An axis symmetric 2D description of the process of the growth of a single crystal Si tube growth from the melt by pulling down method. Part1

TL;DR

This paper presents an axisymmetric mathematical model for single crystal silicon tube growth via micro-pulling-down, analyzing free surface equations, pressure differences, and stability to improve understanding and automation of the process.

Contribution

It introduces a detailed axisymmetric description of silicon tube growth, including free surface equations, pressure limits, and stability analysis, which was not previously modeled in this way.

Findings

Numerical investigation of pressure differences in silicon tube growth

Analysis of static stability of free surfaces during growth

Insights into process automation potential

Abstract

This paper is the first part of an axis symmetric description of a single crystal tube growth process by micro-pulling-down method.the description concerns the following aspects:the free surfaces equations and the pressure difference across the free surfaces (section 2) , limits of the pressure differences across the free surfaces (section 3) ;static stability of the capillary free surfaces (section 4). In section 5 the above aspects are numerically investigated in case of a silicon tube growth.This investigation can be helpful in the better understanding the growth process and in the automation of manufacturing.In section 6 some general conclusion are given.Section 7 is an annex which contains the proof of the general statements formulated in sections 3 and 4.