Density functional theory (DFT) - Based GW+BSE calculations to investigate the influence of substitution of Ga with Al on the band gap and the optical spectra of Al _x Ga_{1- x}N (x = 0, 0.125, 0.25, 1)

Semiconductors have long been the main materials used in the manufacture of charge-based as well as photonic-based electronic devices. GaN, owing to its wide-band gap, is often used for light-emitting diodes, and other optoelectronic applications. To adjust to the desired energy band gap, GaN is often combined with Al in form of Al_xGa_1-xN, which is expected to have a wider band gap than that of pure GaN. The increase of aluminum content yields an increase of electron activation energy. Here, we theoretically investigate how the band structure and optical spectrum evolve as the aluminum content is varied, by performing Density Functional Theory (DFT) calculation on pure wurtzite GaN and Al_xGa_1-xN (with x = 0.125 and 0.25). Simple band structures without rigorous treatment of the electron-electron interactionss are obtained through Plane-Wave Self-Consistent Field (PWSCF) calculation of DFT. The correction to the band gap due to electron-electron interactions is expected from the implementation of GW method. While, excitonic signal in optical spectrum is expected to arise upon the implementation of Bethe-Salpeter equation. Our calculation results show that the band gap increases with x in the region of x values we study.