Modeling and Stability of the Horizontal Ribbon Growth Process

<p>This thesis contains a theoretical analysis of the Horizontal Ribbon Growth (HRG) process for growing silicon wafers. In the HRG process, a thin silicon ribbon is crystallized and extracted continuously from the melt, using the fact that silicon oats on its melt just like ice oats on top of water. In our work, we assess two technical issues reported in previous experimental studies: meniscus stability and interface stability. The first law of thermodynamics along with the tools of variational calculus are used to find the existence and stability conditions of the meniscus formed between the silicon wafer and the surface of the crucible. Analytical expressions describing the shapes of the meniscii are found in terms of a single-valued function and in parametric form. These functions give the feasible configurations of the HRG system in terms of operating parameters and material properties, such as ribbon length and thickness, melt level, pulling angle, contact angle, and crucible edge geometry. From the existence conditions we show that the feasible configurations place a part or the entire meniscus above the melt level. The stability condition shows that every part of the meniscus must remain above the surface of the crucible. A dynamic crystallization model that incorporates an extended version of the Mullins-Sekerka analysis describes the stability of the solid-liquid interface. The effect of solute segregation in the system and its effect on interface stability is measured as a function of the crystallization velocity. Two surface cooling methods-active and passive- are used to model the crystallization of a silicon ribbon of a given thickness. We show that low temperature gradients promote the homogeneous segregation of impurities in the melt, whereas high temperature gradients induce the formation of a solute enriched boundary layer. For both cases we found the thermal conditions that impede the growth of applied sinusoidal perturbations to the interface. We found that setting the crystallization model in a Lagrangean frame of reference provides an alternative way to calculate the shape of the silicon wafer.