DOI: 10.5281/zenodo.7857107
title: Simulation of convergent-beam low-energy electron diffraction on Si(001) reconstructions

description: Research results based upon this code and data are published at http://doi.org/10.1016/j.apsusc.2019.05.274. The image simulation of convergent beam low energy electron diffraction (CBLEED) patterns are used to determine the sensitivity of CBLEED to atomic-scale displacements of several reconstructed variants of the Si(001) surface. The CAVATN code is used to determine the dynamical LEED intensities as a function of the incident electron energy (E<sub>i</sub>), angle (theta, phi) and at each of the miller indices (h,k), up to the third order. The CBLEED code then maps these intensities into reciprocal space, allowing the visualisation of CBLEED patterns to be made as a function of incident electron energy (E<sub>i</sub>). The data files for the CBLEED simulations are stored in a .txt format, with an accompanying .png image displaying the result of the simulation. This data is then analysed to determine the sensitivity of CBLEED patterns to small atomic displacements. <strong>CAVATN code:</strong> Relevant documentation, electron beam files and the crystal structure files are all included. The CAVATN dynamical LEED package, developed from the CAVLEED code, is also included, where the code employs the muffin-tin potential approximation and involves a set of phase shifts for each atom type (which are treated as spherically symmetric scatterers in a crystal) that can be evaluated using phase shift calculation packages or tables. In the simulations performed here, complex phase shifts were used to simulate temperature dependent scattering effects at T = 293<em>K</em>. The inner potential is treated as energy independent and is split into real U<sub>or</sub> = 5 <em>eV </em>and imaginary U<sub>oi</sub> = 10 <em>eV </em>parts to respectively treat refraction (via the vacuum and muffin-tin zero difference) and absorption (due to in- elastic processes). Multiple scattering between atoms within a layer is calculated using the chain method and the multiple scattering between layers is included by the renormalized forward scattering perturbation method to evaluate the wave amplitudes of diffracted beams at the surface, and hence the intensities of the LEED pattern. <strong>CBLEED code:</strong> The dynamical CBLEED package is included as ‘cbleed_analysis_script.py’, where the CBLEED patterns are simulated by uniformly partitioning the convergent cone into square areas as shown in Figure 1. An incident electron beam is located at the centre of these squares and defined directionally by and . Each of the incident electron beams of the sampled convergent cone was then used as input to the dynamical LEED program CAVATN, so that the corresponding multiply scattered intensities could be determined and mapped into reciprocal space. All the output data files from the CBLEED code is available for the following structures in the ‘output’ folder; Si(001)-1x1-ideal, Si(001)-2x1-symmetric, Si(001)-2x1-buckled, Si(001)-2x1-dH (for dimer height displacements) and Si(001)-2x1-dL (for dimer length displacements). The data for the sensitivity to atomic-scale displacements is included in the ‘sensitivity_output’ folder, which determines both the partial and whole pattern sensitivities.