Open Access

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

Journal of Inequalities and Applications20082008:381604

Received: 24 July 2007

Accepted: 16 February 2008

Published: 16 April 2008


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 across the free surface. Inequalities are deduced for , 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.

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Authors’ Affiliations

Computer Science Department, West University of Timisoara
Faculty of Physics, West University of Timisoara


© S. Balint and A. M. Balint. 2008

This article is published under license to BioMed Central Ltd. 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.