Abstarct: In this thesis, the electronic structure and optical properties of silicon nitride (Si 3 N 4 ) semiconductors in β - phase (hexagonal), were investigated. The calculations were carried out baxsed on density functional theory (DFT) using wien2k code and the generalized gradient approximation( GGA) and local density approximation(LDA) for bulk, pure and Oxygen (%6.25, %12.5 and %25)-doped β−Si3N4 nano-sheets. For these purposes, the band structure and density of states (DOSs), real and imaginary parts of the dielectric function, refraction coefficient, extinction and absorption coefficients, reflectivity, optical conductivity, and electron energy- loss function were investigated. Our results showed that bulk β−Si 3 N 4 has an indirect bandgap. Using GGA and LDA the calculated bandgap was in the range of 4.2 and 4.18 eV, respectively. In β−Si3N4 nano-sheets the bandgap was converted to direct. This calculated direct bandgap was about 3.5 and 3.2 in GGA and LDA, respectively. In O- doped β−Si3N4 nano-sheets some impurity bands related to Oxygen atoms appeared in the bandgap around the Fermi level. Moreover, the bands in the valance band and the conduction band of the doped β−Si3N4 compared to the un-doped samples were condensed.