Structural, phonon and thermal properties of $\rm{Al_{x}Ga_{1−x}As}$ alloy for different values of x (x = 0.0, 0.25, 0.5, 0.75 and 1.0) have been investigated by quasiharmonic Debye–Einstein model and Quantum Espresso package. The correction of Vegard’s law for lattice constant has been examined and has a good agreement with other experimental and theoretical works. TO–LO splitting at gamma point, which is related to breaking of cubic symmetry, has been calculated by optical phonon mode calculation. It is found that by increasing the amount of Al in $\rm{Al_{x}Ga_{1−x}As}$ alloy, specific heat at constant pressure and Debye temperature will be increased.

In this paper, structural, electronic, thermal and thermoelectric properties of Al$_{0.75}$B$_{0.25}$As under 0, 2, 4 and 6 GPa pressure have been investigated based on density functional theory. Values of band gaps under 4 and 6 GPa pressure have been increased. The values of group velocity have been increased with increment in pressures from 0 GPa, too. The value of band gap at 0 GPa using the GGA(PBE) exchange-correlation potential and the mBJ method are close to each other. It is due to the good muffin-tin radius selection for atoms of the compound. Thermal properties have been investigated by calculating the heat capacity at constant volume (phonon and electronic contributions) and Debye temperature. Heat capacity at constant volume has been reduced and Debye temperature increased in comparison with AlAs. In Seebeck coefficient charge carriers are holes. Electrical conductivity in most of temperatures and electronic thermal conductivity in all the temperatures show increment with the increase in temperature and pressure.

In this paper, structural, electronic, thermal and thermoelectric properties of Al$_{0.5}$B$_{0.5}$ As alloy at 0, 4 and 8 GPa pressure have been investigated. In electronic properties, the obtained band gaps in the present work with GGA(PBE) potential are close to the other works with the TB-mBJ method at 0 GPa pressure. Band gaps reduce by increasing pressure. Thermal properties consisting of phonon contribution of heat capacity at constant volumeand Debye temperature at 0, 4 and 8 GPa pressure in the temperature range of 0–1000 K have been calculated. The diagrams of Seebeck coefficient (S), electrical conductivity (σ ) divided by relaxation time ($\tau$ ), power factor (S$^2$σ/$\tau$), electronic thermal conductivity (κe) divided by relaxation time ($\tau$) and electronic contribution of heat capacity at a constant volume in the temperature range of 100–1000 K at 0, 4 and 8 GPa pressure have been plotted.