Mechanism of Crystal Twisting during Czochralski Si Growth: A Modeling Study

Abstract

During the constant-diameter growth of Czochralski Si single crystals, excessively high pulling speeds can induce a “crystal twisting” phenomenon, which degrades crystal quality. In this study, numerical simulations using CGSim software combined with theoretical analysis are employed to investigate the formation mechanism of crystal twisting. The solid–liquid interface morphologies, temperature distributions, and melt convection patterns are analyzed at pulling speeds of 30, 60, and 90 mm/h for a 300 mm diameter Si crystal. The results show that when the pulling speed reaches 90 mm/h, an annular undercooling zone appears near the triple point, transforming the interface from concave/flat to convex. This undercooling zone triggers local asymmetric protrusion growth. Under the response lag of the diameter control system and the coupling effect with crystal rotation, the asymmetry evolves into spiral twisting and axis deviation. A critical criterion is proposed, stating that the ratio of ΔZ (the height of the highest point of the growth interface above the melt surface) to the crystal diameter exceeds approximately 8% under twisting conditions. Furthermore, a mathematical model linking the axial fluctuation spacing, pulling speed, radial growth velocity, and thermal field gradient is established. This work provides quantitative guidelines for optimizing pulling speed and preventing crystal twisting.