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Photoelectron Energy Loss in Al(002) Revisited: Retrieval of the Single Plasmon Loss Energy Distribution by a Fourier Transform Method

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Abstract

A Fourier transform (FT) algorithm is proposed to retrieve the energy loss function (ELF) of solid surfaces from experimental X-ray photoelectron spectra. The intensity measured over a broad energy range towards lower kinetic energies results from convolution of four spectral distributions: photoemission line shape, multiple plasmon loss probability, X-ray source line structure and Gaussian broadening of the photoelectron analyzer. The FT of the measured XPS spectrum, including the zero-loss peak and all inelastic scattering mechanisms, being a mathematical function of the respective FT of X-ray source, photoemission line shape, multiple plasmon loss function, and Gaussian broadening of the photoelectron analyzer, the proposed algorithm gives straightforward access to the bulk ELF and effective dielectric function of the solid, assuming identical ELF for intrinsic and extrinsic plasmon excitations. This method is applied to aluminum single crystal Al(002) where the photoemission line shape has been computed accurately beyond the Doniach–Sunjic approximation using the Mahan–Wertheim–Citrin approach which takes into account the density of states near the Fermi level; the only adjustable parameters are the singularity index and the broadening energy Г (inverse hole lifetime). After correction for surface plasmon excitations, the q-averaged bulk loss function, <Im[− 1 / ε(E, q)]> q , of Al(002) differs from the optical value Im[− 1 / ε(E, q = 0)] and is well described by the Lindhard–Mermin dispersion relation. A quality criterion of the inversion algorithm is given by the capability of observing weak interband transitions close to the zero-loss peak, namely at 0.65 and 1.65 eV in ε(E, q) as found in optical spectra and ab initio calculations of aluminum.

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Acknowledgements

We wish to thank A. Le Pottier and B. Lépine for the technical help in the Al sample preparation, along with S. di Matteo and D. Sébilleau (IPR, Rennes University) for the valuable discussions on photoemission theory and Prof. A. Ferreira da Silva (UFBa, Brazil) for his steady support.

Funding

C.G. is grateful to the CNPq agency (Brazil) for a visiting researcher grant (PVE 400691/2012-4) from the Ciência Sem Fronteiras programme. D.D. is grateful to the CAPES agency (Brazil) for a senior researcher grant (BEX 0281/15-8) and University of Rennes 1 for an invited professor position. V.S. is grateful to the CAPES agency (Brazil) and Rennes Métropole for PhD grants.

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  1. Instituto de Fisica, Universidade Federal da Bahia, Campus Universitário de Ondina, Salvador, Bahia, 40210-340, Brazil

    Victor Mancir da Silva Santana, Denis David & Jailton Souza de Almeida

  2. Univ Rennes, CNRS, IPR (Institut de Physique de Rennes) - UMR 6251, F-35000, Rennes, France

    Christian Godet

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  2. Denis David
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Correspondence to Denis David or Christian Godet.

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Santana, V.M.d., David, D., de Almeida, J.S. et al. Photoelectron Energy Loss in Al(002) Revisited: Retrieval of the Single Plasmon Loss Energy Distribution by a Fourier Transform Method. Braz J Phys 48, 215–226 (2018). https://doi.org/10.1007/s13538-018-0566-8

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