Quantifying nanoscale order in amorphous materials: simulating fluctuation electronmicroscopy of amorphous silicon

Abstract

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