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Mathematical modeling and numerical simulation of Czochralski Crystal Growth

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Abstract

A detailed mathematical model and numerical simulation tools based on the SUPG Finite Element Method for the Czochralski crystal growth has been developed. In this presentation the mathematical modeling and numerical simulation of the melt flow and the temperature distribution in a rotationally symmetric crystal growth environment is investigated. The temperature distribution and the position of the free boundary between the solid and liquid phases are solved by using the Enthalpy method. Heat inside of the Czochralski furnace is transferred by radiation, conduction and convection. The melt flow is governed by the incompressible Navier-Stokes equations coupled with the enthalpy equation. The melt flow is numerically demonstrated and the temperature distribution in the whole Czochralski furnace. (author)
Authors:
Jaervinen, J; Nieminen, R [1] 
  1. Center for Scientific Computing, Espoo (Finland)
Publication Date:
Dec 31, 1996
Product Type:
Conference
Report Number:
TKK-V-B117; CONF-9606318-
Reference Number:
SCA: 360602; PA: FI-97:003307; EDB-97:062101; SN: 97001773814
Resource Relation:
Conference: 3. colloquium on process simulation, Espoo (Finland), 11-14 Jun 1996; Other Information: PBD: 1996; Related Information: Is Part Of The 3rd colloquium on process simulation. Proceedings; Jokilaakso, A. [ed.]; PB: 359 p.
Subject:
36 MATERIALS SCIENCE; CZOCHRALSKI METHOD; FLOW MODELS; HEAT TRANSFER; FINITE ELEMENT METHOD; SIMULATION
OSTI ID:
464570
Research Organizations:
Helsinki Univ. of Technology, Otaniemi (Finland). Lab. of Materials Processing and Powder Metallurgy
Country of Origin:
Finland
Language:
English
Other Identifying Numbers:
Other: ON: DE97740683; ISBN 951-22-3092-5; TRN: FI9703307
Availability:
OSTI as DE97740683
Submitting Site:
FI
Size:
pp. 373-399
Announcement Date:
May 14, 1997

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Citation Formats

Jaervinen, J, and Nieminen, R. Mathematical modeling and numerical simulation of Czochralski Crystal Growth. Finland: N. p., 1996. Web.
Jaervinen, J, & Nieminen, R. Mathematical modeling and numerical simulation of Czochralski Crystal Growth. Finland.
Jaervinen, J, and Nieminen, R. 1996. "Mathematical modeling and numerical simulation of Czochralski Crystal Growth." Finland.
@misc{etde_464570,
title = {Mathematical modeling and numerical simulation of Czochralski Crystal Growth}
 author = {Jaervinen, J, and Nieminen, R}
 abstractNote = {A detailed mathematical model and numerical simulation tools based on the SUPG Finite Element Method for the Czochralski crystal growth has been developed. In this presentation the mathematical modeling and numerical simulation of the melt flow and the temperature distribution in a rotationally symmetric crystal growth environment is investigated. The temperature distribution and the position of the free boundary between the solid and liquid phases are solved by using the Enthalpy method. Heat inside of the Czochralski furnace is transferred by radiation, conduction and convection. The melt flow is governed by the incompressible Navier-Stokes equations coupled with the enthalpy equation. The melt flow is numerically demonstrated and the temperature distribution in the whole Czochralski furnace. (author)}
 place = {Finland}
 year = {1996}
 month = {Dec}
 }