Multiple elastic scattering of electrons in condensed matter

• Published in: Computer physics communications 2017-01, Vol.210, p.92-102
• Main Author: Jablonski, A.
• Format: Article
• Language: English
• Subjects: Angular distribution; Computer simulation; Condensed matter; Elastic electron backscattering from surfaces; Elastic electron scattering on atoms; Elastic scattering; Electron energy; Electron inelastic mean free path; Electron transport in condensed matter; Mathematical analysis; Mathematical models
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2016.08.018

Since the 1940s, much attention has been devoted to the problem of accurate theoretical description of electron transport in condensed matter. The needed information for describing different aspects of the electron transport is the angular distribution of electron directions after multiple elastic collisions. This distribution can be expanded into a series of Legendre polynomials with coefficients, Al. In the present work, a database of these coefficients for all elements up to uranium (Z=92) and a dense grid of electron energies varying from 50 to 5000 eV has been created. The database makes possible the following applications: (i) accurate interpolation of coefficients Al for any element and any energy from the above range, (ii) fast calculations of the differential and total elastic-scattering cross sections, (iii) determination of the angular distribution of directions after multiple collisions, (iv) calculations of the probability of elastic backscattering from solids, and (v) calculations of the calibration curves for determination of the inelastic mean free paths of electrons. The last two applications provide data with comparable accuracy to Monte Carlo simulations, yet the running time is decreased by several orders of magnitude. All of the above applications are implemented in the Fortran program MULTI_SCATT. Numerous illustrative runs of this program are described. Despite a relatively large volume of the database of coefficients Al, the program MULTI_SCATT can be readily run on personal computers. Program title: MULTI_SCATT Program Files doi:http://dx.doi.org/10.17632/cvt9yz9gj8.1 Licensing provisions: GNU General Public License 3 (GPL) Programming language: Fortran 90 Nature of problem: Typically, elastic electron backscattering probabilities are estimated from results of Monte Carlo simulations of electron trajectories in a solid. This approach, although very convenient for a programmer, has major drawbacks: (i) the solid acceptance angles of analyzers are rather small, thus a large number of electron trajectories must be generated to obtain reasonable statistics; (ii) large running times are needed to reach an acceptable precision; (iii) results are always burdened with a statistical error. In the program MULTI_SCATT, an analytical formalism is implemented which leads to an accuracy comparable with Monte Carlo simulations, however it is faster by several orders of magnitude. Solution method: The program MULTI_SCATT requires presence of the d