Mathematical modelling of the Czochralski crystal growth process

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dc.contributor.advisorMyers, Timothy Gen_ZA
dc.contributor.authorBrakel, Thomas Wen_ZA
dc.date.accessioned2014-07-31T08:06:23Z
dc.date.available2014-07-31T08:06:23Z
dc.date.issued2006en_ZA
dc.descriptionIncludes bibliographical references (leaves 142-149).
dc.description.abstractIn this document a mathematical model for the Czochralski crystal growth process is developed. The trend in current research involves developing cumbersome numerical simulations that provide little or no understanding of the underlying physics. We attempt to review previous research methods, mainly devoted to silicon, and develop a novel analytical tool for indium antimonide (lnSb) crystal growth. This process can be subdivided into two categories: solidification and fluid mechanics. Thus far, crystal solidification of the Czochralski process has been described in the literature mainly qualitatively. There has been little work in calculating actual solidification dynamics. Czochralski crystal growth is a very sensitive process, particularly for lnSb, so it is crucial to describe the system as accurately as possible. A novel ID quasi-steady method is proposed for the shape and temperature field of an lnSb crystal, incorporating the effects of the melt. The fluid mechanics of the Czochralski melt have been modelled by numerous researchers,with calculations performed using commercial software. However, a descriptionof the buoyancy and rotation interaction in the melt has not been adequatelyperformed. Many authors have presented flow patterns but none have indicated either: melt conditions preferential for crystal growth or at least a description of a typical melt structure. In this work, a scale analysis is performed that implies an idealized flow structure. An asymptotic model is then derived based on this order of magnitude analysis, resulting in a fast and efficient fluid flow calculation. The asymptotic model is validated against a numerical solution to ensure that the macroscopic features of the flow structure are present. The asymptotic model does not show exact agreement, but does provide an estimate of the melt heat flux that is necessary for the solidification calculation. The asymptotic model is also used to predict macroscopic changes in the melt due to rotation.en_ZA
dc.identifier.apacitationBrakel, T. W. (2006). <i>Mathematical modelling of the Czochralski crystal growth process</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/4868en_ZA
dc.identifier.chicagocitationBrakel, Thomas W. <i>"Mathematical modelling of the Czochralski crystal growth process."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2006. http://hdl.handle.net/11427/4868en_ZA
dc.identifier.citationBrakel, T. 2006. Mathematical modelling of the Czochralski crystal growth process. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Brakel, Thomas W AB - In this document a mathematical model for the Czochralski crystal growth process is developed. The trend in current research involves developing cumbersome numerical simulations that provide little or no understanding of the underlying physics. We attempt to review previous research methods, mainly devoted to silicon, and develop a novel analytical tool for indium antimonide (lnSb) crystal growth. This process can be subdivided into two categories: solidification and fluid mechanics. Thus far, crystal solidification of the Czochralski process has been described in the literature mainly qualitatively. There has been little work in calculating actual solidification dynamics. Czochralski crystal growth is a very sensitive process, particularly for lnSb, so it is crucial to describe the system as accurately as possible. A novel ID quasi-steady method is proposed for the shape and temperature field of an lnSb crystal, incorporating the effects of the melt. The fluid mechanics of the Czochralski melt have been modelled by numerous researchers,with calculations performed using commercial software. However, a descriptionof the buoyancy and rotation interaction in the melt has not been adequatelyperformed. Many authors have presented flow patterns but none have indicated either: melt conditions preferential for crystal growth or at least a description of a typical melt structure. In this work, a scale analysis is performed that implies an idealized flow structure. An asymptotic model is then derived based on this order of magnitude analysis, resulting in a fast and efficient fluid flow calculation. The asymptotic model is validated against a numerical solution to ensure that the macroscopic features of the flow structure are present. The asymptotic model does not show exact agreement, but does provide an estimate of the melt heat flux that is necessary for the solidification calculation. The asymptotic model is also used to predict macroscopic changes in the melt due to rotation. DA - 2006 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2006 T1 - Mathematical modelling of the Czochralski crystal growth process TI - Mathematical modelling of the Czochralski crystal growth process UR - http://hdl.handle.net/11427/4868 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/4868
dc.identifier.vancouvercitationBrakel TW. Mathematical modelling of the Czochralski crystal growth process. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2006 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/4868en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematics and Applied Mathematicsen_ZA
dc.titleMathematical modelling of the Czochralski crystal growth processen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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