Multifrequency eddy current diagnostics of axial and radial thermal profiles during silicon crystal growth

Abstract Two-dimensional thermal profiles of growing Czochralski silicon crystals have been determined in situ using an eddy current probe. An analysis of multifrequency eddy current data was accomplished by modelling the interactions of the induced electromagnetic fields with the growing crystal and silicon melt. A two-dimensional numerical solution of the governing electromagnetic wave equation derived from Maxwell's relations was employed to translate multifrequency data into axial and radial crystal thermal profiles. Experiments were conducted in a resistance-heating type CZ puller with a 203 mm (8 inch) hot-zone and 6.5 kg charge capacity. The silicon crystals grown were 80 mm in diameter and monitored with an encircling eddy current coil. It was found that crystal thermal profiles are greatly influenced by the radiant interaction with the environment and crucible position within the hot-zone. Some of the eddy current data were correlated with heat transfer model calculations as well as experimental measurements found in the literature. Heat transfer model predictions were consistent with our crystal surface temperature measurements. However, the radial gradients near the crystal surface were larger than those predicted by the same heat transfer models. This finding is significant since any sharp gradients can be responsible for creep damage during growth.