Equipment Models for Process Optimization and Control Using Smart Response Surfaces

摘要

An equipment model has been developed for the low pressure chemical vapor deposition of polycrystalline silicon in a horizontal tube furnace. The model predicts the wafer-to-wafer deposition rate down the length of the tube. Inputs to the model include: silane flow rates from three injectors, injector locations, locations of and temperatures of three thermocouples, operating pressure, the number of wafers, wafer diameter, the location of the wafer load, and other physical dimensions of the furnace such as tube length, and inner diameter. The model is intended to aid the process engineer in the operation of equipment, and the equipment designer in the design of new equipment. The one dimensional finite difference model encompasses the convective and diffusive fluxes of silane and hydrogen in the annular space between the wafer load and tube walls. The reaction of silane is modeled, including the generation and transport of hydrogen. Kinetic and injection parameters in the model were calibrated using a series of nine statistically designed experiments. The model accurately predicts the axial deposition profile over the full range of experimentation and demonstrates good extrapolation beyond the range of experimental calibrations. The model was used to predict a set of process parameters that would result in the least variation of deposition rate down the tube. The predicted parameters agree well with experimentally determined optimum conditions. Keywords: Gas flow. (KR)