Nearly-Hyperuniform Network Models of Amorphous Silicon

Abstract

A hyperuniform solid has a structure factor S(k) that approaches zero as the wavenumber k goes to 0. We define a NHN as an amorphous network whose structure factor S(0) is smaller than its 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, i.e. smaller S(0) that is significantly below the frozen liquid value and that correlates with the width of the electronic band gap and with other measurable features in S(k) at intermediate and large k.

We compare the structural properties predicted by these NHN models to the results of highly sensitive transmission X-ray scattering measurements performed at the Advanced Photon Source at Argonne National Laboratory, on high-purity a-Si samples with density close to that of crystalline silicon (c-Si). The best theoretical NHN model produced so far possesses S(0) = 0.010 +/- 0.002, which is consistent with the experimentally observed value S(0) = 0.0075 +/- 0.0005. Our theoretical studies predict an increase in the degree of hyperuniformity with annealing, which is also observed in these experiments. Both theoretical models and experimental measurements show that increasing the degree of hyperuniformity is correlated with increasing the height and narrowing the width of the first diffraction peak, and with extending the range of oscillations in the pair correlation function. This work suggests that there is a greater diversity of theoretical network structures and experimental realizations of amorphous silicon than was previously recognized.

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