Temperature And Diameter Tracking Control Of CZ Method Single Crystal Based On Finete Element Model

Silicon single crystals is an important basic material for semiconductor integrated circuits and photovoltaic power generation,and silicon crystals are usually grown by Czochralski(CZ).With the continuous development of large-scale integrated circuit technology,silicon single crystals are required to develop toward large diameter and high quality.However,the increase in the size of the silicon single crystal increases the nonlinearity,large time lag,and time-varying characteristics during crystal growth,which makes it more difficult to establish an accurate crystal growth model,and thus it is also difficult to achieve precise control of the growth process of the silicon single crystal.Therefore,in order to adapt to the development trend of large-size and high-quality silicon single crystals,it is important to establish a more accurate and practical crystal growth control model for simultaneous control of crystal diameter and quality.In the crystal growth process of Cz method,the influence of crystal diameter control effect on crystal quality is often ignored.However,the crystal quality is closely related to the temperature distribution inside the crystal.For this reason,based on the principle of pulling dynamics in crystal growth process and the heat transfer equation inside the crystal,a system structure based on finite element numerical simulation for simultaneous control of silicon single crystal growth temperature and crystal diameter is proposed.Firstly,according to the established crystal growth pulling dynamics model,the design controller realizes the real-time control of the crystal shape.Secondly,under the conditions of strong and weak thermal radiation between the crystal surface and the external environment,the dynamic finite element numerical model of the internal heat transfer of the crystal is established,and the heater radiation height and crystal temperature monitoring point are determined by CGSim numerical simulation.Then,under the constraint of temperature gradient and heater input power,the best heater radiation power trajectory and optimal temperature trajectory are obtained by ALO optimization.Finally,according to the established internal heat transfer model of the crystal,the controller is designed to realize the tracking control of the internal temperature distribution of the crystal while changing the crystal shape.The results show that the CZ method silicon single crystal growth temperature and diameter tracking control system based on finite element model can achieve simultaneous control of crystal diameter and crystal temperature.Moreover,it has interference suppression performance and strong robustness.In addition,in order to improve the PID crystal diameter control performance,the bio-inspired model is introduced to suppress the control amount jitter caused by the large heat flux deviation at the solid-liquid interface,and the crystal diameter control accuracy is well improved.Under the action of weak thermal radiation,the MPC control performance based on the state equation is better than the PID control and meets the real-time requirements.Under the action of strong heat radiation,the convergence speed of the model is reduced.In order to balance the accuracy and real-time performance,the control effect of MRAC is obviously better than that of conventional PID and MPC,which helps to avoid the possibility of crystal dislocation defects.