Model experiments for melt flow in Czochralski growth of silicon

Abstract

The melt flow plays a key role in the Czochralski (Cz) growth of silicon crystals, and in-situ measurement data are crucial for efficient process development. We present new low-temperature model experiments and numerical simulations for Cz type melt flow studies. A novel cylindrical setup is equipped with a traveling magnetic field (TMF), and with an advanced ultrasound (US) based measurement technique for 2D flow imaging. The setup has been designed for comprehensive flow measurements in a GaInSn melt under well-defined thermal and TMF forcing conditions to generate as exact as possible experimental data to validate flow simulations. The applied numerical models combine time-dependent 3D flow calculations under adjusted heat flux boundary conditions with a 2D treatment of the Lorentz force. The dependence of the buoyant flow on the boundary conditions as well as the interaction between the buoyant flow and a symmetric TMF-forced flow are studied in detail. Special attention is paid to the investigation of flow transitions between symmetric toroidal and non-symmetric roll-like structures. In terms of the dimensionless Grashof (Gr) and magnetic forcing (F) numbers, such transitions are found to occur at around Gr = 3 × 107 and for F < Gr. The results are compared with recent studies in the literature, and a concept to transfer experimental and numerical flow modeling to real Cz growth of silicon is briefly outlined. The observed flow structures may significantly influence the convective heat and mass transport in Cz growth.