Effect of crystal rotation on the three-dimensional mixed convection in the oxide melt for Czochralski growth

Abstract

The three-dimensional flow field in the melt has significant effect on the quality and stability of the growing oxide single crystal by the Czochralski method. The flow field exhibits different characteristics in terms of periodic and non-periodic three-dimensional nature depending on the process parameters. In this paper, the role of crystal rotation rate on the characteristics of the three-dimensional turbulent flow field in the oxide melt has been studied. Based on a block-structured finite-volume Navier–Stokes solver, quasi-direct numerical simulations were carried out to analyze the flow field in a crucible with different crystal rotation rates from 0.0 to 6.0 rpm. The crystal rotation rate has been found to be a sensitive parameter and has a significant effect on the characteristics of the flow field. While the flow field with a crystal rotation rate of 4.0 rpm (Gr/Re 2=343) attains a non-periodic state from the initial periodic state, the flow field with a crystal rotation rate of 6.0 rpm (Gr/Re 2=192) remains always periodic. It was shown that the criterion of (Gr/Re 2<235) as recently proposed by the authors [S. Enger, B. Basu, M. Breuer, F. Durst, J. Crystal Growth 219 (2000) 144] could be used to ensure periodic thermal and flow field in the melt during the growth of oxide crystals.