<span style="font-style:italic"> Ab initio</span> calculation of structural and electronic properties of Al$_x$Ga$_{1-x}$N and In$_x$Ga$_{1-x}$N alloys

Abstract

Using the density functional theory (DFT) with the generalized gradient approximation (GGA), we calculated the structural and electronic properties of wurtzite AlN, GaN, InN, and their related alloys, Al$_x$Ga$_{1-x}$N and In$_x$Ga$_{1-x}$N. We have performed accurate ab initio total energy calculations using the full--potential linearized augmented plane wave (FP--LAPW) method to investigate their structural and electronic properties. We found that in both alloys the fundamental parameters do not follow Vergard's law. The lattice parameters, $a, c,$ and $u$, for the Al$_x$Ga$_{1-x}$N alloy are found to exhibit positive bowing parameters, while for In$_x$Ga$_{1-x}$N there is a negative bowing for the $a$ and $c$ parameters and a positive bowing for the internal parameter, $u$. We calculated as well the nearest neighbor and next nearest neighbor distances, as a function of the concentration, and we obtained a good agreement with experimental results. Furthermore, we found that for both alloys, the band gap does not follows the Vegard law. As a by--product of our electronic band structure calculations, the effective masses of the binary compounds and their alloys were calculated. All the calculated properties show good agreement with most of the previously reported results. Finally, using the frozen phonon approach, the A$_1(TO)$ mode for the different systems studied in this work was calculated. Our calculations show good agreement with experimental values reported for the binary compounds. For the ternary alloys, our calculations reproduce experimental values for Al$_x$Ga$_{1-x}$N as well as theoretical predictions for In$_x$Ga$_{1-x}$N.