Numerical study of three-dimensional instabilities in a hydrodynamic model of Czochralski growth

Alexander Gelfgat; A. Rubinov; P. Z. Bar-Yoseph; A. Solan

doi:10.1016/j.jcrysgro.2004.10.116

Numerical study of three-dimensional instabilities in a hydrodynamic model of Czochralski growth

Alexander Gelfgat^*, A. Rubinov, P. Z. Bar-Yoseph, A. Solan

^*Corresponding author for this work

School of Mechanical Engineering

Technion-Israel Institute of Technology

Research output: Contribution to journal › Conference article › peer-review

16 Scopus citations

Abstract

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 approach is based on finite volume discretization and consists of a Newton-type solver for the calculation of the steady flow states and an Arnoldi solver for the solution of the eigenvalue problems associated with the linear stability of the flow. Preliminary test calculations and examples of stability studies for the Czochralski melt flow are reported.

Original language	English
Pages (from-to)	e7-e13
Journal	Journal of Crystal Growth
Volume	275
Issue number	1-2
DOIs	https://doi.org/10.1016/j.jcrysgro.2004.10.116
State	Published - 15 Feb 2005

Funding

Funders	Funder number
Asher Space Research Institute, Technion

Keywords

A1. Computer simulation
A2. Czochralski method
Fluid flows
Instabilities

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10.1016/j.jcrysgro.2004.10.116

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abstract = "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 approach is based on finite volume discretization and consists of a Newton-type solver for the calculation of the steady flow states and an Arnoldi solver for the solution of the eigenvalue problems associated with the linear stability of the flow. Preliminary test calculations and examples of stability studies for the Czochralski melt flow are reported.",

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AU - Gelfgat, Alexander

AU - Rubinov, A.

AU - Bar-Yoseph, P. Z.

AU - Solan, A.

PY - 2005/2/15

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N2 - 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 approach is based on finite volume discretization and consists of a Newton-type solver for the calculation of the steady flow states and an Arnoldi solver for the solution of the eigenvalue problems associated with the linear stability of the flow. Preliminary test calculations and examples of stability studies for the Czochralski melt flow are reported.

AB - 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 approach is based on finite volume discretization and consists of a Newton-type solver for the calculation of the steady flow states and an Arnoldi solver for the solution of the eigenvalue problems associated with the linear stability of the flow. Preliminary test calculations and examples of stability studies for the Czochralski melt flow are reported.

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KW - A2. Czochralski method

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KW - Instabilities

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Numerical study of three-dimensional instabilities in a hydrodynamic model of Czochralski growth

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