Theoretical studies of structural, elastic, electronic and lattice dynamic properties of AlxYyB1−x−yN quaternary alloys

A theoretical study on the structural, elastic, electronic and lattice dynamic properties of Al_xY_yB_1−x−yN quaternary alloys in zinc-blend phase has been carried out with first-principles methods. Information on the lattice parameter, the lattice matching to available substrates and energy band-gaps is a prerequisite for many practical applications. The dependence of the lattice parameter a, bulk modulus B, elastic constants C₁₁, C₁₂ and C₄₄, band-gaps, optical phonon frequencies (ω_TO and ω_LO), the static and high-frequency dielectric coefficients ε (0) and ε (∞) and the dynamic effective charge Z^? were analyzed for y=0, 0.121, 0.241, 0.362 and 0.483. A significant deviation of the bulk modulus from linear concentration dependence was observed. A set of isotropic elastic parameters and related properties, namely bulk and shear moduli, Young's modulus, Poisson's ratio are numerically estimated in the frame work of the Voigt-Reuss-Hill approximation. The resistance to changes in bond length and lateral expansion in Al_xY_yB_1−x−yN increase with increasing y concentration. We observe that at y concentration about 0.035 and 0.063, Al_xY_yB_1−x−yN changes from brittle to ductile and Γ-X indirect fundamental gap becomes Γ-Γ direct fundamental gap. There is good agreement between our results and the available experimental data for the binary compound AlN, which is a support for those of the quaternary alloys that we report for the first time.