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Comparison of the Oxygen Concentration in Czochralski Silicon Crystal Obtained by a Simple Lumped-Parameter Model and Sophisticated 2D-3D Simulations
J. Friedrich, M. Trempa, H. Koch, F. Mosel, A. Mühe
Czochralski (Cz), Crystal Growth, Silicon, Convection, Computer Simulation
Silicon Materials and Cells
Subtopic: Feedstock, Crystallisation, Wafering, Defect Engineering
Event: 38th European Photovoltaic Solar Energy Conference and Exhibition
Session: 2DV.4.4
347 - 351
ISBN: 3-936338-78-7
Paper DOI: 10.4229/EUPVSEC20212021-2DV.4.4
0,00 EUR
Document(s): paper, poster


In the present work a simple boundary layer model for the oxygen transport during Cz silicon crystal growth is revisited and extended by introducing classical scaling laws for the thicknesses of the different boundary layers at the crucible wall, at the free melt surface and at the solid-liquid interface. This lumped model is used to calculate the influence of crystal and crucible rotation on the oxygen transport during Cz growth of 100kg heavy silicon crystals with 210mm diameter in a 24” hot zone geometry. The results of this reduced order model are compared to results from sophisticated, coupled 2D-3D, global numerical simulations of the whole Cz puller. It is found that at a first glance the accuracy of the boundary layer model can be sufficient for certain coarse case studies. However, the boundary layer model hits quickly the wall, when a precise analysis of the oxygen transport is required. The root cause is believed to be the complex flow structure, which results from the combination of crystal and crucible rotation in the vicinity of the solid-liquid interface. For an accurate analysis of oxygen transport sophisticated simulations are indispensable.