Analysis of Droplets and Bubbles in Crystal Growth Processes: Migration and Engulfment

Abstract

The crystal growth process for certain materials faces the problem of foreign particles, drops or bubbles getting lodged into the solid as it is grown. There can be significant risks associated with such impurities. In materials such as sapphire and silicon being grown from the melt, bubbles could enter the melt phase and make their way into the crystal by the process of engulfment. This is very commonly observed in sapphire crystals. There is also a chance for growth instabilities during certain solution growth processes, which could result in pockets of high solute concentration in certain places. This has been seen in scintillator crystals such as cadmium zinc telluride and even Arctic ice. This work is divided into two parts. In the first part, the engulfment of bubbles into a crystal is studied using detailed finite element modelling. The effect of various process parameters is studied and an effort is made to understand process conditions under which such engulfment can be avoided. In the second part, a simplified one-dimensional transport model is developed for the temperature gradient zone melting technique, in which a thermal gradient is applied across a solid to move any liquid drops stuck inside it to one end of the sample. Analytical expressions for drop size, speed and position as a function of time are derived for a drop undergoing such thermal migration. The derivation is also used to gain insight into process physics and some important time scales.