Journal of Inequalities and Applications 
Volume 2008 (2008), Article ID 381604, 14 pages
doi:10.1155/2008/381604
Research Article

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

Stefan Balint1 and Agneta M. Balint2

 1Computer Science Department, West University of Timisoara, Bulv. V.Parvan 4, 300223 Timisoara, Romania
2Faculty of Physics, West University of Timisoara, Bulv. V.Parvan 4, 300223 Timisoara, Romania
Received 24 July 2007; Revised 26 November 2007; Accepted 16 February 2008

Recommended by Kok Teo

Abstract

A second-order nonlinear differential equation, of which some solutions describe the static meniscus free surface (the static liquid bridge free surface between the shaper and the crystal surface) occurring in single crystal ribbon growth, is analyzed. The analysis is focusing on the dependence of the solutions of the equation on the pressure difference p across the free surface. Inequalities are deduced for p, which are necessary or sufficient conditions for the stable and convex free surface of a static meniscus. The obtained results are numerically illustrated in the case of a silicon single crystal ribbon growth. The advantage of these kinds of inequalities is that from them special results can be gleaned concerning the experiment planning and technology design. With this aim this study was undertaken.