Simulation of silicon wafers heating during rapid thermal processing using “UBTO 1801” unit

Abstract

The present work is devoted to determination of the dependence of the heating temperature of the silicon wafer on the lamps power and the heating time during rapid thermal processing using “UBTO 1801” unit by irradiating the wafer backside with an incoherent flow of constant density light. As a result, a mathematical model of silicon wafer temperature variation was developed on the basis of the equation of nonstationary thermal conductivity and known temperature dependencies of the thermophysical properties of silicon and the emissivity of aluminum and silver applied to the planar surface of the silicon wafer. For experimental determination of the numerical parameters of the mathematical model, silicon wafers were heated with light single pulse of constant power to the temperature of one of three phase transitions such as aluminum-silicon eutectic formation, aluminum melting and silver melting. The time of phase transition formation on the wafer surface during rapid thermal processing was fixed by pyrometric method. In accordance with the developed mathematical model, we determined the conversion coefficient of the lamps electric power to the light flux power density with the numerical value of 5.16∙10-3 cm-2 . Increasing the lamps power from 690 to 2740 W leads to an increase in the silicon wafer temperature during rapid thermal processing from 550°to 930°K, respectively. With that, the wafer temperature prediction error in compliance with developed mathematical model makes less than 2.3 %. The work results can be used when developing new procedures of rapid thermal processing for silicon wafers.