Properties of hexagonal polytypes of group-IV elements from first-principles calculations

Abstract

Results of ab initio calculations are reported for hexagonal polytypes of C, Si, and Ge in equilibrium and under hydrostatic pressure. For each polytype $2H,$ $3C,$ $4H,$ and $6H,$ the atomic geometry, the energetics, and the electronic structure are studied. The resulting lattice parameters are in good agreement with measured values. While $3C$ is the most stable polytype for each element, pressure-induced phase transitions to hexagonal modifications are found to be possible. Silicon is the most favorable candidate in this respect. The results are interpreted within the axial next-nearest-neighbor Ising model. It simultaneously allows the derivation of formation energies for stacking faults in agreement with other calculations and measurements. We predict significant differences in the band structures between the hexagonal polytypes and the diamond structure. This holds especially for the energy gaps and the location of the conduction-band minima. Trends with the hexagonality of the polytype and the element are derived.