Analytical differential cross section of electron elastically scattered by solid targets in the energy range up to 100 keV A. Bentabet a, * , Z. Chaoui b , A. Aydin c , A. Azbouche d a SM Department, Sciences and Technology Institute, Bordj Bou Arreridj University Center, Bordj Bou Arreridj, 34000, Algeria b Laboratory of Optoelectronics and Devices, University of Setif, UFA Setif, Setif 19000, Algeria c Balıkesir University, Faculty of Sciences and Literature, Department of Physics,10145 Balıkesir, Turkey d Nuclear Research Center of Algiers, 2 Boulevard Frantz Fanon Alger, Algeria article info Article history: Received 18 August 2009 Received in revised form 26 April 2010 Accepted 4 May 2010 Keywords: Electron elastic cross-section Elastic scattering Screening Rutherford cross section Backscattering coefficient Mean penetration depth Monte Carlo simulation abstract In this paper, we propose a new approach to determine the adjustable parameters of differential elastic cross-section of Bentabet et al. approximation. The resultant approximation is an analytical expression that can be used to study the interaction of electron beams with solid targets. This approximation is applied for the energy range up to 100 keV, to calculate some quantities such as: the mean penetration depths, the mean number of wide angle collisions and the backscattering coefficient (BSC) of Al, Cu, Ag and Au semi-infinite solid targets. BSC was calculated by using both the Monte Carlo method and the Vicanek and Urbassek analytical model. The obtained results are compared with the experiment and good agreement is remarked. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction The electron material interaction has a great importance in the areas of micro and optoelectronics and in material analysis techniques such as: electron probe microanalysis, energy-loss-spectroscopy, Auger electron spectroscopy, etc. The theoretical study on the effects of irradiation of solid targets by charged particles has recently received great attention [1e5]. Backscattering of low to medium electron beams from thin films has impact on a range of surface sciences techniques [6e10]. Purely analytical models and simple approaches using closed formulas are not able to give satisfactory results. However, the rapid evolution of computer calculation capability has made it possible. A great deal of theoretical investigations and the Monte Carlo approach have been recognized as powerful techniques for performing certain calcula- tions [6,11]. As recently shown by Vicanek and Urbassek [12] and by Vukanic et al. [13], the backscattering coefficient (BSC) is strongly related to the mean number n of wide angle collisions suffered by the particle before slowing down to rest. n depends on the type of particles, on their primary energy, and on the target mean atomic number. It is, indeed, a function of the elastic and inelastic processes suffered by the particles traveling in the solid target [1]. Thus, the calculation of n requires a very accurate knowledge of the elastic and inelastic scattering processes [1]. The elastic collisions are described in the present work by using the same mathematical expression of differential elastic cross-section proposed by Bentabet et al. [14]. This mathematical expression depends on two adjustable parameters a and b. The method used in the determi- nation of adjustable parameters (or the differential elastic cross- section) has been applied only in bass energy from 0 to 4 keV to study the electron and the positron transport in the solid target [14e20]. However, its application for high energies necessitates a new approach for the determination of the adjustable parameters [20]. Therefore, we have proposed a new approach to determine those parameters and seems to be valid from low to medium and even to high energies (the test is done in the energy range up to 100 keV). In the work we have employed not only the Monte Carlo procedure which has the same general structure as that was used in our previous papers [18e20], but also included a new approach of the differential elastic scattering cross-section of Bentabet et al. approximation. We also report on the results for transport cross section, backscattering coefficients and mean penetration depths of full Monte Carlo simulations of the slowing down process for 1e 100 keV electrons penetrating into some semi-infinite elements * Corresponding author. E-mail address: a.bentabet@gmail.com (A. Bentabet). Contents lists available at ScienceDirect Vacuum journal homepage: www.elsevier.com/locate/vacuum 0042-207X/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2010.05.004 Vacuum 85 (2010) 156e159