MATHEMATICAL-MODELING OF EPITAXIAL SILICON GROWTH IN PANCAKE CHEMICAL VAPOR-DEPOSITION REACTORS

A fundamental understanding of pancake reactors is necessary for the establishment of process-property relationships in these systems. Here, a mathematical model of the gas flow, transport phenomena, and growth rate profiles of epitaxial silicon in a pancake reactor is presented and the resulting modeling equations are solved. Two-dimensional conservation equations of momentum, energy, and mass developed in cylindrical coordinates along with appropriate boundary conditions are solved numerically with finite element methods. Streamlines of the gas flow in the reactor show that the shearing force of the inlet flow yields a recirculation zone inside the reactor and a separation point on the susceptor. As the inlet volumetric flow rate increases, the gas flow direction over the susceptor changes from inwards to outwards, resulting in another reverse circulating flow above the susceptor. The temperature and concentration profiles obtained show that steeper thermal and concentration boundary layers develop above the susceptor at higher volumetric flow rates. Under the assumption of a first-order deposition reaction on the substrate, growth rate profiles are calculated along the radial direction. The effects of total gas mixture flow rates, magnitude of the deposition rate constant, susceptor temperature, and thermal diffusion upon growth rate profiles are investigated. The agreement between observed and predicted growth rates at various temperatures is seen to be satisfactory.