Density Functional Theory (DFT) has in recent years gained a lot of popularity and has become an efficient and reliable tool in the study of material properties. This is specifically due to its computational convenience and excellent results in the prediction of material properties, which is aided by the development of highly efficient and accurate functionals. DFT has successfully been applied in a vast study of material at both ground and excited states. In this study based on DFT structural, optical, electronic properties and phonon frequency of silicon nitrides of different phases were studied using the GGA as exchange-correlation functional. For the electronic band gap calculation the results was obtained using the GGA and the hybrid HSE06 respectively for α -Si3N4 with space group (P31c), β-Si3N4 with space group (P63/m) and γ-Si3N4 phase polymorph with space group (14‾3d). Results obtained for the phases α -Si3N4 shows a narrow indirect band gap while β and γ -Si3N4 indicate a wide indirect band gap material for wide possible application in high temperature and high-power applications. Cohesive energy calculation and phonon frequencies were obtained to check the mechanical and dynamic stability of the three different phases. Results obtain for density of states, partial density of states and the optical properties, such as absorption coefficient, refractive index, extinction coefficient, reflectivity and electron energy loss spectra which all show good agreement with previous studies and relative experimental data.
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