Numerical modeling of gas-phase nucleation and particle growth during chemical vapor deposition of silicon

A numerical model was developed to predict gas-phase nucleation of particles during silane pyrolysis. The model includes a detailed clustering mechanism for the formation of hydrogenated silicon clusters containing up to ten silicon atoms. This mechanism was coupled to an aerosol dynamics moment model to predict particle growth, coagulation, and transport. Both zero-dimensional transient simulations, at 1-2 atm pressure, and one-dimensional steady-state stagnation-point flow simulations, at 1-2 Torr pressure, were conducted. The effects of carrier gas, temperature, pressure, silane concentration, and flow rate were examined. The results predict that hydrogen as carrier gas, compared to helium, suppresses nucleation, and that particle formation for the case of hydrogen carrier gas increases strongly with increasing initial silane-to-hydrogen ratio. For the conditions examined, predicted particle nucleation rates increase dramatically with increasing temperature. The effect of total pressure depends on the pressure regime: at 1-2 atm pressure particle formation is predicted to be insensitive to pressure, whereas at 1-2 Torr particle formation is predicted to increase strongly with increasing pressure. The predicted effects on particle formation of temperature, pressure, carrier gas, and silane concentration are all qualitatively consistent with published experimental results. In the stagnation-point flow simulations the flow rate is found to affect particle dynamics because of the opposed effects of convective transport toward the heated water and thermophoretic transport away from the wafer.