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Register a new userNonlinear dynamics in the flexible shaft rotating-lifting system of silicon crystal puller using Czochralski method
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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.
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Chaos is shown to occur in the flexible shaft rotating-lifting (FSRL) system of the mono-silicon crystal puller. Chaos is, however, harmful for the quality of mono-silicon crystal production. Therefore, it should be suppressed. Many chaos control methods have been proposed theoretically and some have even been used in applications. For a practical plant displaying harmful chaos, engineers from a specified area usually face with the challenge to identifying chaos and to suppressing it by using a proper method. However, despite of the existing methods, chaos control method selection in the FSRL system is not a trivial task. For example, for the OGY method, if one cannot find a practical adjustable parameter, then the OGY method cannot be applied. An impulsive control method is being proposed which is efficiently able to suppress chaos in the FSRL system. The selection of the control parameters is obtained by using the Melnikov method. Simulation results show the correctness of our theoretical analysis and the effectiveness of the proposed chaos control method.
The model system manifesting phenomena peculiar to complex analytic maps is offered. The system is a non-autonomous ring cavity with nonlinear elements and filters,
Czochralski-grown silicon crystals were studied by the techniques of the low-angle mid-IR-light scattering and electron-beam-induced current. The large-scale accumulations of electrically-active impurities detected in this material were found to be different in their nature and formation mechanisms from the well-known impurity clouds in a FZ-grown silicon. A classification of the large-scale impurity accumulations in CZ Si is made and point centers constituting them are analyzed in this paper. A model of the large-scale impurity accumulations in CZ-grown Si is also proposed. In addition, the images of the large-scale impurity accumulations obtained by means of the scanning mid-IR-laser microscopy are demonstrated.
Recently the phase space structures governing reaction dynamics in Hamiltonian systems have been identified and algorithms for their explicit construction have been developed. These phase space structures are induced by saddle type equilibrium points which are characteristic for reaction type dynamics. Their construction is based on a Poincar{e}-Birkhoff normal form. Using tools from the geometric theory of Hamiltonian systems and their reduction we show in this paper how the construction of these phase space structures can be generalized to the case of the relative equilibria of a rotational symmetry reduced $N$-body system. As rotations almost always play an important role in the reaction dynamics of molecules the approach presented in this paper is of great relevance for applications.
Electrically detected magnetic resonance is used to identify recombination centers in a set of Czochralski grown silicon samples processed to contain strained oxide precipitates with a wide range of densities (~ 1e9 cm-3 to ~ 7e10 cm-3). Measurements reveal that photo-excited charge carriers recombine through Pb0 and Pb1 dangling bonds and comparison to precipitate-free material indicates that these are present at both the sample surface and the oxide precipitates. The electronic recombination rates vary approximately linearly with precipitate density. Additional resonance lines arising from iron-boron and interstitial iron are observed and discussed. Our observations are inconsistent with bolometric heating and interpreted in terms of spin-dependent recombination. Electrically detected magnetic resonance is thus a very powerful and sensitive spectroscopic technique to selectively probe recombination centers in modern photovoltaic device materials.
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