First-principles calculations of the structural properties, stability, and band structure of complex tetrahedral phases of germanium: ST12 and BC8

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Abstract
We report the results of a first-principles study of the structural properties, stability, and band structure of Ge in two complex tetrahedral phases: the ST12 phase (simple tetragonal with 12 atoms per unit cell) and the BC8 phase (body-centered cubic with 8 atoms per cell). We focus mainly on the ST12 phase, which is well established as being formed in Ge after release of pressure from the β-tin phase. Local-density-functional calculations of total energies, forces, and stresses were carried out using the plane-wave-pseudopotential method. At each fixed volume considered, the structures were fully relaxed with respect to their structural degrees of freedom (five for ST12, one for BC8). A comparison with the β-tin and diamond phases allows us to study the phase stability and pressure-induced phase transformations of these structures. For the ST12 and BC8 phases we find zero pressure volumes in good agreement with the experimental values. The ST12 phase turns out to be metastable, which is consistent with its formation on release of pressure from the β-tin phase. The BC8 phase is found to be less stable than the ST12 phase over the entire pressure range investigated (0–200 kbar). ST12 Ge is found to have a direct band gap, whereas BC8 is found to be semimetallic in our calculations.