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. The current breadth of this industry makes the method indespensible. The International Technology Roadmap for Semiconductors forecasts the use of 35 nm technology on 64 Gbit DRAM and 10 GHz processor speeds by the end of this decade. This implies the need for higher quality crystals, and therefore improved growth systems. Furthermore, 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 current state of the system as well as the predicted path of the industry served to motivate development of a new control scheme. The first objective of this work was to develop or enhance a first-principles based model of the process. This model must be kept at a manageable order to accommodate online simulation while still capturing the dominant process physics. The model must also be formulated as a time differential equation in order to apply the desired control theories. The second objective of this work was to answer industry's question regarding elimination of pull rate as a manipulated input. The final objective of this work was to use the model to design a new control algorithm. The control development includes consideration of the time delay between heater and the crystal. The work is based on silicon growth, but the developments are kept as generic as possible for future application to other materials. Data from industry crystal growths as well as experimental results reported in literature will be used to gauge the effectiveness of the new designs.