Quantifying nanoscale order in amorphous materials: Simulating fluctuation electron microscopy of amorphous silicon

Fluctuation electron microscopy (FEM) is explicitly sensitive to 3- and 4-body atomic correlation functions in amorphous materials; this is sufficient to establish the existence of structural order on the nanoscale, even when the radial distribution function extracted from diffraction data appears entirely amorphous. However, it remains a formidable challenge to invert the FEM data into a quantitative model of the structure. Here, we quantify the FEM method for a-Si by forward simulating the FEM data from a family of high quality atomistic models. Using a modified WWW method, we construct computational models that contain 10-40 vol% of topologically crystalline grains, 1-3 nm in diameter, in an amorphous matrix and calculate the FEM signal, which consists of the statistical variance V (k) of the dark-field image as a function of scattering vector k. We show that V (k) is a complex function of the size and volume fraction of the ordered regions present in the amorphous matrix. However, the ratio of the variance peaks as a function of k affords the size of the ordered regions; and the magnitude of the variance affords a semi-quantitative measure of the volume fraction. We have also compared models that contain various amounts of strain in the ordered regions. This analysis shows that the amount of strain in realistic models is sufficient to mute variance peaks at high k. We conclude with a comparison between the model results and experimental data.