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== Abstract ==
 
== Abstract ==
  
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El objetivo de este trabajo es introducir y resolver numéricamente el modelo matemático para el comportamiento del líquido semiconductor en el proceso Czochralski de obtención de cristales semicondutores bajo la acción de un campo magnético. Dicho modelo corresponde a las ecuaciones de la Magnetohidrodinámica. La resolución numérica de este modelo matemático presenta dificultades importantes debido a que en él están involucrados fenómenos de Mecánica de Fluidos, Electromagnetismo y Transferencia de Calor. Para la resolución numérica de este modelo se emplea un método de elementos finitos estabilizado basado en la versión algebraica de las subescalas de malla, lo cual permite satisfacer tanto la condición de divergencia nula sobre la velocidad del fluido como la condición de divergencia nula sobre el campo magnético además de evitar oscilaciones numéricas. El esquema usado en este trabajo está basado en el esquema propuesto en (1). El esquema de elementos finitos antes mencionado se aplica al ejemplo numérico propuesto por Bückle (2). Dicho ejemplo es la comparación numérica más extendida para el proceso de Czochralski. Los casos analizados en este trabajo sólo difieren de los propuestos por Bückle en el hecho de que se les ha añadido un campo magnético . El empleo de campos magnéticos en el proceso de Czochralski está encaminado a reducir y eliminar las perturbaciones en el fluido que pudieran dar origen a defectos en el cristal semiconductor. Summary The objective of this work is to introduce and numerically solve the mathematical model for the bahavior of liquid semiconductors in the Czochralski process to obtain semiconductor crystals under the influence of a magnetic field. Such model is framed within the Magnetohydrodynamics equations. The numerical solution of this mathematical model presents important difficulties due to the involvement of phenomena from Fluid Mechanics, Electromagnetism and Heat Transfer. In order to numerically solve this model a stabilized finite element approximation based on tha algebraic version of a subgrid scale model in used. This approach makes possible to satisfy the free divergence condition over the velocity of the fluid together with the free divergence condition over the magnetic field and also to avoid numerical oscillations. The numerical scheme used in this work is based on the scheme proposed in (1). This numerical scheme is applied to the numerical benchmark proposed by Bückle (2). Such example is the most common numerical benchmark for the Czochralski process. The cases analysed in this work only differ from those proposed by Bückle in the fact that a magnetic field has been added. The use of magnetic fields in the Czochralski process is headed to diminish and suppress the perrturbations inthe liquid which can originate defects in the semiconductor cristal.
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The objective of this work is to introduce and numerically solve the mathematical model for the bahavior of liquid semiconductors in the Czochralski process to obtain semiconductor crystals under the influence of a magnetic field. Such model is framed within the Magnetohydrodynamics equations. The numerical solution of this mathematical model presents important difficulties due to the involvement of phenomena from Fluid Mechanics, Electromagnetism and Heat Transfer. In order to numerically solve this model a stabilized finite element approximation based on tha algebraic version of a subgrid scale model in used. This approach makes possible to satisfy the free divergence condition over the velocity of the fluid together with the free divergence condition over the magnetic field and also to avoid numerical oscillations. The numerical scheme used in this work is based on the scheme proposed in (1). This numerical scheme is applied to the numerical benchmark proposed by Bückle (2). Such example is the most common numerical benchmark for the Czochralski process. The cases analysed in this work only differ from those proposed by Bückle in the fact that a magnetic field has been added. The use of magnetic fields in the Czochralski process is headed to diminish and suppress the perturbations inthe liquid which can originate defects in the semiconductor cristal.
  
 
== Full document ==
 
== Full document ==
 
<pdf>Media:draft_Content_803678358RR263E.pdf</pdf>
 
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Latest revision as of 10:58, 14 June 2017

Abstract

The objective of this work is to introduce and numerically solve the mathematical model for the bahavior of liquid semiconductors in the Czochralski process to obtain semiconductor crystals under the influence of a magnetic field. Such model is framed within the Magnetohydrodynamics equations. The numerical solution of this mathematical model presents important difficulties due to the involvement of phenomena from Fluid Mechanics, Electromagnetism and Heat Transfer. In order to numerically solve this model a stabilized finite element approximation based on tha algebraic version of a subgrid scale model in used. This approach makes possible to satisfy the free divergence condition over the velocity of the fluid together with the free divergence condition over the magnetic field and also to avoid numerical oscillations. The numerical scheme used in this work is based on the scheme proposed in (1). This numerical scheme is applied to the numerical benchmark proposed by Bückle (2). Such example is the most common numerical benchmark for the Czochralski process. The cases analysed in this work only differ from those proposed by Bückle in the fact that a magnetic field has been added. The use of magnetic fields in the Czochralski process is headed to diminish and suppress the perturbations inthe liquid which can originate defects in the semiconductor cristal.

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Published on 01/07/10
Accepted on 01/07/10
Submitted on 01/07/10

Volume 26, Issue 3, 2010
Licence: CC BY-NC-SA license

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