Two ab initio calculations on amorphous silicon and one on amorphous carbon close the the experimentally measured density have been presented in this chapter. The initial starting configurations were identical in all cases. Since it is believed that the binding is more reliably described in these calculations than by empirical rules, the atoms were distributed at random within the supercell subject only to the constraint the atomic pseudopotential cores should not overlap. Considering that the initial atomic configurations were the same in all cases, the difference in relaxed structures between silicon and carbon are found to be remarkably different.
In both silicon simulations, the bonding is found to be predominantly in nature although the spread in bond angle in rather large (cf. the BC8 and ST12 structures) but centred on the perfect tetrahedral angle. The comparison between neighbouring bond lengths is also interesting. It is found that the first four neighbour distances are all in the region of 2.4Å which seems to be independent of the unit cell size in systems-I and II, that is, independent pressure and manufacturing conditions. This is not the case for the fifth neighbour distance. As the density of the sample is increased, the fifth neighbouring atom becomes closer. Both BC8 and ST12 silicon exhibit this behaviour under pressure. This trend is seen to increase with increasing disorder in the system from BC8 through ST12 to amorphous structures. In the extreme case, the fifth neighbour becomes becomes bonded to the central atom creating locally a fully five coordinated structure.
The electronic structure of amorphous silicon is dominated by the short ranged interactions of the bonds. Unlike in carbon, undercoordinated silicon atoms do not seem to form -bonded structure, but instead favour the retention of the -bonded system with dangling bonds. These states are found to be close to the Fermi level but still localised on specific sites.
Carbon, on the other hand, does not form over coordinated sites. Similar to that of both silicon simulations, the carbon structure is dominated by diamond-like tetrahedral bonding, but no 5-fold `defects' are found. It appears that amorphous carbon forms only 3 and 4 fold coordinations. Carbon 3-fold graphitic-like sites form a very stable configuration and are found throughout the sample. Although they appear in low concentrations, it is the electrons which govern the optical properties of amorphous carbon. It therefore seems that the complex tetrahedral structures BC8 and ST12 will not form a good model for the electronic properties of amorphous carbon due to the importance of low concentrations of -bonding that appears in the system.
Another interesting structure that was found in the amorphous carbon simulation which did not appear in silicon was that of the three fold rings. Such a structure has not been included in any model of amorphous carbon so far, and is in fact conventionally (and incorrectly) excluded from the model. Examination of the bonding orbitals of the 3-fold ring indicate that a low energy 3-centre orbital is evident in the configuration. Associated with this though, is a higher energy state localised around the three atoms in the structure. This unusual feature cannot be found simply from the radial distribution function because the atomic separations are very similar to other 2-centre covalent bonds. Instead, three-body information is required such as the bond angle distribution function.
In conclusion, the amorphous structures of silicon and carbon contain a rich mixture of possible bonding topologies. It has been possible to model such a wide range of electronic structures because of the use of the plane wave basis set in the ab initio calculations. It would not be possible to find some of the configurations obtained here, such as five fold coordination and 3-centre orbitals, by use of an empirical potential unless it is specifically fitted to such structures. It is also very unlikely that a single potential could describe this large range of bonds. It is found that the properties of amorphous silicon are dominated by the short ranged nature of the material. This indicates that the complex tetrahedrally bonded systems discussed in earlier chapters do form good crystalline models of amorphous silicon. Conversely, the structural and optical properties of amorphous carbon are found to be mainly governed by the intermediate ranged interactions of the states in the structure. Thus, the BC8 and ST12 structures do not form such a good model for amorphous carbon.