  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.
