Extended-range order in tetrahedral amorphous semiconductors: The case of amorphous silicon

TL;DR

This study reveals extended-range atomic order in amorphous silicon, showing radial oscillations up to 40 angstroms that do not significantly affect the primary diffraction features, thus enhancing understanding of its structural properties.

Contribution

It provides the first detailed analysis of extended-range order in amorphous silicon using large atomistic models and information-theoretic methods, linking atomic correlations to diffraction features.

Findings

Extended-range radial oscillations exist up to 40 angstroms.

These oscillations originate from propagation of order from initial atomic shells.

The oscillations do not significantly influence the main diffraction peak.

Abstract

This paper reports the presence of extended-range ordering in the atomic pair-correlation function of amorphous silicon ($a$-Si) using ultra-large atomistic models obtained from Monte Carlo and molecular-dynamics simulations. The extended-range order manifests itself in the form of radial oscillations, on the length scale of 20-40 angstrom, which are examined by directly analyzing the radial distribution of atoms in distant coordination shells and comparing the same with those from a class of partially-ordered networks of Si atoms and disordered configurations of crystalline silicon from an information-theoretic point of view. The study suggests that the extended-range radial oscillations principally originate from the propagation of radial ordering from the first few atomic shells to a distance of up to 40 angstrom. The effect of these oscillations on the first sharp diffraction peak (FSDP) in the structure factor is addressed by obtaining a semi-analytical expression for the static structure factor of $a$-Si, and calculating an estimate of the error of the intensity of the FSDP associated with the truncation of radial information from distant shells. The results indicate that the extended-range oscillations do not have any noticeable effects on the position and intensity of the FSDP, which are primarily determined by the medium-range atomic correlations of up to a length of 20 angstrom in amorphous silicon.