PRACTICAL COMPUTER-SIMULATION TECHNIQUE TO PREDICT OXYGEN PRECIPITATION BEHAVIOR IN CZOCHRALSKI SILICON-WAFERS FOR VARIOUS THERMAL-PROCESSES

A practical computer simulation technique has been developed to predic t oxygen precipitation behavior in Czochralski silicon wafers during v arious thermal processes. In this simulation, an empirical factor is i ntroduced in the initial and boundary conditions of the Fokker-Planck equation of the oxygen precipitation in order to make up an incomplete assumption of a homogeneous nucleation process proposed bg Schrems et al.(1) The empirical factor is constructed as a function of heat-trea tment temperature and interstitial oxygen concentration so as to descr ibe characteristic phenomena of the precipitation nucleation processes in the 450 to 800 degrees C range. Futhermore, an experimentally meas ured thermal history during a crystal growth process, which strongly i nfluence the oxygen precipitation behavior in the subsequent thermal p rocess, has been taken into consideration. The calculated results agre e fairly well with the experimental results for a variety of thermal p rocesses. This semi-empirical simulation technique thus provides an ad vantageous tool for industrial optimization of the oxygen precipitatio n characteristics.