Research on method of reconstructing temperature field of silicon melt based on eigenfunction interpolation

摘要

Traditional single point detection of temperature of the thermal field in the single crystal furnace can't get the temperature distribution inside the silicon melt. In this paper, TDR-120 semiconductor silicon single crystal furnace is taken as the research object, and a method of reconstructing temperature field of silicon melt based on eigenfunction interpolation is proposed. The paper takes the finite element method to get the eigenfunctions based on the heat conduction equation. According to the contribution of the eigenfunctions to the reconstruction of the temperature field, the partial eigenfunctions with larger contribution are selected by the threshold function, which are used as a set of basis to reconstruct the temperature field. And the weight coefficients are estimated using the temperature of multiple monitoring points. Then, the temperature distribution in the area under study is obtained by solving the inverse problem. Moreover, aiming at the influence of temperature monitoring points on the reconstruction accuracy, the multipopulation genetic algorithm is used to optimize the placement of sensor monitoring points for measuring the temperature on the free liquid surface so as to improve the reconstruction accuracy of the temperature field. Simulation results show the effectiveness of the proposed method.