Modeling of High-Temperature Low-Pressure Silicon-Refining Process

Abstract

An improved method for the modeling of the impurity reduction factor during high-temperature low-pressure silicon treatment is suggested. The implementation of a modified logistic function in a mathematical model allows it to be utilized for any range of treatment temperatures. The new model defines the maximum reduction factor for each impurity element present in liquid silicon and defines a critical treatment temperature value. Evaporation increase constant, with high adaptability for the implementation of new process parameters, indicated rapid increase in impurity removal at treatment temperatures slightly above melting point of silicon. Various statistical parameters for the logistic regression method were considerably lower for the 16 studied impurity elements than for the linear or logarithmic correlations.