(6bn) Computational Models for Growth and Defects of Melt-Grown Crystals

Computational models for growth and defects of melt-grown crystals

Crystals form the basis of many technologies.  While semiconductor devices and solar cell industries rely on high quality crystalline silicon (Si) wafers, laser and radiation detector technologies use high quality fiber crystals of materials like sapphire.  In order to make high quality crystals, it is crucial to develop an understanding of the crystal growth processes.  Computational models can provide invaluable insights into the crystal growth process.  For example, a thermal-capillary model of a fiber growth process known as “Micro-pull-down” (μ-PD) can reveal operating limits and the underlying mechanisms.  In an investigation of sapphire fiber growth through μ-PD, we have used a thermal-capillary model to find various failure modes of the process and identified underlying mechanisms.

            On the other hand, it is a formidable challenge to control the amount of defects in crystals grown from commercial growth processes like “Czochralski” (Cz).  Controlling the quantity of defects in crystals is necessary for successful development of any device technology based on them.  Computational modeling of defects can provide quantitative predictions which can be used to successfully engineer them.  For example, using classical nucleation theory (CNT) based model of oxygen precipitation in Cz-Si, the number density of oxygen precipitates can be quantitatively estimated as a function of time and temperature.  We have developed a new nucleation rate model which is more suitable for quantitative estimation of oxygen precipitate density nucleated at temperatures lower than 750 C.    

            As we continue to develop new computational models and improve current ones to better predict crystal growth and defects, it is also important to teach these approaches to future generations.  One effective way to teach computational methods is by engaging the students in the development of a full simulation.  The full simulation problem may be disintegrated into several sub-problems which covers the entire coursework.  Complexities can be reduced by using an established solver platform to develop the simulation.