Theoretical Modeling of Czochralski Crystal Growth

Abstract

The growth of single crystals with precisely controlled properties is one of the most demanding goals of modern materials processing, and its realization depends on the application of fundamentals from solid-state physics, chemistry, thermodynamics, and transport phenomena. Bulk semiconductor substrates and many high-power solid-state laser host materials are typically produced by solidification from the melt. The quality of the crystals produced this way hinges on process conditions which are predominantly determined by the transport of heat, mass, and momentum in the melt and crystal. Accurate modeling of melt crystal growth promises to enhance our understanding of existing systems and improve the design and control of future processes, thereby accelerating the development of advanced materials and devices.Theoretical modeling is often the only way to probe the complex interactions which characterize melt crystal growth, especially the effects of process changes on internal features of growth that cannot be directly measured on-line, such as the shape of the melt/crystal interface or temperature gradients within the growing crystal. In this way, computer simulation can serve as a design tool for developing control strategies and process innovations. Further, modeling serves as a test-bed for theoretical experiments which extend our knowledge of how fundamental physical phenomena govern the process.This report attempts to provide a glimpse of how analysis and modeling have impacted the understanding of Czochralski (CZ) crystal growth. The reader is referred to several excellent reviews for more in-depth information regarding melt crystal growth modeling.