Modeling And Control Of The Czochralski Crystal Growth Process

The Czochralski process is a method of pulling crystal from the melt that is widely used by the semiconductor industry. By the end of this decade, the need for higher quality crystals and improved growth systems is fiercely. Toward control structure, industry has noted a problem with rapid pull rate variation contributing to structural defects in the grown crystals. It was proposed by industry to investigate elimination of the pull rate as a control input.The first objective of this thesis was to develop a mathematical model of the crystal growth process based on energy and quality balance. The model must be kept at a manageable order to accommodate online simulation while still capturing the dominant process physics. The basic model and radiation-enhanced model have been established based on approximate and precise view factor solutions. The model must also be formulated as a time differential equation in order to apply the desired control theories. The nonlinear dynamic process of Czochralski crystal growth is studied by the perturbation method. The solution of this method can be used to predict, quantitatively, how a crystal growth with constant crystal radius is perfectly controlled by the desired of crystal pull rate and bulk melt temperature. The third objective of this thesis was to use the linear model design a advance PID control scheme. Using Artificial Neural Network and Genetic algorithm formulate BP-PID, RBF-PID and GA-PID control strategy optimize PID parameter. Simulation result express the advance-PID structure more stable, fast and accurate than the common PID control scheme. The final objective of this thesis was to design the high resolution weighing system using ADuC824, and the system effective resolution has reached 2/10000. Weighing system as one of the most important component part of the whole control structure, bring the feedback weigh signal directly to the input and the weight error is the whole system driving force. The main recreations include introduce LaPlace-Young equation, establish the most outstanding character of crystal growth process-meniscus contact angle state equation and research the relationship between meniscus contact angle and other meniscus state values. Establish the enclosure region above melt inside the crucible radiation heat transfer circuit analogy which make the solution of system heat transfer become convenient. Through research on the dynamic of nonlinear crystal growth process, the melt height trajectory has gained. Besides it is found that for growth under constant bulk temperature(pull rate), the pull rate(bulk melt temperature)will increase with increasing ambient Biot number and/or decreasing melt Biot number. Furthermore, if the melt cannot be super cooled, we can formulate themaximum pull rate analytically.