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

This paper reports the presence of extended-range ordering in the atomic pair-correlation function of amorphous silicon $(a\text{\ensuremath{-}}\mathrm{Si})$ using ultralarge 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 \AA{}, which is 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 effect of the oscillations on the first sharp diffraction peak (FSDP) in the structure factor is addressed by obtaining a semianalytical expression for the static structure factor of $a\text{\ensuremath{-}}\mathrm{Si}$, 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 is primarily determined by the medium-range atomic correlations of up to a length of 20 \AA{} in amorphous silicon.