TEM-simulation of amorphous carbon films: influence of supercell packaging

Recent developments in thin film technology allow to prepare deliberately amorphous carbon films with structures widely varying between graphite-like (sp2) and diamond-like (sp3) atomic bonds. This leads to amorphous structures with correspondingly varying densities. By periodically changing deposition conditions, nanometer multilayers may be prepared consisting of carbon layers of different density. Simulation of the electron microscopic imaging allows to differentiate between such real structural details (on the nanometer scale) and artefacts induced by the imaging procedure. But it must be assured that the modeled structure reflects the real one with sufficient accuracy. Thorough comparison of different simulation strategies shows that for the adequate simulation of TEM imaging of amorphous materials, the thickness of the layer with independently distributed atoms has to exceed a certain limit. Then, the statistical scattering of the randomly distributed atoms will be averaged. Otherwise, if the model of the transmission electron microscopy sample is constructed as iteration of thin identical supercells, the superposition of scattering waves with constant phase differences results in enhanced local fluctuations burying the multilayer structure. For thicker packages of supercells with independent random distributions, the effect of statistical atomic arrangements is more and more leveled off. Hence, nanometer structures based on regions with different density will be visible more distinctively in the random background. For carbon, this critical thickness amounts to about 4 nm. This is of special importance for the visualization of nanoscaled heterogeneities like multilayers or nanotube-like inclusions in amorphous matrices.