Abstract
Accurate modelling of Czochralski crystal growth requires calculating the temperature distribution in the melt, crystal, crucible and the surrounding components of the system, convection and dopant transport in the melt, and the shapes of the melt/crystal and melt-ambient interfaces and the crystal shape. This paper reviews a hierarchy of models designed for analysis of transport processes in Czochralski and liquid-encapsulated Czochralski crystal growth. The models are based on a common thermal-capillary description of the coupling between heat transfer in the melt and crystal and the shapes of the unknown surfaces and on a common finite-element/Newton analysis for simultaneous calculation of the temperature field and interface shapes. This coupling between heat transfer and the surface shapes has been demonstrated by analyses based solely on conductive heat transfer in the melt. The extensions of the thermal-capillary model and the finite-element/Newton method to include melt convection, diffuse-gray radiation and heat transfer in the entire system are discussed. Sample results are presented for the crystal growth of silicon.
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