Three-Dimensional Simulation of Melt Convection and Oxygen Transport in CZ-Si Crystal Growth with Cusp Magnetic Fields

Abstract

The application of magnetic fields has become a standard control technique in the CZ-Si growth industry. To investigate the impact of cusp-shaped magnetic fields (CMF) on heat and mass transfer in the melt, a series of transient three-dimensional simulations were conducted for the growth of a 100 mm CZ-Si crystal with a cylindrical crucible. The turbulent melt motion was modeled using the large eddy simulation (LES) method. Six configurations of CMF with various zero-Gaussian plane (ZGP) positions were examined and numerically compared. The computed results showed that different ZGP positions resulted in distinct types of melt convection, buoyant plumes, and thermal waves. Additionally, it was observed that the studied CMF configurations effectively reduced oxygen dissolution from the crucible wall along with oxygen impurity incorporation into the crystal. These findings demonstrate the potential for precise control of the heat and mass transfer process in CZ-Si growth through the application of suitable CMF.

Keywords

• Czochralski method
• numerical simulation
• large eddy simulation
• melt convection
• oxygen transport
• cusp magnetic field