Quantitative assessment of an integrated hydrodynamic thermal-capillary model for large-diameter Czochralski growth of silicon: comparison of predicted temperature field with experiment

Abstract

Accuracy in the prediction of the thermal field in a Czochralski (CZ) crystal growth system is crucial for quantitative application of models. Predictions of the integrated hydrodynamic thermal-capillary model (IHTCM) are compared to experimental measurements of the thermal field from growth of 83 mm diameter crystals and the melt/crystal interface shape of a 100 mm diameter crystal obtained in a conventional CZ system. The temperature measurements show good quantitative agreement with predictions irrespective of the model for melt convection. However, the predicted melt/crystal interface shape is much more sensitive to the type and state of convection in the melt. The IHTCM includes steady-state laminar flows driven by crystal and crucible rotation, natural convection and thermocapillarity. Although flows at the correct intensity can be computed for each mechanism separately, solutions for the combined driving forces only are found when the viscosity of the melt is set artificially high. Calculated values of the thermal stress in the crystal exceed the critical resolved shear stress near the melt/solid interface for all flow conditions. The maximum stress at the melt/solid interface depends on the interface shape and varies between 2.8 and 6.2 times the critical resolved shear stress, depending on the flow.