Analysis Of Silicon Melt Temperature Field In Single Crystal Furnace And The Optimal Placement Of Temperature Sensor Measuring Point

Silicon single crystal has been widely used in many fields,especially in the semiconductor industry.With the requirements of the semiconductor integrated circuit devices to large diameter and high quality silicon single crystal getting higher,which makes a variety of parameters in preparation of single crystal silicon are more precise.And the temperature as the most important parameters of crystal growth plays a decisive role in the preparation of high-quality silicon single crystal.Based on the above analysis,this article has carried on a series of studies about silicon melt temperature effect analysis in the equal diameter of crystal growth,interpolation reduction of silicon melt temperature field and optimal placement of finite temperature sensors measurement points with how to use the temperature measurement points on the free surface to reduce the silicon melt temperature field.Some main works are as follows.Firstly,the temperature field of silicon melt in the equal diameter of crystal growth is analyzed.The two-dimensional axisymmetric model of single crystal furnace silicon melt is established,and the temperature field change in the silicon melt of the equal diameter stage is studied according to the finite element simulation method.Then combined with the boundary conditions in the actual working environment,the temperature distribution is obtained,which is compared with the temperature simulation results obtained by the professional software,it can ensure the correctness of the results obtained by the simplified model.These conclusions lay the foundation for the optimal placement of temperature sensor measurement point.Secondly,a method for reduction the temperature distribution of silicon melt based on eigenfunction interpolation is proposed,and the optimal placement of the temperature sensor measurement point is introduced in this process,two aspects of work are mainly included:(1)In order to simplify the model,a threshold function is defined to select a part of the eigenfunction for reducing the temperature distribution of silicon melt.(2)The temperature monitoring points on the free surface of the silicon melt of the two models are optimized by genetic algorithm and its improved algorithm,and then based on the optimized points,the temperature distribution of the silicon melt is obtained using the eigenfunction interpolation method.At last the error analysis is carried out with the standard temperature distribution,the result shows that the temperature distribution of the silicon melt obtained by the optimized position combination has high reduction accuracy.The results of the above study lay the foundation for reduction the temperature distribution of silicon melt in the equal diameter of crystal growth by a finite temperature measurement points.