IT and the Applied Theory of Random Processes to Solve the Technological Problem of Semiconductor Materials

The article addresses the problem of analysis on fluctuations at the output of the technological process of growing single crystals by the Czochralski method. The diameter of the crystal and the concentration of impurities play the role of such parameters. Special approach based on IT and the applied theory of random processes is proposed to provide opportunities for a joint analysis of the physical-thermal processes of growing a crystal from a melt and the process control system. The approach includes the introduction into consideration of a two-link dynamic model for each of the determining technological parameters, the use of the dynamic models description as of the "black box" type model, the consideration of the entire growing process as the system which have a variable dynamics. The assumptions that made it possible to obtain analytical relations for estimating the variance of fluctuations at the output of a dynamic channel as a function of the determining parameters were introduced. Changes in process parameters known from practice are introduced and approximated to conduct a qualitative analysis. The results of the analysis and the simulation enabled a first explanation of the extreme nature (known from the literature) of changes in fluctuations of crystal parameters along the length of the ingot.