A multidimensional model has been developed and applied to simulate the chemical vapor deposition (CVD) of silicon nitride from silicon tetrafluoride and ammonia in a low-pressure hot-wall reactor. The purpose of this work is to evaluate the effects of gas-phase transport and reactant depletion on the uniformity and rate of deposition of silicon nitride by CVD in order to provide a basis for reactor scaling and process control. Two irreversible surface reactions are used to model the deposition chemistry. Diffusion is shown to be important relative to convection in transporting gas-phase reactants to the surface where the chemical reactions occur. Reactant depletion also has a significant impact on the deposition. Multicomponent diffusion of the five reacting species is studied by solving the Stefan Maxwell equations; the results are compared with those obtained using the simpler mixture-averaged approximation to multicomponent diffusion.