The effect of the hydrostatic pressure and the temperature on the electronic structure in GaN semiconductor has been calculated using the local empirical pseudopotential method. The variation of the direct and indirect energy gaps with the pressure up to 120 kbar and with the temperature up to 500 K has been done. The calculated fundamental energy gap at different pressures and different temperatures are calculated and compared with the available experimental data which show excellent agreement. The effect of pressure and temperature on the refractive index of the considered materials has also been studied.

In this work, the electronic, optical, and mechanical properties of BN, AlN, and InN under the action of pressure are calculated. For each of these compounds, the energy band structure, band gaps , refractive index (n), dielectric constants (), elastic constants (), and relevant parameters such as bulk (), shear (), and Young's () moduli are studied, and other important parameters such as bond-stretching (α), bond-bending (β) force constant, internal-strain parameter (ζ), effective charges (), anisotropy factor (), Poisson's ratio (), Cauchy ratio (), the ductility index (), and linear compressibility () are also calculated. The effects of pressure on all studied properties are investigated. Our results are in good agreement with the available experimental and theoretical data for BN, AlN, and InN.