Structural, optoelectronic, and thermodynamic properties of Y$_x$Al$_{1-x}$N semiconducting alloys

Abstract

The structural, electronic, optical, and thermodynamic properties of Y$_x$Al$_{1-x}$N alloys were computed using first-principles calculations. The effects of exchange and correlation have been considered by means of the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof parametrization. In addition, the Tran–Blaha-modified Becke–Johnson potential (TB-mBJ) was applied to give a better description of the band-gap energies and optical spectra. The lattice parameters, bulk modulus, and band-gap energy show nonlinear dependence on concentration x. Results for rock-salt Y$_x$Al$_{1-x}$N alloys show that the band gap undergoes an indirect ($\Gamma \rightarrow X$)-to-direct ($\Gamma \rightarrow \Gamma$) transition at a given yttrium composition, followed by a direct ($\Gamma \rightarrow \Gamma$)-to-indirect ($\Gamma \rightarrow X$) transition in a higher yttrium concentration. For wurtzite Y$_x$Al$_{1-x}$N alloys, the band gap presents a direct ($\Gamma \rightarrow \Gamma$)-to-indirect ($M\rightarrow \Gamma$) transition at a given yttrium composition, followed by an indirect ($M\rightarrow \Gamma$)-to-indirect ($M\rightarrow \Sigma$) transition in a higher yttrium concentration. The real dielectric function, imaginary dielectric function, refractive index, and extinction coefficient were calculated using the TB-mBJ potential. Using a regular solution model, slightly lower mixing enthalpies for wurtzite Y$_x$Al$_{1-x}$N alloys were found. The mixing enthalpy for a given concentration differs depending on structures, and on the interaction between atoms of constituents. The effect of temperature on the volume, bulk modulus, Debye temperature, and the heat capacity for Y$_x$Al$_{1-x}$N alloys was analyzed using the quasi-harmonic Debye model. Results show that the heat capacity is fairly sensitive to composition as temperature increases.