Elastic constants and related properties of tetrahedrally bonded BN, AlN, GaN, and InN

Abstract

The results of first-principles full-potential linear muffin-tin orbital calculations of the elastic constants and related structural and electronic properties of BN, AlN, GaN, and InN in both the zinc-blende and wurtzite structures are presented. The results include all of the equilibrium lattice constants, the bulk moduli, the TO-phonon frequencies at \ensuremath{\Gamma}, their mode Gr\"uneisen parameters, the full set of cubic elastic constants, and deformation potentials. The elastic constants for the wurtzite crystals are first obtained from those calculated for zinc blende by Martin's transformation method. The components related to strains along the c axis (${\mathit{C}}_{13}$ and ${\mathit{C}}_{33}$) are found to be less accurate than the others. An elaboration of Martin's approach utilizing first-principles calculation for distortions which maintains hexagonal symmetry but allows for a nonideal c/a ratio is implemented. As a byproduct of the relaxation calculations of the wurtzite internal parameter u we also obtain the ${\mathit{A}}_{1}$ and an estimate of the ${\mathit{E}}_{1}$ TO-phonon frequencies in the hexagonal materials. Good agreement is obtained with recent experimental results for the elastic constants of wurtzite AlN and GaN and zinc-blende BN as well as for the other properties mentioned above for all materials. Our results provide predictions for the remaining crystal structure materials combinations for which no direct experimental data are presently available. From these results and experimental LO-TO splittings, we determine the bond-stretching and bond-bending parameters \ensuremath{\alpha} and \ensuremath{\beta} of Keating's semiempirical valence-force-field model. We use this model to rationalize some of the observed trends in the behavior with the cation. The shift and splittings of the energy bands due to strains are used to obtain a complete set of deformation potentials for the zinc-blende crystals at symmetry points for several of the important eigenvalues. We also define deformation potentials for the valence-band maximum of the wurtzite structure and relate them to the corresponding [111] strain deformation and optical mode deformation potentials in zinc blende. \textcopyright{} 1996 The American Physical Society.