Urbach tails of amorphous silicon

In earlier work, we showed that exponential (Urbach) band-edge states were localized on connected subnetworks of short bonds for the valence tail and long bonds for the conduction tail for high-quality continuous random network models of amorphous silicon. Here, we study size effects by computing the electronic density of states for a 105-atom model of α-Si proposed by G. T. Barkema and N. Mousseau [Phys Rev. B 62, 4985 (2000)] and show that the model indeed possesses exponential tails, consistent with earlier calculations on a 4096-atom system. Next, we study the structure of the network near the shortest bonds. These bonds consistently create a slightly densified region, and we discuss the strain field associated with these defects. The dynamics of the short-bond clusters is briefly examined next. We show that there are significant fluctuations in the atoms with instantaneous short bonds, even at 300 K, and we compare the electronic density of states and valence edges between models with filaments and without filaments. We close with speculations on how to determine if the connected subnetwork hypothesis is unique in its ability to produce exponential tails.