Predicting intrawafer film thickness uniformity in an ultralow pressure chemical vapor deposition reactor

Abstract

We present a reaction engineering analysis of a multiple wafer-in-tube ultrahigh vacuum chemical vapor deposition reactor which allows an estimate of wafer throughput for a reactor of fixed geometry and a given deposition chemistry with specified film thickness uniformity constraints. The model employs a description of ballistic transport and reaction based on the pseudosteady approximation to the Boltzmann equation in the limit of pure molecular flow. The model representation takes the form of an integral equation for the flux of each reactant or intermediate species to the wafer surfaces. Expressions for the reactive sticking coefficients (RSC) for each species must be incorporated in the term which represents reemission from a wafer surface. In our model we use a published expression for the RSC of silane as a function of flux and wafer temperature developed from molecular beam measurements. Numerical solution of the resulting integral equation using Gauss–Legendre quadrature yields quantitative estimates of intrawafer film thickness uniformities for epitaxial silicon deposition from silane for specified process conditions and wafer radius:wafer separation. For given reactor dimensions and specified uniformity, throughputs can then be estimated.