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 which represents the controllable part of the pressure difference across the free surface. Inequalities are established for 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 . With this aim this study was undertaken.
Highlights
According to 1, modern engineering needs crystals with prescribed shapes and sizes ribbon, rod, and tube-shaped crystals that allow one to use them as final products without additional machining
Crystals of specified sizes and shapes are required to be grown from the melt
As the crystal is not restricted by the crucible walls, its cross-section depends upon the growing parameters
Summary
According to 1 , modern engineering needs crystals with prescribed shapes and sizes ribbon-, rod-, and tube-shaped crystals that allow one to use them as final products without additional machining. If there exists a solution z x of 2.1 which describes the convex free surface of a static meniscus on the closed interval x1, x0 , the following inequalities hold:
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
