One of the most challenging problems in condensed matter physics today is the description of the properties of non-crystalline materials. The immediate difficulty arises from the need to describe the `structure' of the amorphous phase. The amorphous forms of silicon and germanium have other important topological properties in addition to the absence of long range order. One of the more important of these is that amorphous silicon and germanium are tetrahedrally coordinated having bondlengths close to those of their crystalline counterparts. Similarly, this is true for the high density bonded form of amorphous carbon.
Fortunately, it is these short range properties which, to a large extent, govern the electronic and vibrational properties of the amorphous phases of these elements. This is shown, for example, by the presence of an energy gap in the electronic density of states of amorphous semiconductors and in the similarity of the vibrational spectra between amorphous and crystalline materials. It might, at first, be expected that any successful model of an amorphous semiconductor would necessarily involve a very large number of atoms in order to sensibly describe a non-repeating structure, but the above considerations regarding the importance of short ranged correlations in the structure suggest a more economical strategy. One would instead consider a sequence of more complex crystalline structures having increased short range disorder but still retain relatively small unit cells. This would allow reliable theoretical methods to be applied to such complex crystalline materials.
Such structures metastably exist in silicon and germanium, although as yet, none have been found in carbon. The trends in the electronic and vibrational properties of these complex semiconductors give unique insight into the nature of the amorphous phase. It is in this context that the dense polymorphs of semiconductors are of the greatest value.
In view of the considerable difficulties associated with performing a full theoretical study of non-crystalline solids, these complex phases and also the bonding topologies in defected crystals are useful in that an understanding of their properties provides insight into the essential physics of amorphous tetrahedral semiconductors.