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

Hai-Peng Ren*, Zi-Xuan Zhou, Celso Grebogi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
10 Downloads (Pure)


Silicon crystal puller (SCP) is key equipment in silicon wafer manufacture, which is, in turn, the base material for the most currently used integrated circuit 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 an increasing height, though it causes serious swing phenomenon of the crystal seed. The strong swing of the seed increases the possibility of defects in the mono-silicon rod and the risk of mono-silicon growth failure. The main aim of this paper is to analyze the nonlinear dynamics in flexible shaft rotating–lifting (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 is analyzed. The stability of the equilibrium, bifurcation, and chaotic motion is demonstrated, which have been observed in practical situations. Melnikov method is used to derive the possible parameter region which leads to chaotic motion. Three routes to chaos are identified in the FSRL system, including period doubling, symmetry-breaking bifurcation, and crisis. The work in this paper analyzes and explains the complex dynamics in FSRL system of the SCP, which will be helpful for the designers in the designing process in order to avoid the swing phenomenon in the SCP.
Original languageEnglish
Pages (from-to)771-784
Number of pages14
JournalNonlinear Dynamics
Issue number2
Early online date4 Apr 2020
Publication statusPublished - Oct 2020

Bibliographical note

The project is supported by the Key Program of National Natural Science Foundation of China (Grant No. 61533014).


  • Silicon crystal puller
  • Flexible shaft rotating–lifting system
  • Swing of crystal seed
  • Period doubling bifurcation
  • Symmetry-breaking bifurcation
  • Interior crisis
  • Chaos
  • Flexible shaft rotating-lifting system


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