Atomistic modelling of diamond-type Si_xGe_yC_zSn_{1- x - Y - z} crystals for realistic transmission electron microscopy image simulations

The realistic simulation of transmission electron microscopy (TEM) images requires an accurate definition of the positions of all atoms, which are linked to the mechanical properties of the material. This paper proposes an optimized atomistic modeling approach to model the lattice parameters and elastic properties of Si, Ge, diamond, alpha-tin, and related diamond alloys, with an approach compatible with systems bigger than 50 000 atoms. In order to compute precisely the elastically strained Si xGe yC zSn 1 - x - y - z diamond crystals, a dedicated parameterization of the Keating force field is provided. An original periodic boundary strategy is provided. Our tool is successfully used to interpret experimental TEM data with a reasonable accuracy and precision in a time scale about 10 000 times faster than ab initio methods. The method predicts the correct lattice parameters and elastic constants of elementary compounds and alloys with a deviation inferior to 8.1%. We show that subsequent Monte-Carlo simulations predict original self-ordering effects in C in good agreement with the theory. An original approach is used to quantify the short-range and long-range order in comparison with high-resolution cross-sectional TEM experiments: the projected radial distribution function (p-RDF) appears to be a universal and very sensitive analytical tool to quantify the matching between our atomistic model and the experimental HR(S)TEM results. For our reference Si-Ge multilayer with 20 millions of atoms, a maximum broadening of 100 pm is obtained for the third-nearest neighbor (3nn) simulated peak of the p-RDF compared to the experimental one. The same value is obtained from a template matching analysis of the maximum local displacements between the projected experimental atomic positions and the corresponding simulation.