Analysis of medium-range order based on simulated segmented ring detector STEM-images: amorphous Si

Highlights: • A dynamic multislice fluctuation electron microscopy (FEM) simulation approach using multiple thin annular detectors and analysis is introduced. • An amorphized amorphous silicon sample is compared to the simulation of a simulated a-Si molecular dynamic box. • The simulation of different molecular dynamic boxes using different potentials and cooling rates is compared and investigated in terms of its medium range order and flexibility volume. • The detectability of different relaxation states is shown by simulation. • The connection between the pair persistence approach to topological or medium range order is investigated using variable resolution FEM. -- Abstract: Properties of amorphous materials are connected to the local structure at the nanoscale, which is typically described in terms of short- and medium-range order (SRO, MRO). Variable resolution fluctuation electron microscopy (VR-FEM) is a sensitive method to characterize the underlying characteristic length scale of MRO of amorphous samples (Voyles, Gibson and Treacy, J. Electron Microsc. 49 (2000) 259). VR-FEM data was acquired using scanning transmission electron microscopy (STEM), collecting a large number of nano-beam diffraction patterns (NBDPs) with various probe sizes. Here we present an advanced method to accelerate the calculation of simulated FEM normalized variance profiles using a newly developed simulation and analysis approach with segmented ring detectors using the program STEMcl (Radek et al., Ultramicroscopy 188 (2018) 24). VR-FEM simulations are based on structures obtained from molecular dynamics (MD) simulations. A comparison between simulated and experimental VR-FEM profiles with respect to peak position, ratio and shape (and intensity) show good agreement. Moreover, a crystalline cluster of 1 nm in size was embedded into the MD box to test the validity of the paracrystalline approximation with the pair-persistence analysis suggested by Gibson et al. (Gibson, Treacy and Voyles, Ultramicroscopy 83 (2000) 169). The corresponding VR-FEM simulation and calculation of MROs yield close results to the size of the initially embedded crystalline cluster, which supports both the paracrystalline approach and the validity of the segmented detector simulation. Additionally, we conclude that continuous random network (CRN) amorphous silicon models contain a higher degree of MRO than experimentally expected.