Research On Diameter Modeling And Control Of Czochralski Monocrystalline Silicon During Equal Diameter Growth Process

Monocrystalline silicon,as one of the raw materials for integrated circuits and solar new energy,has advantages such as high purity,long service life,flexible adaptability,and stable work efficiency.With the vigorous development of semiconductor integrated circuit technology,the diameter of semiconductor grade silicon wafers is increasingly increasing,making the production and manufacturing of monocrystalline silicon face stricter requirements.At present,the Czochralski method is the main method chosen by people to prepare monocrystalline silicon due to its advantages such as observable growth process and easy operation.In the preparation process of CZ monocrystalline silicon,the control of crystal diameter during the equal diameter growth process is the most important control indicator,which directly determines the quality of the crystal product and affects the later processing and utilization.Therefore,in order to achieve the goal of preparing large-sized and highquality single crystal silicon,studying the diameter control problem in the equal diameter growth process of CZ single crystal silicon has profound guiding significance and practical application value.Modeling is the foundation for achieving control objectives.However,as an extremely complex and dynamic time-varying process,the growth process of Czochralski monocrystalline silicon is difficult to achieve in practical production processes using mechanism modeling methods based on a large number of ideal assumptions.In order to establish an accurate crystal growth process model,a novel idea of data modeling and mechanism modeling is adopted to establish a mixed model of Czochralski silicon equal diameter growth process,namely,the thermal field temperature model and the pulling dynamics model.Among them,the thermal field temperature model uses the VMD-BILSTM-ELM nonlinear modeling method to describe the relationship between the heater power input data and the thermal field temperature output data,with the aim of solving the nonlinear and time-delay problems of the heat transfer process;The pulling dynamics model uses mathematical reasoning to describe the relationship between the thermal field temperature,pulling speed,and crystal diameter of the meniscus.An improved grey wolf optimization algorithm is used to optimize the VMD-BILSTM-ELM network structure to reduce the complexity and contingency of artificial selection parameters.The simulation experiment based on industrial data collection shows that the proposed VMD-BILSTM-ELM based thermal field temperature model accurately predicts the thermal field temperature,effectively combines the pull-up dynamics model,and completes the establishment of a mixed model under the goal of crystal diameter control.Based on the hybrid model of Czochralski silicon growth process established above,a data-driven crystal diameter control method is proposed in this paper,namely Model Free Adaptive Predictive Control(MFAPC),which adopts the concepts of "error" and "error sum" to achieve multi-step prediction function and improve the robustness of the controller.Based on the traditional crystal growth structure,a novel dual closed-loop single crystal silicon control scheme was designed,which includes a power controlled closed-loop subsystem using an MFAPC controller and a diameter controlled closed-loop subsystem using an MFAC controller.The simulation experimental results show that the designed dual closed-loop control scheme not only achieves accurate tracking of the diameter reference value,but also maintains relative stability of the thermal field temperature,which has great advantages compared to traditional PID controllers set by limited manual experience.In addition,by using particle filter algorithms to estimate the growth angle and meniscus height,stable experimental results can further ensure high-quality crystal growth.