A 2D description of the single crystal thin plate growth from the melt by micro - pulling - down method. Part 1

Abstract

This paper is the first part of a 2D description of a single crystal thin plate growth by micro-pulling–down (μ-PD) method. This part concerns the following aspects: the free surface equation and the pressure difference across the free surface (section 2); limits of the pressure difference p across the free surface (section 3); static stability of the free surface (section 4); the plate half thickness change rate due to the change of the pressure difference p across the free surface and the half half-thickness control (section 5). Numerical illustrations of the above aspects is given in case of a Si thin plate of 0.0001 [m] by using the Maple 17 software. The advantage of this description is that it helps to better understand the dependence of the meniscus free surface shape and size on the pressure difference across the meniscus free surface and may help the automation of manufacturing.

Keywords

• modelling
• thin plate growth from the melt
• micro-pulling-down method