Multi-component diffusion phenomena in multiple-wafer chemical vapour deposition reactors

A comparative study has been made as to different methods for modelling diffusion phenomena in multi-component reacting gas mixtures in multiple-wafer low-pressure chemical vapour deposition reactors. Two typical processes for the deposition of thin films on silicon wafers in microelectronics manufacturing were studied: the deposition of tungsten from WF₆ and the deposition of polycrystalline silicon from SiH₄. The two-dimensional axisymmetric equations for the hydrodynamics and the concentration distributions in the reactor were solved numerically. Multi-component diffusion was accounted for through either Fick's law for binary diffusion in the carrier gas, or Wilke's effective diffusivity approach, or the Stefan-Maxwell equations. It has been shown that, compared to the exact Stefan-Maxwell equations, the use of Fick's law or Wilke's approach can lead to inconsistent results when the reactant gases and the reaction product gases are not sufficiently diluted in a bulk carrier gas. This is especially true when there are large variations in the molar masses and in the diffusivities of the various gases in the mixture.