| Fluctuation electron microscopy (FEM) is a statistical technique that measures topological order on the 1 -- 3 nm length scale in amorphous materials. Extracting quantitative information about the nanoscale order from FEM data has been an on-going challenge due to issues both in experimental procedures, as well as in development of data analysis and modeling methods. The use of the STEM mode in FEM enables detection and correction of some experimental artifacts, and advanced methods such as variable resolution FEM (VR-FEM) afford some quantitative information on the length scale of the order.;Here, we investigate another significant source of experimental non-ideality in STEM-FEM, namely, the electron probe coherence. Although commonly over-looked, variations in coherence have a significant effect on the magnitude of the FEM data, which consist of a statistical variance. By comparing STEM-FEM results performed independently at several facilities, we demonstrate that a change in probe coherence can alter the variance magnitude by as much as 300 %, even when keeping the same nominal electron probe size. Careful fitting of electron probe image to theory provides a universal method to quantify coherence, and confirms that a higher probe coherence results in significantly higher FEM variance magnitude. Using this knowledge, we are able to perform reliable VR-FEM and extract a quantitative measure of the size of the nanoscale order in amorphous Ge2Sb2Te5 thin films.;We also establish a higher-order statistical analysis method, the scattering covariance, computed at two non-degenerate Bragg reflections. Covariance 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 Ge2Sb 2Te5. The samples contain a wide variety of ordered states. Comparison of experimental data with the covariance simulation clearly reveals different regimes of nanoscale topological order.;STEM-FEM also allows us to distinguish subtle differences in nanoscale order in various amorphous materials. We report evidence that as-deposited amorphous Ge2Sb2Te5 thin films contain nanoscale clusters that exhibit a preferred orientation, attributed to the earliest stages of heterogeneous nucleation. FEM reveals structural order in the samples, but (220)-related contributions are suppressed. When homogeneous nucleation is promoted via electron bombardment, the sample remains diffraction amorphous but the (220) contribution appears. We simulated data for randomly oriented nanoscale order using ab initio molecular-dynamics models of Ge2Sb2Te5. The simulated (220) contribution always has larger magnitude than higher-order signals; thus, the lack of the experimental signal indicates a significant preferred orientation. Separately, we use STEM-FEM to differentiate the nanoscale order in ion-implanted vs. sputter-deposited amorphous silicon. The difference in order, which is attributed to nano-void formation during the sputtering process, manifests itself in the FEM data, as well as in the mechanical properties and short-range order (pair-pair correlation) of the materials. |
