Nitridation of silicon surface is an important step in GaN or AlN nanostructures growth process which determines quality of fabricated devices. In this work modeling of gas-surface reaction of the Si(111) surface nitridation was performed using density functional theory calculations. We show that interface structure corresponding to first stoichiometric Si3N4 monolayer may be generated in a great number of different ways by means of vacancy-assisted mechanism. The nearly continuum distribution of total energies may be associated with such structures formed after exothermic reaction with considerable energy gain. Nevertheless founded global minimum corresponds to abrupt interface and crystalline-like Si3N4 monolayer structure. Suggested mechanism of silicon nitride film growth is based on the calculated energy barriers for diffusion of volatile species such as N, N-2, SiN and SiN2 which are building blocks for the growth of Si3N4 film. At first stage atomic nitrogen diffusion from vacuum to substrate occurs. Then silicon vacancies in substrate and volatile SiN radicals are formed. The back diffusion of SiN from substrate to Si3N4-vacuum side is the main mechanism responsible for silicon nitride film growth.