(298d) Stable Configurations in the Horizontal Ribbon Growth Process

In the Horizontal Ribbon Growth (HRG) process, a thin crystal ribbon is produced and extracted continuously from a molten substrate. The advantage of this technique is its capacity to achieve large rates of production compared to conventional crystal growth processes, such as the Czochralski and Bridgman. However, despite its potential and efforts to develop the technology for more than 50 years, many technical and experimental challenges have been reported regarding the difficulty in trying to maintain a continuous and stable ribbon production.

One of the principal causes of disruption is the freezing of the ribbon to the end of the crucible. The reason for this is that there is no melt present between the ribbon and the crucible. The solid surface of the crucible offers plenty of nucleation points for the ribbon to crystallize onto as it is being pulled. The opposite problem can also arise: an excess of melt flow that causes the melt to spill over the crucible. In an ideal operation, a space between the ribbon and the lip of the crucible must be maintained to avoid undesired nucleation points, and a meniscus must be pinned between the crucible lip and the ribbon to avoid melt spill-over.

In this work, we present a theoretical analysis to assess these technical difficulties. We analyze the conditions under which a meniscus exists between the ribbon and the crucible and stays pinned to its corner, as well as the allowable range of melt levels that give rise to stable menisci. Assuming that the existence of the meniscus is defined by hydrostatics, we use a theoretical model based on the governing Young-Laplace equation to solve analytically for the shape of the meniscus. Then, we show the range of operating conditions that are physically viable in a silicon system, and construct the possible stable configurations. We show that these stable configurations depend mainly on the pulling angle, the melt level, and the type and shape of the crucible.