Известия Томского политехнического университета: Инжиниринг георесурсов (May 2019)
Mathematical model of multizone thermal installation for crystal growth by Bridgman method
Abstract
The work is devoted to the solution of the problem of developing the complex of mathematical models to solve scientific-technical tasks in the design multizone thermal installations for crystal growing by Bridgman method. The relevance of the research is related to continuously increased requirements to the quality of the growing crystals, for example, for the development of energy-efficient production, renewable energy on the basis of solar battery, created on the basis of mono- and multi-crystalline silicon, in instrumentation as optical and laser components, integrated circuit substrates, soft and hard radiation detectors, in quantum electronics, nonlinear optics, etc. and consequently with the necessity to improve thermal installations and technological processes. The main aim of the study is to develop the mathematical models that allows in real-time mode with acceptable accuracy forecasting a course of crystal growing in variable thermal conditions. The methods used in the study. The developed model is implemented on base of the method of elementary balances adopted for the calculation scheme in Matlab. The model allows evaluating the installation temperature field, exploring the mutual influence of thermal processes in the system «growth container - thermal installation», simulating thermal processes in the installation at all stages of the crystal growing, as well investigating various algorithms of controlling thermal power of heaters. The results. The authors have obtained the estimation of both crystallization isotherm position and crystal growing rate for the vertical Bridgeman technique with mechanical movement of growth container. Basing on these estimations the conclusion was made that a change of the temperature field in the growth container at its mechanical movement results in sufficient influence on crystallization isotherm position. Herewith the growth rate can reach the area of negative values that will lead to partial melting of already grown crystal. Besides, the actual time of crystal growing may differ significantly from the planned one on the base of assumption on constant growth rate. The data obtained by calculations should be taken in consideration both at design of new facilities and planning of experimental works on crystal growing.
