Thermal Transport During Seeding and Shouldering in the Czochralski Crystal Growth

Czochralski (Cz) growth during seeding and shouldering of silicon single crystal has been studied. During seeding, the diameter increases from a small value to the desired value of the fully-grown crystal. The convection in the melt, conduction in the crystal and radiation from the melt surface and crystal, surface tension at the free surface of the melt and crystal rotation have been considered to investigate the effect of seeding on thermal transport. The rotational Reynolds number, the radiation from the crystal and Marangoni number are varied to investigate their effect on the interface shape. A few selected cases have been studied using a cylindrical crystal to understand the effect of geometry on the heat transfer rate and subsequently on the interface shape. The governing equations are solved using the curvilinear finite volume discretization scheme and the grids are redistributed using the multizone adaptive grid generation after each iteration. The movement of free surface is taken care by employing suitable equations for energy and stress balance. Results show the dependency of both the radiation from the crystal and rotation of the crystal on the interface shape.