Exploring the Barkas effect with keV-electron scattering

Abstract

The energy loss of fast ions at close collision is mainly due to electron-ion collisions. The electrons are approximately stationary and they collide with a fast-moving ion. Here we study the same collision experimentally, in a reference system where the ions (or atoms) are stationary and interacting with keV electrons. Scattering cross sections under these conditions deviate from Rutherford, and we link these deviations, at higher energies, to the Z 3 contributions to the electronic stopping and the related Barkas effect and, at lower energies, also to quantum interference. The present measurements are well described by partial-wave calculations of the elastic cross section of electrons scattering from atoms. Encouraged by this agreement we use these calculations to estimate the Barkas factor for all elements and many energies. A universal curve for the Barkas factor due to close collisions is obtained for neutral projectiles and similar curves with smaller magnitude are found for ions.

A comparison of ERBS spectra of compounds with Monte Carlo simulations

“…The HfO 2 sample was a 60 nm thick HfO 2 layer grown by atomic layer deposition on a silicon wafer. Results of these films were published elsewhere; here, the focus is on the investigation of the influence of multiple scattering on the experiment, as well as an illustration of how ERBS can be used to determine the sample composition for a wide range of samples.…”

“…For Hf, the partial‐wave cross section is substantially larger at backward angles than the Rutherford one. The cause of this is discussed elsewhere, and for Hf, the term ‘electron Rutherford backscattering’ is not strictly appropriate.…”

Notes on Barkas-Andersen effect

“…[11]. While the validity of the approach has gradually been accepted, it is not clear whether, as implied by Lindhard, his approach covers the complete phenomenon or, as implied recently [17][18][19], that one deals with two independent mechanisms, one for distant collisions found by Ashley et al, and another one for close collisions found by Lindhard. This aspect will be studied here by comparing the distant-collision limit of Lindhard's approach to that of Ashley et al…”

“…Although this feature is not mentioned in ref. [17], it may be the reason why Lindhard's procedure has been considered to concern only close collisions [17][18][19].…”

“…Recently, Grande & Vos [19] explored cross sections for elastic scattering of electrons from ions and neutral atoms with the specific purpose to explore the Barkas effect. Such measurements provide information about the screening potential of an ion in a given charge state in a way that is rather directly related to the quantity needed in a calculation of the stopping cross section of a free electron gas for a screened ion, namely via the differential scattering cross section.…”