Keep it simple, silicon

Left: structural model of amorphous silicon. Right: The electronic energy levels of amorphous silicon

Amorphous materials, that is, materials which don’t have long-range order, are critical for both windows (silica glass) and Windows (amorphous silicon for TFT screens). Despite their technological importance, we still do not fully understand how the structures of amorphous materials relate to their properties. The relative paucity of experimental information available from X-ray and neutron scattering experiments on amorphous materials (in comparison to crystals) makes determination of their structures challenging. Even once we know how the atoms are connected, it is not trivial to explain their resultant properties.

In this paper we take the simplest ’tricky’ amorphous material, amorphous silicon, as an exemplar and show the idea of structural simplicity (the degree to which the atoms exist similar arrangements to each other) can help explain both its structure and its electronic properties. Amorphous silicon, like its crystalline counterpart, is a semiconductor: there is a gap between energy levels filled by electrons and those left unoccupied. The origin of this band gap is therefore one of the critical questions in amorphous silicon: in this disordered and random material, why are there specific energies that are avoided?

We began by trying to make the simplest possible model which is still consistent with the diffraction data (or equivalently, has same distribution of inter-atomic distances as the real material). We were able to show that just by forcing all the silicons to have similar environments we could make much more realistic models of amorphous silicon. We were confident that these models were more representative not only because the geometry around the silicon atoms was consistent with what was already known, but because the models were lower in energy. In fact, the energy of the models was dramatically reduced just by making it simpler. Not only that, but this model also has a (pseudo) band gap between filled and empty states. This hints at a close relationship between simplicity and existence of energy gaps. We also show that if you take complex, high energy models and relax them to reduce their energy, they become simpler. This suggests that, despite all the apparent complexity of their structures, simplicity might well be a guiding principle for amorphous materials.