beta-Si3N4 is used as the gate dielectric for surface passivation in GaN-based, high-electron mobility transistors(HEMTs). In this study, the electrical and optical characteristics of the hexagonal beta-Si3N4 crystal structure were calculated using density functional theory (DFT) and local-density approximation (LDA). Calculations of the electronic band structure and the density of states (DOS) were made for the pure beta-Si3N4 crystal structure and the beta-Si3N4 crystal doped with an arsenic (As) impurity atom. In addition, the optical properties such as the static dielectric constant, refractive index, extinction coefficient, absorption coefficient and reflection coefficient were examined depending on the photon energy. As a result of these calculations, it was observed that the As impurity atom drastically changed the electrical and optical properties of the pure beta-Si3N4 crystalline structure, and improvements are suggested for potential further studies. (C) 2016 Elsevier Ltd. All rights reserved.