Modeling Chemical Vapor Deposition of Silicon with Local Equilibrium Consideration at the Substrate

Abstract

The purpose of this article is to present a general purpose mathematical model for describing the transport phenomena and the resulting rate of deposition in chemical vapor deposition (CVD) reactors. The model employs a finite difference scheme to solve the governing partial differential equations in order to predict the velocity field, temperature distribution, and concentration profiles of various gas species in a CVD reactor. The model predicts the rate of deposition for CVD reaction whose rate is mass transport controlled, for example, silicon deposition by the reaction of silicon tetrachloride and hydrogen at temperatures above 1050 °C. Silicon deposition by reaction of SiCl4 and H2 in a vertical CVD reactor with a rotating substrate is studied to compare the predicted and the experimental deposition rates. The effects of inlet gas composition, reactor pressure, and speed of substrate rotation on the rate of silicon deposition have been studied to verify the model's predictions. Local equilibrium and flux balance concepts have been used to determine the partial pressures of species at the substrate as well as the consequent deposition rate of silicon. The effects of thermal diffusion, grid size, and etching by HC1 on the deposition rate have also been studied. The results show that implementation of the local equilibrium concept and the flux balance principle, use of sufficiently small grid size above the substrate, thermal diffusion of SiCl4 away from the substrate, and etching of deposited silicon by HC1 are all very important in evaluating the rate of silicon deposition in the mass transport-controlled regime. With all of the above-mentioned effects taken into consideration, model predictions agree well with the experimental data over a wide range of operating conditions for the system considered. Finally, use of the optimized design of a flow control device (FCD) in the reactor shows that once properly validated, the model can be used as a tool in computer-aided process optimization.