Theoretical description of electron transport in solids is important in radiation physics, electron lithography, electron-probe microanalysis, analytical electron microscopy, and surface analysis by Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS). In these and other applications, the trajectories of electrons in a solid are generally modified by single and multiple elastic-scattering events. An evaluation of the effects of elastic scattering on the process of interest requires knowledge of the cross sections for electron elastic scattering by the constituent atoms of the particular solid. Although calculated and measured electron elastic-scattering cross sections are available in the literature for selected elements and a limited number of electron energies, this information is incomplete and insufficient for general use.

NIST released Version 1.0 of the Elastic-Electron-Scattering Cross-Section Database (SRD 64) in 1996. This version provided differential and total elastic-scattering cross sections for elements with atomic numbers from 1 to 96 and for electron energies between 50 eV and 9999 eV in steps of 1 eV. These cross sections were calculated using the Thomas-Fermi-Dirac potential to describe the interaction between an electron and an atom, and using both relativistic and non-relativistic models. This version was designed for analyses of the transport of signal electrons in AES and XPS although it could, of course, be used for other applications.

Version 2.0 of the database was released in 2000. In this version, the upper electron-energy limit was extended to 20 keV, and phase shifts and transport cross sections were also provided. The elastic-scattering cross sections, phase shifts, and transport cross sections, however, were obtained only with a relativistic model because this was believed to be more reliable than the non-relativistic model.

Version 3.0 of the database was released in 2002 and contained two major changes. First, the differential elastic-scattering cross sections, total elastic-scattering cross sections, phase shifts, and transport cross sections were calculated from a relativistic Dirac partial-wave analysis in which the potentials were obtained from Dirac-Hartree-Fock electron densities computed self-consistently for free atoms. This potential is believed to be more reliable than the Thomas-Fermi-Dirac potential used previously [1]. Differences in elastic-scattering cross sections and transport cross sections resulting from this change of potential were described in a review article [1].

In addition, it is possible in Version 3.0 to create and/or print files illustrating variation of differential elastic-scattering cross sections versus scattering angle for one or more elements or for one or more energies. Some of the database screens were redesigned as a result of the increase in the upper electron-energy limit to 300 keV.

Version 3.1 of the database, issued in August, 2003, contains two corrections to Version 3.0. First, a numerical mistake was found in the calculation of differential cross sections for a small number of elements and energies (e.g., F at 300 eV). Second, the routine used for interpolations between differential cross sections at certain scattering angles was found to be inadequate in the vicinity of deep minima in the differential cross sections (e.g., Cu at 319 eV). The libraries of cross-section data and the software have been revised to correct these problems.

Version 3.2 of the Electron Elastic-Scattering Cross-Section Database had the following capabilities:

• Graphical display of differential elastic-scattering cross sections in different coordinate systems
• Graphical display of the dependence of transport cross sections on electron energy
• Display of numerical values of differential elastic-scattering cross sections, total elastic-scattering cross sections, and transport cross sections
• Creation of files containing differential elastic-scattering cross sections for specified elements, energies and coordinates
• Creation of files containing plots of differential elastic-scattering cross sections versus scattering angle for one or more elements or for one or more electron energies
• Creation of files containing phase shifts for specified elements and for energies up to 20 000 eV
• Creation of files containing transport cross sections for specified elements and energies
• Creation of random number generators providing the polar scattering angles to be used in Monte Carlo simulations of electron transport in solids; and
• Runs of the random number generators

Version 4.0 of the database was released in August 2016. The database has been redesigned to operate in a user’s browser rather than as an installed database on a personal computer with the Windows operating system. All screens have been redesigned. The database now provides differential elastic-scattering cross section and transport cross sections, as in previous versions. Graphical displays of these cross sections are available as before. Three types of data files can be downloaded:

• Comma separated variable (CSV) files that can be opened by spreadsheet software
• Text files that can be easily read by user programs.

Phase Shifts are not provided in Version 4.0 of the database.

Version 5.0 of the database was released in December 2023. Most screens were redesigned. An option was added to provide samplers of polar elastic-scattering angles that can be used in Monte Carlo simulations of electron transport in solids (as was possible in Version 3.2 and earlier versions). However, a more accurate numerical method has been implemented in Version 5.0, as described in Appendix A. The new sampler is designed to generate scattering angles for electron energies between 50 eV and 20 keV.

The differential elastic-scattering cross sections (DCSs) were calculated using the relativistic Dirac partial-wave method, as described by Walker [3]. The scattering potential was obtained from the self-consistent Dirac-Hartree-Fock electron density for free atoms [4] with the local exchange potential of Furness and McCarthy [5]. The numerical calculations were performed with the algorithm described by Salvat and Mayol [6]. Transport cross sections were calculated from the DCSs as described by Jablonski et al. [1].

Cross sections are expressed in units of the square of the Bohr radius, a0, which is 0.52917721 x 10^-10 m.

References

• [1] A. Jablonski, F. Salvat, and C. J. Powell, J. Phys. Chem. Ref. Data 33, 409 (2004).
• [2] F. Salvat, A. Jablonski, and C. J. Powell, Comput. Phys. Commun. 165, 1571 (2005).
• [3] D. W. Walker, Advances in Physics 20, 257 (1971).
• [4] J. P. Desclaux, Computer Physics Communications 9, 31 (1975); erratum ibid 13, 71 (1977).
• [5] J. B. Furness and I. E. McCarthy, J. Phys. B: At. Mol. Phys. 6, 2280 (1973).
• [6] F. Salvat and R. Mayol, Computer Physics Communications 74, 358 (1993).
• [7] A. Jablonski, F. Salvat, and C. J. Powell, NIST Electron Elastic-Scattering Database Users' Guide, September, 2016;