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

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.

Bi-directional impulse chaos control in crystal growth

“…The working principle and modeling of the FSRL system have been investigated in [1]. The perturbation analysis of the system is conducted using multiple scales method.…”

“…The large mono-silicon crystals play an important role in semiconductor integrated circuits and solar panels industry. An undesirable irregular swing has been an impediment during the seeding stage in the FSRL system [1]. It is found that the irregular swing, associated with chaos, disrupts the atoms to crystalize in a predefined and perfect array, causing defective mono-silicon crystal production.…”

“…Due to the lack of understanding about the intrinsic chaotic dynamics of the FSRL system in the past, the field engineers attributed the irregular swing phenomenon to the imperfections in manufacturing, trying to suppress it by fine mechanical adjustments. However, these methods could not eliminate the swing phenomenon, intrinsic to the nonlinear dynamics of the FSRL system as systematically analyzed in [1]. Thus, chaos control methods have been recognized as a solution to suppress the irregular swing.…”

“…That must be suppressed since it does harm the crystal quality. The dynamics and the presence of chaos in the FSRL system was first investigated in [1]. The irregular swing has been identified for some time, traditionally considered as being part of an imperfect manufacturing.…”

“…Although this solution is somewhat effective, it comes at high cost, making it often a too expensive solution for such competitive industry. For this reason and after the dynamics being understood as a chaotic vibration problem [1], there is the possibility to solve the problem by chaos (vibration) control methods. There exist much theoretical research about chaos control.…”