Electron energy loss spectroscopy of core-electron excitation in anisotropic systems: Magic angle, magic orientation, and dichroism

Abstract

A general theory for the detection of the core-level electronic excitation in anisotropic systems using angular integrated electron energy-loss spectroscopy ͑EELS͒ has been presented. Magic angle conditions, at which spectra are independent of specimen orientation, are proved to be valid for all anisotropic systems. Discrepancies in the magic angle determination are thoroughly investigated from the theoretical point of view. The magic angle electron energy loss spectroscopy ͑MAEELS͒ can be directly interpreted as spherical averaged spectroscopy. From the explicit expression for the EELS cross section for all the anisotropic systems, a magic specimen orientation is also found to exist in certain low symmetry systems, where spectra acquired are also equivalent to the fully orientationally averaged spectra. Our analysis provides a useful guide for the experimental determination of electronic structure information in anisotropic systems, including their dichroic signals.

Advanced spectroscopic analyses on a:C-H materials: Revisiting the EELS characterization and its coupling with multi-wavelength Raman spectroscopy

“…2). According to the literature, the R value determined at this angle coincides with the one that would be obtained in magic angle condition [68,75]. In addition, this angle, which is nearly the maximum angle experimentally that can be obtained, has been chosen to minimize the uncertainty on the determination of R, as it lies close to the center R=f(δ) curve.…”

“…Graphite is then the ideal reference sample. However, it is an anisotropic material and the second pitfall lies in the sensitivity of the EELS spectra to the anisotropy of the material [45,46,55,[68][69][70][71][72][73].…”

“…The spectral weight of the π * and σ * components of anisotropic carbon-base materials depends then strongly on the specimen orientation and on the convergence and collection angles [68][69][70]74]. A particular setup of convergence and collection angles can be used to alleviate the dependence of the C-K edge spectrum with the specimen orientation (the so-called magic-angle condition) [68][69][70][71][72]75].…”

“…A particular setup of convergence and collection angles can be used to alleviate the dependence of the C-K edge spectrum with the specimen orientation (the so-called magic-angle condition) [68][69][70][71][72]75]. The collection angle at magic angle condition for an energy-loss of 290 eV should be 4.9 mrad at 80 kV, 1.2 mrad at 200 kV and 0.7 mrad at 300 kV.…”

Layer-dependent anisotropic electronic structure of freestanding quasi-two-dimensionalMoS2

“…EELS has been long recognized as an alternative nonoptical tool to probe electronic structures of semiconductors and has been used to study the valence electron excitation such as band-gap transition [21,22] and plasmonics [23,24]. In EELS, the momentum transfer vector ( q = k i − k f ) plays the role of the polarization vector in optical absorption [25], where k i and k f are the wave vectors of the incident and outgoing electrons, respectively. The angular-(or momentum-) resolved EELS is thus particularly suited to probe the anisotropy of the electronic transitions because the directions of the momentum transfer can range from being parallel to being perpendicular to the incident direction around the characteristic scattering angle (θ E = E/2E 0 ) [26], where E is the energy loss and E 0 is the kinetic energy of incident electrons.…”