A model for the growth kinetics of a dielectric film obtained by oxidation of silicon in nitrous oxide environment is presented. The complete logarithmic form of oxidation kinetics is introduced for understanding the oxynitridation mechanism which includes information of the role of nitrogen in oxide film. The model fits experimental data excellently both for short and long growth times. The chemical reaction energies of 1.81 and 1.1 eV are required or the oxynitridation for short and long growth times, respectively This result suggests that the initial stage of the dielectric growth requires the higher reaction energy to form the SiOxNy layer and the lower energy is needed for the bulk oxide formation from the reaction with the interfacial layer of the SiOxNy. For the N2O oxidation, there are two barriers for the chemical reactions for NO and O-2 species dissociated from N2O molecules.