Silicon melt temperature field reconstruction method based on free liquid level temperature measurement value and feature function interpolation

Abstract

The invention discloses a silicon melt temperature field reconstruction method based on a free liquid level temperature measurement value and a feature function interpolation. The feature value problem of a heat conduction equation is used for analyzing the silicon melt model of the equal-diameter stage of the two-dimensional axial symmetry crystal growth process of a single crystal furnace, and a feature value and a corresponding feature function are obtained by calculation; a threshold scalar function is used for calculating the function of each feature function for an area to be reduced; a scalar value is set as a measuring standard for selecting the feature function; on the basis of a multi-population genetic algorithm, the arrangement position of a temperature sensor measuring point is optimized; finally, the group of temperature measurement values combined on an optimization position and the selected feature function are used for carrying out calculation to obtain a weight factor which reflects he characteristics of a silicon melt area; and an inner product operation is carried out with the feature function of each point in the silicon melt to obtain the temperature distribution of the silicon melt. By use of the method, the influence of a complex structure for an arrangement temperature sensor is reduced, the method is free from a heat conduction physical problem, and expansibility is good.

Description

technical field [0001] The invention belongs to the technical field of crystal growth equipment, and in particular relates to a silicon melt temperature field reconstruction method based on free liquid surface temperature measurement and characteristic function interpolation. Background technique [0002] In the process of growing silicon single crystal by Czochralski method, oxygen is the most important impurity in silicon single crystal, and the distribution and change of the temperature field of molten silicon have an important influence on the content and distribution of oxygen in the crystal. The large temperature gradient and fast flow rate of molten silicon will lead to an increase in the oxygen content in the crystal. When excessive oxygen precipitates in the silicon wafer, it will cause warpage during processing, which is not conducive to the electrical performance of silicon materials and integrated circuit devices. On the other hand, as a part of the silicon melt,...

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Problems solved by technology

[0004] The purpose of the present invention is to provide a silicon melt temperature field reconstruction method based on free liquid surface temperature measurement and characteristic function interpolation, to solve the problem that the existing silicon melt temperature field cannot be effectively reconstructed, thereby improving the temperature of silicon single crystal. Quality and optimization of process parameters for single crystal furnaces

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