Study On The Optimization Of Key Parameters Of CZ Single Crystal In Equal Diameter Growth Stage

With the rapid development of large scale integrated circuits,higher requirements are put forward for the quality and size of silicon single crystals.Czochralski method is usually used to prepare high-quality IC grade silicon single crystals in large quantities.The whole process of crystal preparation lasts for dozens of hours,and the equal diameter growth stage is the most time-consuming and important step in the growth process of silicon single crystals.The process parameters of CZ silicon single crystal growth determine the quality of silicon single crystal.At present,the process parameters of silicon single crystal growth are obtained through repeated experiments,which are time-consuming and costly.Therefore,the optimization of key parameters in the growth process of silicon single crystal is an urgent problem in the field of crystal growth.Crystal diameter is an important index to evaluate the quality of silicon single crystal in the stage of equal diameter growth of silicon single crystal,while a large number of characteristic parameters are involved in the process of equal diameter growth of CZ silicon single crystal,and the parameters interact with each other,so it is necessary to eliminate the irrelevant and redundant features related to crystal diameter,identify the key parameters affecting crystal diameter,establish the model of key parameters and crystal diameter,by adjusting the key parameters of equal diameter stage to control the crystal diameter.To optimize the key parameters of silicon single crystal equal diameter growth and improve the quality of silicon single crystal.Although the nonlinear,large time delay and time-varying characteristics in the growth process of silicon single crystal make the mechanism modeling process complex and the model solution difficult,but the input and output data of the growth process and the operation process data of the growth equipment are easy to collect,so this thesis builds the system model based on the growth process data of silicon single crystal.This thesis focuses on the identification of the key parameters that affect the crystal diameter during the equal diameter growth stage of CZ silicon single crystal,the establishment of a nonlinear dynamic model of the key parameters and the large time delay of crystal diameter,and the control of the consistency of crystal diameter by adjusting the key parameters,so as to achieve the optimization of the key parameters.1.Key parameter identification,the control parameters of single crystal furnace are selected as the characteristic parameters.From the perspective of feature dimensionality reduction,based on the theory of information entropy,the redundancy and correlation between feature parameters and crystal diameter are analyzed by using Pearson correlation coefficient and MIC algorithm,and the MIC of heater temperature and crystal diameter is 0.9465,which has the greatest influence on crystal diameter.2.Model identification,the heater temperature and crystal diameter measurement data of CZ silicon single crystal in equal diameter stage are selected for filtering and normalization preprocessing,and fuzzy approximation and Lipschitz quotient rate of change are used to identify the time delay and input-output order of the heater temperature-crystal diameter model;after the model structure is determined,the heater temperature and crystal diameter are used as the model input,and the crystal diameter is used as the model input for model output,the parameters of the model are identified based on BP neural network,SVR and NARX neural network,and the identification results of the three algorithms are compared and analyzed.The identification error based on NARX neural network is maintained at ± 0.02 mm,which is the highest identification accuracy compared with BP neural network and SVR support vector regression,and can better predict and track the actual crystal diameter.3.Consistency control of crystal diameter,a non-linear predictive control algorithm is used.The multi-step prediction model of crystal diameter is established based on NARX neural network and the reference trajectory is set according to the set value of crystal diameter.LM algorithm is used to optimize the performance index and solve the optimal control input sequence.The simulation results show that the crystal diameter controlled by the predictive control algorithm based on NARX neural network fluctuates less than that before the control,and the deviation from the crystal diameter setting value is maintained at ± 1mm,which can better track the crystal diameter setting value,obtain the optimal heater temperature input sequence,and realize the optimization and precise adjustment of the heater temperature parameters.