Interfacial instabilities during the solidification of a pure material from its melt.

摘要

Solidification of materials is important in the semiconductor and electronics industry. It is ordinarily required that crystals grown industrially have uniform mechanical and electrical properties to ensure better quality and reproducibility of the final devices that are produced from them. Thus there is a considerable economic incentive in producing uniform crystals. However, the occurrence of morphological defects at the growing solidification interface arising from growth instabilities leads to undesirable electro-mechanical properties of such crystals. It is the goal of this work to thoroughly understand the physics and causes of morphological instability in solidification.; Inasmuch as the problem of morphological instability of a solid-liquid interface has been considered in the past, many questions remain unanswered. Of central interest is the pattern that evolves when an instability occurs. To begin to answer this question one begins to address the earlier question of what the magnitude of the wavelength of the initial instability might be. My research focuses on this earlier issue. And a set of questions begin to present themselves. They are: What is the reason for the instability at a solid-liquid interface? When does the instability set in? How can one explain the dependence of roughness growth rate on its wave number? Why is a maximum growth rate seen in problems like precipitation and solidification? What happens after the instability sets in? Does the front speed up or slow down compared to its predicted base value? Why are cellular patterns observed in solidification whereas precipitation is incapable of giving anything as interesting? Can one determine the nature of the branching to the non-planar steady state in the post-onset regime? Many important findings have been made in the course of answering these questions.; The primary discoveries of this work are: First, the shapes of the disturbance growth curves in solidification require the effect of transverse heat diffusion for their explanation. The neutral curves in solidification are found to give rise to the possibility of a cellular pattern at the onset of instability whereas for other solid-liquid front growth problems independent of thermal transport, such as precipitation from a supersaturated solution or electrodeposition of a metal from an ionic electrolyte, the onset of an instability from a planar state leads to a single crest and trough. Second and more important, a solid-liquid front that grows on account of temperature gradients is the only one amongst all solid-liquid front growth problems where a critical wavelength, independent of surface energy, can occur. This critical wavelength is of the order of the size of the container in which the growth takes place and as such is the only critical point with which fluid convection can interact. Third, a solidification front always demonstrates a "speed-up" upon becoming unstable, which is to say that it always moves ahead of its predicted base value. This is in contrast with other solid-liquid growth instability problems like precipitation. Finally the nature of the bifurcation in a solid-liquid growth problem where growth occurs on account of thermal gradients may be a forward pitchfork, leading to cellular growth, or a backward pitchfork, leading to dendritic growth. This stands in contrast to other growth problems where the post onset region is ordinarily characterized by dendritic growth.