Modeling And Numerical Analysis Of Temperature Field In The Growth Process Of Czochralski Silicon

As an important raw material for the semiconductor industry,higher quality of Silicon single crystal is required with the rapid development of informatization.In the process of preparing crystals by the Czochralski method,the phase transition temperature field is the driving force for single crystal growth and determines the quality of crystal growth.However,the diameter of the crystal grown in the non-uniform phase transition temperature field is not uniform,which greatly reduces the intrinsic quality of the crystal.Therefore,based on the non-uniformity of phase transition temperature field at solid-liquid interface,this paper studies the temperature field modeling during the crystal growth process of the Czochralski method,which is of great significance to stabilize the crystal diameter and improve the crystal quality.1.During the Czochralski crystal growth process,the non-uniformity of the phase transition temperature field is mainly caused by the change of the crystal growth boundary,the thermal convection in the melt,and the drop of the melt free surface position.And the non-uniform phase transition temperature field affects the solid-liquid interface shape,V/G and crystal diameter.Therefore,studying the influencing factors of the non-uniform characteristics of the phase transition temperature field and the effect on the crystal quality lays a theoretical foundation for establishing a temperature field model of the crystal growth process.2.In the modeling of temperature field during crystal growth,aiming at the problem that non-uniformity of the phase transition temperature field of the solid-liquid interface is caused by the change of the crystal domain boundary and the decrease of the melt free surface position,during the Czochralski crystal growth process,an improved lifting dynamics model was established to determine the evolutionary dynamics relationship of domain boundaries.Under time-varying boundary conditions,the temperature model based on the parabolic Partial Differential Equation(PDE)convection diffusion process is studied,and the unidirectional coupling of the domain motion on the convection diffusion system is described.In order to solve the infinite dimensional heat transfer model,the spectral method is used to reduce the dimensionality of the model,and the crystal growth temperature is controlled by the linear quadratic form.The simulation results show that the improved lifting kinetic model can effectively maintain the stability of the solid-liquid interface position,the model can obtain a relatively stable crystal growth rate,and reduce the fluctuation of the growth diameter.Spectral method can realize the dimensionality reduction of the heat transfer model in the convection diffusion process.Under the linear quadratic optimal control,the radial temperature gradient of the phase change temperature field is gradually reduced,and finally a uniform phase change temperature distribution is obtained.3.Aiming at the effect of forced convection in the melt on the uniformity of the phase transition temperature field during the crystal growth process of the Czochralski method,the temperature distribution of the phase transition interface at different crucibles and crystal rotation speeds was analyzed by numerical simulation.The numerical simulation results show that the rotation of the crucible can gradually move the radial temperature distribution of the melt in the crucible to the central axis,and the rotation of the crystal makes the isotherm in the melt move below the crystal.Therefore,reasonable adjustment of these two process parameters can effectively improve the uniformity of the phase transition temperature distribution at the solid-liquid interface.