(169d) Stability Analysis of Solar Silicon Wafer Manufacturing By the Horizontal Ribbon Growth Process

The increasing demand for energy and the prospect of global warming urges the world community to seek cleaner and cheaper energy resources to replace non-renewable fossil fuels. The silicon based photo-voltaic system is one of the most promising renewable energy resources. Its application has grown rapidly during the past 2-3 decades as production cost has been reduced and the potential for application is virtually without limit.

This promotes the project of cost reduction for silicon wafer via different technology development. Traditional silicon growth processes are either expensive or compromise the material efficiency for faster production speed. The horizontal ribbon growth (HRG) process has the potential to overcome these limitations. In the HRG process, heat is removed through the top surface of the molten silicon pool, meanwhile, a thin silicon solid sheet is produced and extracted continuously. However, despite the theoretical and experimental efforts to develop and commercialize this technology for more than 60 years, many technical challenges have been reported to achieve a stable and fast ribbon production.

One of the principal challenges encountered is the instability at the wafer-melt interface due to various coupled effects. Theoretical studies have been developed for the instabilities during unidirectional solidification. In 1964, Mullins and Sekerka developed the foundation for the thermal and solutal conditions to ensure the stable crystallization front under an arbitrary sinusoidal perturbation of infinitesimal amplitude to the interface [1]. However, the flow pattern in the melt during the crystallization also plays an important role on the impurity distribution, which alters the micro-structure and macro material property of the grown crystal. This flow pattern can be induced by the rotation of the crucible or crystal, withdrawal of the material, density change during crystallization, etc. Coriell and Sekerka performed extensive studies in the coupled convective and morphological instabilities. [2][3]

In this work, we developed a linear stability theory to study the crystallization interface of the Horizontal Ribbon Growth (HRG) process. The conditions for the onset of stability are investigated theoretically and numerically on the basis of diffusion-convection equations for the thermal, solutal fields coupled to the Navier-Stokes equation describing the flow field in the molten pool near the interface. In order to understand the unexplained â??facet linesâ? observed in the experiments, the interface stability conditions of the system under different operating conditions are tested.

1. Mullins, W. W., & Sekerka, R. F, â??Stability of a planar interface during solidification of a dilute binary alloy,â?Â Journal of applied physics, 35(2), 444-451(1964).
2. Coriell, S. R., Cordes, M. R., Boettinger, W. J., & Sekerka, R. F, â??Convective and interfacial instabilities during unidirectional solidification of a binary alloy,â?Â Journal of Crystal Growth, 49(1), 13-28 (1980).
3. Coriell, S. R., McFadden, G. B., Boisvert, R. F., & Sekerka, R. F, â??Effect of a forced Couette flow on coupled convective and morphological instabilities during unidirectional solidification,â?Â Journal of crystal growth,69(1), 15-22 (1984).