Channeling effects in high-angular-resolution electron spectroscopy

L. J. Allen, S. D. Findlay, M. P. Oxley, C. Witte, and N. J. Zaluzec

Phys. Rev. B 73, 094104 – Published 3 March 2006

Abstract

Momentum-transfer-resolved electron spectroscopy is a technique for examining the electronic structure of materials and requires the use of detectors accepting a small range of momentum transfers. For crystalline specimens, it is necessary to consider the channeling behavior of the fast electrons both before and after inelastic scattering to adequately describe the signals produced. Using oxygen $K$ -shell core loss in NiO as a case study, we examine channeling in high-angular-resolution electron-channeling electron spectroscopy. The roles of nonlocality and sample thickness as they relate to the channeling effect are explored. Particular attention is given to the behavior arising from the channeling of the scattered electrons, as compared with models in which only the incident electrons channel. Calculations allowing for the channeling of both the incident and the scattered electrons are computationally demanding and we explore approximations that can be made for detectors with small acceptance angles.

Received 21 September 2005

DOI:https://doi.org/10.1103/PhysRevB.73.094104

Authors & Affiliations

L. J. Allen¹, S. D. Findlay¹, M. P. Oxley², C. Witte¹, and N. J. Zaluzec³

¹School of Physics, University of Melbourne, Victoria 3010, Australia
²Condensed Matter Sciences Division, Oak Ridge National Laboratory, P. O. Box 2008, Oak Ridge, Tennessee 37831-6030, USA
³Electron Microscopy Center, Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA

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Vol. 73, Iss. 9 — 1 March 2006

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Images

Figure 1
(a) Oxygen $K$ -shell energy loss spectrum from NiO in the symmetric orientation of the ⟨200⟩ systematic row. (b) Integrated intensity over a $100 eV$ energy window above ionization threshold. Background subtraction was carried out based on extrapolation from a $50 eV$ window prior to the edge. A unit of 1.0 on the orientation axis puts the (100) beam in the exact Bragg orientation, a tilt of $3.0 mrad$ . (c) Surface plot of the orientation dependence of the background-corrected oxygen $K$ -shell EELS structure as a function of energy loss.Reuse & Permissions
Figure 2
(a) Effective ionization potential $W (x, x^{'})$ for $K_{⊥} = 0$ shown on a $2 \times 2$ supercell. The location of the oxygen atoms on the diagonal is shown by white rings. (b) Inelastic scattering coefficients $μ_{G, G} (K)$ as a function of $K_{⊥}$ $[K_{⊥} = - orientation \times (100) ∕ 2]$ , for $G = (000)$ and (200). (c) Schematic of the primary scattering mechanism contributing to the detected signal for (I) $K_{⊥} = 0$ and (II) $K_{⊥} = G$ . The dotted circles denote elastic scattering, the dotted stars inelastic scattering.Reuse & Permissions
Figure 3
(a) The cross section per unit area as a function of orientation and thickness in the single-channeling model. (b) The cross section per unit area as a function of thickness at orientations corresponding to the central and Bragg peaks. (c) The contribution per $25 Å$ thick slice to the signal plotted in (b).Reuse & Permissions
Figure 4
(a) The cross section per unit area as a function of orientation and thickness in the double-channeling model. (b) Extracts from (a) at the central and Bragg peaks.Reuse & Permissions
Figure 5
(a) ${∣ S_{0, 0} (K_{⊥} = 0, t - z) ∣}^{2}$ as a function of the event depth $z$ for $t = 1050$ and $1150 Å$ . (b) ${∣ S_{0, 0} (K_{⊥} = 0, z) ∣}^{2} {∣ S_{0, 0} (K_{⊥} = 0, t - z) ∣}^{2}$ as a function of event depth $z$ . The total cross section consists of the sum of integrals over $z$ of such products weighted by the inelastic scattering coefficients.Reuse & Permissions
Figure 6
(a) Fit parameter as a function of the initial thickness $t$ and the thickness range $Δ t$ . (b) Contour plot of the fit parameter in (a) truncated to bring out the structure near the minima. Three significant minima, labeled by the white indices, are evident. The minima correspond to $(t, Δ t)$ parameters (1) $(230 Å, 110 Å)$ , (2) $(450 Å, 120 Å)$ , and (3) $(685 Å, 110 Å)$ . (c) Comparison between the processed experimental data, the best-fit double-channeling simulation using the parameters from minimum 2, and the single-channeling simulation using the same parameters.Reuse & Permissions

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