Nonmixing Cells due to Crucible Rotation during Czochralski Crystal Growth

Abstract

The presence of a stationary crystal in a rotating liquid gives rise to a stationary liquid cell beneath the crystal as predicted from the Taylor‐Proudman theorem. Outside this cell, the liquid rotates as an almost solid body, while inside the cell it is shown that a predictable inner flow must arise. The effects of combined crystal and crucible rotations produce a resultant force field which controls the convection. The liquid flow patterns are discussed in detail. The presence and form of thermal convection in rotating liquids are discussed specifically for typical conditions occurring during Czochralski growth. The observation of such flow behavior must be made carefully, since the relative observer motion effect can obscure the essential flow patterns. Previously observed effects as well as observations and measurements from new simulation experiments are explained by the treatment. Stagnation surfaces which prevent complete bulk liquid mixing in the crucible exist for all cases, except when the crucible rotation rate is zero. When crystal and crucible rotate in the same direction one stagnation surface separates two nonintermixing regions; during counterrotation there can be two stagnation surfaces and three nonintermixing regions. Practically speaking, the stagnation surfaces are absent when the crucible rotation rate is very small compared to the crystal‐rotation rate.