Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 732106, 28 pages
doi:10.1155/2009/732106
Research Article

Inequalities for Single Crystal Tube Growth by Edge-Defined Film-Fed Growth Technique

Stefan Balint1 and Agneta M. Balint2

1Department of Computer Science, Faculty of Mathematics and Computer Science, West University of Timisoara, Blv. V.Parvan 4, 300223 Timisoara, Romania
2Faculty of Physics, West University of Timisoara, Blv. V.Parvan 4, 300223 Timisoara, Romania

Received 3 January 2009; Accepted 29 March 2009

Academic Editor: Yong Zhou

Copyright © 2009 Stefan Balint and Agneta M. Balint. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The axi-symmetric Young-Laplace differential equation is analyzed. Solutions of this equation can describe the outer or inner free surface of a static meniscus (the static liquid bridge free surface between the shaper and the crystal surface) occurring in single crystal tube growth. The analysis concerns the dependence of solutions of the equation on a parameter p which represents the controllable part of the pressure difference across the free surface. Inequalities are established for p which are necessary or sufficient conditions for the existence of solutions which represent a stable and convex outer or inner free surfaces of a static meniscus. The analysis is numerically illustrated for the static menisci occurring in silicon tube growth by edge-defined film-fed growth (EFGs) technique. This kind of inequalities permits the adequate choice of the process parameter p. With this aim this study was undertaken.