Nearly hyperuniform network models of amorphous silicon

We introduce the concept of nearly hyperuniform network (NHN) structures as alternatives to the conventional continuous random network (CRN) models for amorphous tetrahedrally coordinated solids, such as amorphous silicon (a-Si). A hyperuniform solid has a structure factor S(k) that approaches zero as the wavenumber k→0. We define a NHN as an amorphous network whose structure factor S(k→0) is smaller than the liquid value at the melting temperature. Using a novel implementation of the Stillinger-Weber potential for the interatomic interactions, we show that the energy landscape for a spectrum of NHNs includes a sequence of local minima with an increasing degree of hyperuniformity [smaller S(k→0)] that is significantly below the frozen-liquid value and that correlates with other measurable features in S(k) at intermediate and large k and with the width of the electronic band gap.