Modeling, dynamics, and control of the Czochralski crystal growth process

Czochralski crystal growth is a widely used technology for manufacturing semiconductor crystals. Currently, semiconductor manufacturers desire to increase the crystal diameter in order to minimize the unit cost per chip during wafer processing while also reducing dislocation density and micro defect level in order to fabricate circuits with decreasing line widths. However, the ability to meet these advanced manufacturing objectives is limited by the current process control architecture since it has not been explicitly designed to deal with important process complexities including the nonlinear and time varying dynamics and cross coupled physics. In order to design a better control system, a process model is developed to reflect the real equipment features of commercial scale Czochralski crystal growth furnaces and capture the fundamental process physics governed by heat and mass transport processes. The model is used to study the system dynamic characteristics and input-output relations in order to develop an improved control structure and control algorithm.; The model captures three process features critical to understanding the fundamental process physics and dynamics: (a) the influence of crystal geometry variations on the radiation heat transfer and the resulting nonlinear growth dynamics, (b) the curved interface shape between the melt and crystal determined by the changing thermal fields and its effect on dynamics and control objectives, and (c) the time varying nature of the batch process caused by the melt height drop, crucible lift, and crystal lengthening.; To aid control system development, the difference between the linear and nonlinear dynamics is investigated from both system and physics point of view. It is shown that the linear dynamics provides the proper basis for controller design. Variations in the process dynamics are determined as a function of different operating conditions such as the melt height and growth rate and are used to evaluate the need for adaptive control. The actuator effectiveness of pulling speed and heater power is studied in terms of meeting the process objectives. Limitations of the conventional control structure are identified through examination of experimental data. The performance of a new control structure based on controlling the melt surface temperature is evaluated.