Remember the good old days when an amorphous material was just amorphous and nothing else? Sorry, no long range order! Just last month we have been able to view for the first time amorphous silica on graphene via transmission electron microscopy (DOI). More recently though, Treacy & Borisenko have analysed amorphous silicon and find inhomogeneous paracrystalline structures containing local cubic ordering at the 10 to 20 angstrom length scale (DOI).
In the classical model amorphous silicon forms a tetracoordinated continuous random network (CRN), consisting of a random network of 5,6 and 7-membered rings. It is metastable towards crystalline silicon that only has hexacycles. The coordination number for silicon is slightly less then than 4 for amorphous silicon compared to that of crystalline silicon and therefore also slightly less dense. A so-called reduced density function can be obtained from traditional electron diffraction and by modelling and usually the CRN model agrees with both methods.

Treacy & Borisenko manufactured a layer of amorphous silicon by Si ion implantation in a layer of crystalline Si and analysed it using a TEM technique called fluctuation electron microscopy which can measure local variations in density. Then they measured and modelled (Metropolis algorithm) reduced density functions of their own and found experiment and theory supported each other.
The continuous random network was first proposed in 1927. A paracrystalline model dates back to 1962. Figuring out what exactly amorphous silicon looks like may be relevant as ion implantation is an important tool in industrial semiconductor device fabrication.