Elastic phase transition in germanium and silicon

The Landau theory of phase transitions is used to study the cubic-to-tetragonal phase transformation which occurs in group-IV semiconductors at high pressure. Following various authors we assume that a spontaneous tetragonal strain, η∼(2${\mathit{e}}_3$-${\mathit{e}}_1$-${\mathit{e}}_2$), superimposed on the hydrostatic pressure, is the order parameter of ${\mathit{E}}_{\mathit{g}}$(${\mathrm{\Gamma }}_{12}$) symmetry which drives the ${\mathit{O}}_{\mathit{h}}^7$→${\mathit{D}}_{4\mathit{h}}^{19}$ structural phase transition. The theoretical approach is equivalent to a higher-order nonlinear elastic theory. The static aspect of the phase transformation and the anomalies of the elastic properties are studied. Failures of the criteria of Vaidya and Demarest et al., which predict the occurrence of pressure-induced phase transitions involving shear strains, are shown. The Landau criterion for diamond-structure semiconductors involves the ratio (${\mathit{C}}_{11}$-${\mathit{C}}_{12}$)/(${\mathit{C}}_{111}$-3${\mathit{C}}_{112}$+2${\mathit{C}}_{123}$) of the second- to third-order elastic constants associated with the tetragonal strain, or equivalently in terms of valence force-field model, the ratio β/δ of the second- to third-order bond-bending force constants, i.e., the harmonic and the anharmonic interatomic interactions which tend to stabilize the equilibrium angle between covalent bonds. The contribution of the electronic bands to the elastic constants under pressure is also reviewed.