Quantifying nanoscale order in amorphous materials via scattering covariance in fluctuation electron microscopy

Fluctuation Transmission Electron Microscopy (FTEM) has a unique ability to probe topological order on the 1-3 nm length scale in diffraction amorphous materials. However, extracting a quantitative description of the order has been challenging. We report that the FTEM covariance, computed at two non-degenerate Bragg reflections, is able to distinguish different regimes of size vs. volume fraction of order. The covariance analysis is general and does not require a material-specific atomistic model. We use a Monte-Carlo approach to compute different regimes of covariance, based on the probability of exciting multiple Bragg reflections when a STEM nanobeam interacts with a volume containing ordered regions in an amorphous matrix. We perform experimental analysis on several sputtered amorphous thin films including a-Si, nitrogen-alloyed GeTe and Ge₂Sb₂Te₅. The samples contain a wide variety of ordered states. Comparison of experimental data with the covariance simulation reveals different regimes of nanoscale topological order.