Nonlinear dynamics in the flexible shaft rotating-lifting system of silicon crystal puller using Czochralski method

TL;DR

This paper models and analyzes the nonlinear dynamics of the flexible shaft rotating-lifting system in silicon crystal pullers, revealing conditions for chaos and providing insights to improve stability in manufacturing.

Contribution

It introduces a mathematical model for the FSRL system in SCPs and analyzes its nonlinear behaviors, including bifurcations and chaos, to aid in design improvements.

Findings

Identification of parameter regions leading to chaos

Demonstration of bifurcation routes to chaos

Insights into stability conditions for SCP operation

Abstract

Silicon crystal puller (SCP) is a key equipment in silicon wafer manufacture, which is, in turn, the base material for the most currently used integrated circuit (IC) chips. With the development of the techniques, the demand for longer mono-silicon crystal rod with larger diameter is continuously increasing in order to reduce the manufacture time and the price of the wafer. This demand calls for larger SCP with increasing height, however, it causes serious swing phenomenon of the crystal seed. The strong swing of the seed causes difficulty in the solidification and increases the risk of mono-silicon growth failure.The main aim of this paper is to analyze the nonlinear dynamics in the FSRL system of the SCP. A mathematical model for the swing motion of the FSRL system is derived. The influence of relevant parameters, such as system damping, excitation amplitude and rotation speed, on the stability and the responses of the system are analyzed. The stability of the equilibrium, bifurcation and chaotic motion are demonstrated, which are often observed in practical situations. Melnikov method is used to derive the possible parameter region that leads to chaotic motion. Three routes to chaos are identified in the FSRL system, including period doubling, symmetry-breaking bifurcation and interior crisis. The work in this paper explains the complex dynamics in the FSRL system of the SCP, which will be helpful for the SCP designers in order to avoid the swing phenomenon in the SCP.