kim-prb-53-16310

Data for reference kim-prb-53-16310

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

Kwiseon Kim, Walter R. L. Lambrecht, Benjamin Segall

Physical Review B 53(24), 16310 (1996).

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 Gamma,their mode Gruneisen parameters, the full set of cubic elastic constants, and deformation potentials. The elastic constants for the wurtzite crystals are first obtained from those calculated forzinc blende by Martin's transformation method. The components related to strains along the c axis (C₁₃ and C₃₃) are found to be less accurate than the others. An elaboration of Martin's approach utilizing first-principles calculation for distortions whichmaintains hexagonal symmetry but allows for a nonideal c/a ratio is implemented. As a byproduct of the relaxation calculations of the wurtzite internalparameter u we also obtain the A₁ and an estimate of the E₁ TO-phonon frequenciesin 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 propertiesmentioned 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 theseresults and experimental LO-TO splittings, we determine the bond-stretching and bond-bending parameters alpha and beta of Keating's semiempiricalvalence-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 areused 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 thevalence-band maximum of the wurtzite structure and relate them to the corresponding [111] strain deformation and optical mode deformation potentials in zinc blende. © 1996 The American Physical Society.[S0163-1829(96)00324-4]

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