Three-dimensional stability calculations for hydrodynamic model of Czochralski growth
نویسنده
چکیده
Preliminary results obtained by a code aimed to the analysis of three-dimensional (3D) instability of axisymmetric melt flows in Czochralski crucible are described. The CPU time and the computer memory necessary for the comprehensive 3D stability analysis by a second-order finite volume method are estimated. Basing on a certain experimental configuration, we give an example of the stability diagram which shows how the critical temperature difference varies with the crystal rotation. We also show how critical temperature difference can be significantly increased by a weak rotation of the crucible and report corresponding stability diagrams. r 2006 Elsevier B.V. All rights reserved. PACS: 81.10.Fq; 47.20. k
منابع مشابه
Three-dimensional numerical simulation of temperature and flow fields in a Czochralski growth of germanium
For a Czochralski growth of Ge crystal, thermal fields have been analysed numerically using the three-dimensional finite volume method (FLUENT package). The arrangement used in a real Czochralski crystal growth lab included a graphite crucible, heat shield, heating device, thermal insulation and chamber including two gas outlets. We have considered two cases for calculations, which are configur...
متن کاملNumerical study of three-dimensional instabilities in a hydrodynamic model of Czochralski growth
A computational approach to the study of three-dimensional instabilities of flows in a Czochralski crucible is proposed. The flow is driven by buoyancy, thermocapillarity and rotation of the crystal and the crucible. The thermal boundary conditions account for the prescribed temperatures or heat flux, as well as convective and radiative heating or cooling of the boundaries. The numerical approa...
متن کاملHydrodynamic Instabilities in Czochralski Process of Crystal Growth
Abstract. This paper deals with axisymmmetry breaking instabilities in Czochralski process of crystal growth. Numerical linear stability analysis was carried out using the axisymmetric bulk flow model. Stability diagrams of critical Grashof numbers Grc and frequencies ωc dependent on aspect ratio α(=height/radius), 0.4 ≤ α ≤ 1.0 and Prandtl number Pr = 0.01 are shown. Computations were carried ...
متن کاملThree-dimensional calculations of the magnetic fields in a finite superconducting hollow cylinder in an applied axial magnetic field
In this study, a set of self-consistent coupled-integral equations for the local magnetic flux and current distributions in a finite superconducting hollow cylinder under an axial magnetic field has been directly derived by using the Biot-Savart law within the framework of the critical-state model. The equations were first solved numerically in the three-dimensional space before obtaining the h...
متن کاملHybrid Finite-element/finite-volume Method for Integrated Hydrodynamic Thermal Capillary Analysis of Turbulence and Heat Transfer of Czochralski Crystal Growth of Silicon
Modeling turbulent convection in the melt is the most di cult part of the simulation of the transport processes in the growth of large-diameter silicon crystals by the Czochralski (CZ) process. We report the application of hybrid nite-element/ nitevolume methods for the integrated modeling of turbulence in the melt and heat transfer by conduction, convection and radiation throughout the CZ syst...
متن کامل