<title>Computationally efficient modeling of wafer temperatures in an LPCVD furnace</title>

Abstract

This paper presents a new first principles thermal model to predict wafer temperatures within a hot-wall Low Pressure Chemical Vapor Deposition (LPCVD) furnace based on furnace wall temperatures as measured by thermocouples. This model is based on an energy balance of the furnace system with the following features: (a) the model is a transformed linear model which captures the nonlinear relationship between the furnace wall temperature distribution and the wafer temperature distribution, (b) the model can be solved with a direct algorithm instead of iterative algorithms used in all existing thermal models, eliminating potential problems with convergence and local minima related to optimization, and (c) finite area to finite area methods are applied to calculate configuration factors, avoiding the implementation difficulties of numerical integration. The simplicity of the model form makes the model useful for model based run-to-run control. The model predictions agree with experimental data very well. The sensitivity of wafer temperatures to furnace wall temperatures is given analytically. More uniform wafer temperature profile is obtained via optimization.