Modeling and Analysis of Low Pressure CVD Reactors

A detailed mathematical model for the hot wall multiple-disk-in-tube LPCVD reactor is developed by using reaction engineering concepts. This model includes the convective and diffusive mass transport in the annular flow region formed by the reactor wall and the edges of the wafers as well as the surface reactions on the reactor wall. In addition, the model describes the coupling of diffusion between and reaction on the wafers. Variations in gas velocities and diffusion fluxes due to net changes in the number of mols in the deposition are also taken into account as are nonisothermal operating conditions. The combined reactor equations are solved by orthogonal collocation. The deposition of polycrystalline Si from SiH₄ is considered as a specific example, and the model is employed in estimation of kinetic rate constants from published reactor measurements. The effects on the growth rates and film thickness uniformity (within each wafer and from wafer to wafer) of variations in flow rates, reactor temperature profiles, and SiH₄ concentration in the feed stream are analyzed. The model predictions show good quantitative agreement with published experimental data from different sources. Finally, recycle of reactor effluent is considered a typical commercial operating conditions, and it is demonstrated that this modification produces higher growth rates and better film uniformity than can be achieved in conventional LPCVD processing.