A MATHEMATICAL-MODEL OF THE HYDRODYNAMICS AND GAS-PHASE REACTIONS IN SILICON LPCVD IN A SINGLE-WAFER REACTOR

A mathematical model has been developed for the fluid dynamics and the chemical reactions in silicon low pressure chemical vapor deposition (LPCVD) from silane in a cold-wall single-wafer reactor. The fluid dynamics model includes the mass, momentum, heat, and species balance equations and equations for multicomponent (thermal) diffusion. The chemical model includes five reversible homogeneous reactions and five heterogeneous deposition reactions. The equations are solved numerically using a control volume based finite difference method. The mathematical model has been used to simulate silicon growth on large (0.24 m) wafers, at varying pressures, wafer temperatures, and silane concentrations in different carrier gases. It was found that both the fluid dynamics and the chemical kinetics have a large influence on the predicted growth rates. At conventional LPCVD process conditions gas-phase reactions are negligible, and deposition is very uniform, but the growth rate is low. An increase in the wafer temperature leads to an increased growth rate, whereas uniformity is still very good. Increasing the total pressure or the silane partial pressure leads to an increased importance of gas-phase reactions and highly deteriorated uniformity. The model predictions were found to be relatively insensitive to most of the model parameters.