BC8 Si has a small Fermi surface and thus electronically can be regarded as a semimetal as suggested by its band structure. Its fourfold coordination and brittleness suggest that it is predominantly held together by directional covalent bonds. To resolve this apparent contradiction, the valence charge density has been examined within BC8 and ST12. Figure 4.29 shows an electron density isosurface in ST12 silicon. It bears an uncanny resemblance to a ball and stick model of the structure, showing clearly that the electron density is concentrated into four `bonds' emanating from each atom - the covalent picture.
Figure 4.29: Three dimensional representation of a valence charge density
isosurface in ST12 silicon.
This covalency is illustrated even more clearly in Figures
4.7, 4.8 and 4.15 which shows
the valence charge density in the 110 plane of BC8. Along the 111
direction are atoms separated by 
and
alternately. Although these distances
are similar, it can very clearly be seen that the slightly closer pairs
are bonded, while the more distant pairs are not. This effect cannot be
seen in diamond because there are no `second neighbours' as close. An
interesting aspect of this structure is that if the topology of the
crystal is defined by bonds, it requires six steps to get from an atom
to its `second neighbour', and there is only one such second neighbour
per atom. Under pressure the increase in x has the effect of pushing
these second neighbours together, but there is still no increase in the
charge density between the atoms.
It is therefore deduced that while the electronic properties of BC8 are dominated by its small Fermi surface, and hence it is regarded as a semimetal, the cohesion is dominated by covalent bonding of each atom to four neighbours. This observation has been used in constructing a simple empirical model potential for silicon, which will then apply to structural features of the semimetallic BC8 phase. Calculations using the empirical model are presented in Chapter 4.
ST12 is a semiconducting phase, and again the charge density plots suggest that a covalent picture for the bonding is appropriate.