, holding the promise of ultimately becoming a powerful probe of the structure and electronic properties of individual point and extended defects in both crystals and inhomogeneous complex nanostructures. The method can be extended to probe magnetic and vibrational properties with atomic resolution. I. INTRODUCTIONOptical spectroscopies along with energy-band theory were the cornerstones upon which modern solid-state physics was founded. Ultraviolet and X-ray photoemission spectroscopies (UPS and XPS) were subsequently instrumental in the field of surface science. X-ray emission and absorption spectra (XAE and XAS) and their many variants, e.g., resonant x-ray scattering, have also played significant roles in probing the electronic properties of solids. Infrared absorption has been a powerful probe of phonons and lowenergy electronic excitations. The spatial resolution of these spectroscopies, however, is quite limited by the respective photon wavelengths and other factors.[1,2] Nevertheless, they continue to make major contributions in the study of nanostructures.Electron-based spectroscopies have the advantage of ultrasmall de Broglie wave lengths, which enable high spatial resolution. Scanning transmission electron microscopes (STEMs) employ a highly focused electron beam, which produces direct images of crystalline films with atomic resolution. The primary imaging mode of the STEM is Z-contrast imaging, which relies on high-angle Rutherford scattering by atomic nuclei [3]. The intensity of scattered electrons is proportional to approximately the square of the atomic number Z. In addition, inelastic scattering of the foc...

Signatures of distinct impurity configurations in atomic-resolution valence electron-energy-loss spectroscopy: Application to graphene

“…As first demonstrated in ref [27], VEELS signals can produce spatially localized maps even in the absence of impurities or defects. In the case of a single impurity atom, such as discussed above, one might intuitively expect an enhancement of the VEELS signal localized about the impurity and consider this to be due to the excitation of impurity bound states.…”

“…1a shows the averaged VEELS, with the so-called π+σ peak clearly seen at 15 eV. The π peak, which is located at 4.5 eV for pristine graphene (see, for instance, Refs [27,28]) was masked due to the limited energy resolution and tip noise fluctuations in this particular experiment.…”

“…as a convolution with the probe intensity, considered constant in the perpendicular direction z over the effective range of the projected potential [27,35]. By integrating Eq.…”

“…There was a common belief that VEELS have inherently limited spatial resolution, making atomic resolution all but impossible [23][24][25][26]. In recent work, however, we demonstrated that, in a perfect region of monolayer graphene, integration of a VEELS spectrum over selected energy windows as a function of probe position yields detailed 2D maps with atomic-scale contrast [27]. Corresponding simulations carried out by combining density functional theory (DFT) calculations and dynamical scattering theory enable the identification of the type of electronic transitions that are responsible for the observed features.…”

First Principles Determination of Electronic Excitations Induced by Charged Particles

“…Historically, the theoretical treatment of charged particles incident upon materials has most commonly been formulated from the vantage of the incident particle as a scattering problem in the momentum representation. [23][24][25][26][27][28] Modern first principles treatments of the scattering of incident charged particles by materials include multiple scattering Green's function approaches wherein the material's electronic structure is approximated at varying levels of sophistication, [29][30][31][32][33] as well as methods couched in the kinematic treatment of the scattering. 34,35 However, Tsubonoya, Hu, and Watanabe have recently reported the first simulations of low-energy electron wave packet diffraction by graphene nanoflakes, in which the incident electron wave packet and material's electronic degrees of freedom were co-propagated within a real time, real space TD-DFT framework.…”