6533b853fe1ef96bd12ac01e

RESEARCH PRODUCT

Time-dependent simulation of Czochralski silicon crystal growth

Timo TiihonenRisto M. NieminenJari Järvinen

subject

ConvectionComputer simulationChemistryLaminar flowMechanicsCondensed Matter PhysicsThermal conductionFinite element methodPhysics::Fluid DynamicsInorganic ChemistryMonocrystalline siliconClassical mechanicsHeat transferMaterials ChemistryBoundary value problem

description

We have developed a detailed mathematical model and numerical simulation tools based on the streamline upwind/Petrov-Galerkin (SUPG) finite element formulation for the Czochralski silicon crystal growth. In this paper we consider the mathematical modeling and numerical simulation of the time-dependent melt flow and temperature field in a rotationally symmetric crystal growth environment. Heat inside the Czochralski furnace is transferred by conduction, convection and radiation, Radiating surfaces are assumed to be opaque, diffuse and gray. Hence the radiative heat exchange can be modeled with a non-local boundary condition on the radiating part of the surface. The position of the crystal-melt interface is solved by the enthalpy method. The melt flow is assumed to be laminar and governed by the cylindrically symmetric and incompressible Navier-Stokes equations coupled with the calculation of temperature.

yearjournalcountryeditionlanguage
1997-10-01Journal of Crystal Growth
https://doi.org/10.1016/s0022-0248(97)00310-2