Abstract
Solidification of silicon and germanium involves a reconstruction of covalent tetrahedral bonds from a metallic liquid having a higher density and coordination than the solid. We first contrast the metallic liquid structure of germanium with that of its semiconducting amorphous state, in order to emphasize the changes in the atomic structure factor that arise from reconstruction of the interatomic bonds. We then use the density wave theory of freezing to discuss the liquid-solid transition within a pseudo-classical model, which describes the liquid structure by means of partial structure factors giving the pair correlations between atoms and bond particles. The phase transition is viewed as a freezing of the bonds, driven by tetrahedrally constrained attractions between ionic cores and valence electrons and accompanied by an opening of the structure to allow long-range connectivity of tetrahedral atomic units. Quantitative calculations on the bond-particle model illustrate the relationship between the liquid structure and the microscopic Fourier components of the single-particle densities of atoms and bonds. In further support of this picture, we also present calculations for freezing of a liquid having the density and the atomic structure of compacted amorphous germanium.