An axis symmetric 2D description of the dynamics of a single crystal micro fiber growth from the melt by micro- pulling- down method. Part.1

TL;DR

This paper presents an axisymmetric mathematical model of single crystal micro fiber growth via the micro-pulling-down method, focusing on free surface dynamics, pressure differences, and stability, with numerical illustrations for silicon fibers.

Contribution

It introduces a novel axisymmetric description of the fiber growth process, including free surface equations and stability analysis, aiding understanding and automation.

Findings

Numerical simulation of silicon fiber growth with radius 0.0001 m.

Analysis of pressure difference limits and fiber radius control.

Assessment of free surface static stability.

Abstract

In this paper the first part of an axis symmetric description of a single crystal micro fiber growth process by micro-pulling-down method is presented.the description 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 (section3;the fiber radius change due to the change of the pressure difference p,and the fiber radius size control(section 4);the static stability of the free surface (section 5). The above aspects are numerically illustrated in case of the growth of a silicon fiber of radius equal to 0.0001 m by using the Maple 17 software. This description can be helpful in the better understanding of the growth process and in the automation of manufacturing