(12d) Model Development and Control Strategies for Multicomponent Alloy Solidification Processes and Its Application to Solar Cell Manufacturing

In this work we present the mathematical description and a control formulation of solidification processes and their application to the manufacturing of high purity silicon wafers suitable for solar cells.  We apply the results to prove a novel continuous process to produce the wafers from the melt. The theoretical work is part of a larger research program that also involves experimental and computational work. The conceptual design consists of producing a thin film of silicon on top of the melt, making use of the fact that solid silicon floats on its melt just like ice floats on water.  These ideas serve as our main motivation to put our investigation in the context of renewable energies. Model development provides a significant aid in understanding transport phenomena taking place in the system and developing techniques to control it.

The process of solidification involves the segregation of impurities into the melt, which, from a process systems perspective, is a purification process. This is beneficial because we are producing the desired material while purifying it. Purity requirements of solar grade silicon are very stringent in order to achieve optimal solar cell efficiency, and the current processes to produce it need to be carefully managed and controlled [1]. Mathematical models can be used to calculate the extent of purification that can be achieved through solidification of a thin silicon film and its dependence on the system dynamics, specifically, the velocity of the crystallization front and the temperature gradients at the solid-liquid interface, which are intrinsically coupled.  At high interfacial velocities, the formation of a solute enriched boundary layer next to the crystallization front leads to potential interfacial instabilities that affect the quality of the final product [2].

Previous studies [3] provided the initial insights into many aspects of the proposed process through the decoupling of convection in the melt and solidification dynamics for pure silicon.  In this work we extend the formulation to metallurgical grade silicon (multicomponent alloy). Using a finite-difference model, it is shown that for a simple silicon-aluminum alloy, there is an optimal interface velocity where the segregation of impurities achieves complete mixing of the melt and the disappearance of the boundary layer. The model is validated via sensitivity analysis. Process control strategies are also developed to achieve an optimal solute distribution in the melt, by adjusting the heat released and supplied to the system.

[1] Brown,R.A, Theory of Transport Processes in Single Crystal Growth from the Melt, AIChE Journal, 34,881-911,1988.

[2] Mullins, W.W., Sekerka, R.F. Stability of a Planar Interface during solidification of a dilute binary alloy, Journal of Applied Physics, 35,444-451, 1964.

[3] Ruochen Liu, German Oliveros, Sridhar Seetharman and B. Erik Ydstie, Multiscale Modeling of a Silicon Solar Wafer Manufacturing Process, 21st European Symposium on Computer-Aided Process Engineering, 2011, Accepted.