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

Abstract

Fluctuation electron microscopy (FEM) is explicitly sensitive to 3-and 4body 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.

Size analysis of nanoscale order in amorphous materials by variable-resolution fluctuation electron microscopy

“…All detailed FEM studies to date have employed the variable coherence mode [2] at a fixed resolution R$ 1.5 nm. Measurements on films of amorphous silicon (a-Si), hydrogenated amorphous silicon (a-Si:H), amorphous germanium (a-Ge), and amorphous germanium antimony telluride (a-Ge 2 Sb 2 Te 5 ), deposited by various methods at different laboratories, indicate the presence of considerable MRO [3][4][5]. There is no mathematical means to invert FEM data directly into a description of the material structure, although advanced algorithms are under development [3].…”

High (1 1 1) orientation poly-Ge film fabricated by Al induced crystallization without the introduction of AlO x interlayer

“…Our results showed that the fabrication of high (111) oriented Ge from a-Ge deposited by magnetron sputtering was independent of the air exposure process, simplifying the steps. Since a-Ge prepared by the magnetron sputtering method had a low degree of order and a high content of defects [14][15][16][17], and defects in a-Ge can benefit the diffusion of Al in a-Ge [18], so this type of a-Ge is a favorable starting point for the fabrication of high (111) orientation poly-Ge by AIC. Ge grains nucleate primarily at the Al/a-Ge interface, preferentially where Al grain boundaries meet the interface due to the greater ease of reducing the free energy at these sites [19].…”

Fluctuation Transmission Electron Microscopy: Detecting Nanoscale Order in Disordered Structures

“…[19] Shown in Figure 5a is a CRN model for amorphous silicon for which the tetrahedral short-range order is maintained, but the dihedral angles between pairs of tetrahedra are essentially random; this model gives a small, but detectable, variance background. [20] However, it has been shown that a CRN model is not sufficient to explain the magnitude and variety of FTEM variance from experiments (e.g. Figures 2-4).…”

“…[7,8] Simulated variance consistent with experiment is obtained by using models (Figure 5 b) that include small, topologically crystalline regions; owing to the stiff covalent bonding, these regions are strained and the structure remains apparently amorphous in diffraction analyses. [7,8,20,21] Higher medium-range order (i.e. more or larger ordered regions) increases the peak heights in V(k).…”