With the development of semiconductor technology, more and more electronic products, such as mobile phones, tablet computers and smart watches, needed to use silicon-based integrated circuit chips with high computing speed and high storage capacity, this created a huge demand of high grade silicon wafer. At the same time, the minimum line width of IC was up to 3 nm, which needed even strict control of crystal original particles (COP) density and size. It was necessary to develop a more effective function for the control of COP defects in crystal growth furnace. The V/G (V: crystal growth rate, G: axial temperature gradient in the growth interface) theory was the most effective and applicable guiding theory to control the micro defects formation and growth during Czochralski (CZ) silicon single crystal growth, which required that the crystal growth rate was strictly limited during the process of crystal body growth, but a limited growth rate resulted in the out of control of crystal diameter. It was tested that the response time of the crystal diameter to the one-time regulation power adjustment could be more than 15 min in the 32 inch thermal field. When the heater power was adjusted again according to the respond of diameter after 15 min, the deviation of crystal diameter could reach more than 10 mm and an unstoppable oscillate started, even the CCD system could not capture the image signal because of the excessive shrinkage of crystal diameter. The purpose of this study was to find a control function which could overcome the effect of time lag in 32 inch hot zone, so that it could control the crystal diameter by changing the heater power under the condition that the crystal growth rate was strictly limited, so V could always meet the control demand of COP free crystal growth, and the control demand was decided by V/G theory. In order to establish the mathematical model of the relationship between the heating power change and the crystal diameter, the response law of the single power pulse output and the crystal diameter change was studied, it was confirmed that the large amplitude pulsed power output significantly reduced the time lag of the diameter response, a 15 min process could be shorten to 5 min. In the control of crystal diameter, Smith Predictive Controller was introduced to compensate the time-lag effect. (1) When the real diameter was far away from the control target, a bigger Kp was chosen to make the crystal diameter approaches the control target rapidly, a smaller Ki was chosen to prevent the integral saturation, reduce the system oscillation, and weaken the restraint of the differential element to the change trend. (2) When the real diameter was close to the control target, a smaller Kp was chosen to reduce the overshoot, a larger Ki was chosen to reduce the static error, and the role of the differential was enhanced. The simulation results showed that the Smith Predictive Controller could effectively eliminate the influence of the system hysteresis on the controller and greatly improve the system stability. Combined with Smith Predictive Controller, common proportional, integral, differential (PID) control strategy and mold and PID control strategy had better control effect, and mold and PID response was faster, system robustness and anti-interference ability was stronger. The TDR-135B CZ silicon growth furnace was used to grow a single crystal silicon of 300 mm in diameter with 32-inch hot zone and the charge size was 450 kg. Under the condition of 30 mm•h-1 crystal lifting speed, the crystal diameter variation was controlled to ±1 mm by power adjustment. The diameter control method of 300 mm silicon crystal studied in this paper is suitable for the control of the diameter of single crystal silicon with different sizes. In a relatively small size thermal system, the temperature change of the melt caused by the power adjustment could be transferred to the crystal growth front in a shorter time and had effect on the crystal diameter earlier, which meant the time delay in the small thermal field was relatively small, which was favorable for controlling the crystal diameter. The application of magnetic field in the growth of Czochralski silicon single crystal could effectively control the oxygen content and improve the crystal uniformity, but magnetic field restrained the melt convection and the energy transfer from heater to growth interface was delayed. This made diameter control by power adjustment with a constant growth rate even harder. At the same time, with the crystal length increased and the melt weight decreased, it was observed that at a certain crystal length, the crystal diameter fluctuated regularly, this might be caused by the change in the position of the melt relative to the magnetic field, and it was hard to control by the function developed now. In the future research, the big data technology might be used to predict the crystal diameter variation trend, or the effect of thermal inertia of the melt could be predicted. With the support of big date model, the crystal diameter could be better controlled. © Editorial Office of Chinese Journal of Rare Metals. All right reserved.
