Simulation of temperature and flow fields in an inductively heated melt growth system

Abstract

The goal of the research presented here is to apply a global analysis of an inductively heated Czochralski furnace for a real sapphire crystal growth system and predict the characteristics of the temperature and flow fields in the system. To do it, for the beginning stage of a sapphire growth process, influence of melt and gas convection combined with radiative heat transfer on the temperature field of the system and the crystal-melt interface have been studied numerically using the steady state two-dimensional finite element method. For radiative heat transfer, internal radiation through the grown crystal and surface to surface radiation for the exposed surfaces have been taken into account. The numerical results demonstrate that there are a powerful vortex which arises from the natural convection in the melt and a strong and large vortex that flows upwards along the afterheater side wall and downwards along the seed and crystal sides in the gas part. In addition, a wavy shape has been observed for the crystal-melt interface with a deflection towards the melt.

Influence of active afterheater on the fluid dynamics and heat transfer during Czochralski growth of oxide single crystals

“…Accordingly, complicated, deep and wavy crystal-melt interfaces have been observed from this set of calculations and also previous works. 3,7,12,19,27,31 This is a useful and basic method to minimize the thermal gradients in the growth chamber for control of the stress within the grown crystal, because large temperature gradients in the crystal can promote thermal stresses increasing the dislocation density in it. In addition, using a suitable active afterheater prevents the production of sufficient stress to crack the crystal during the cooling process.…”

“…The assumptions and mathematical models of induction heating and heat transfer have been described in detail elsewhere. 6,27,[29][30][31] The basic assumptions are: (1) the system is in steady state and is axially symmetric; (2) melt and gas are incompressible Newtonian fluids satisfying the Boussinesq approximation; (3) the flow is laminar and (4) the crystal and melt are assumed to be semitransparent and opaque, respectively. Under these assumptions, a 2D steady state finite element code, which has been developed by the authors, has been employed to solve the governing equations combined with boundary conditions.…”

“…Although the influence of an active afterheater on the heat generation has already been analyzed in detail, 29 its role on the transport processes in the growth system is less well understood and represents a challenging problem of numerical modeling. 3,6,7,18,27,31 The goal of the research presented here is to apply a global analysis of an inductively heated CZ furnace for a real sapphire crystal growth and predict the characteristics of the temperature and flow fields as well as the crystal-melt interface shape in the system due to the different types of passive and active afterheater. Our challenge is to extend the fundamental understanding of the growth process used for crystal growth technology, because this understanding will enable the growers to optimize existing procedures and improve the crystal quality and the design of new growth systems.…”