1996 Fiscal Year Final Research Report Summary
Instabilities of a Train of Steps and Growth of Step Fluctuation on Crystal Surfaces
| Project/Area Number |
07640510
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物性一般(含基礎論)
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| Research Institution | Nagoya University |
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Principal Investigator |
UWAHA Makio Department of Physics, Nagoya University Associate Professor, 大学院・理学研究科, 助教授 (30183213)
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| Project Period (FY) |
1995 – 1996
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| Keywords | step / morphological instability / growth exponent / bunching / wandring of a step / crystal growth / nonlinear evolution equation |
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| Research Abstract |
Crystal growth of faceted surfaces is controlled by atomic steps. An array of parallel straight steps forms a vicinal surface. In sublimation or in growth of a crystal, wandering instability of a straight step and bunching instability of a step train are offten observed. In addition a straight step becomes rough when it grows as a result of accumulation of random fluctuation. Understanding these motion of steps is essential for controlling the morphology of crystals.
We generalized the standard step model of vapor growth by including the interaction between steps, the asymmetry in step kinetics and the anisotropy of step stiffness. Theoretical analysis and Monte Carlo simulation reveal the following for the motion of steps in the surface diffusion field and for the pattern formation of two-dimensional crystals.
(a) Bunching and/or wandering instability occur when an asymmetry in the diffusion field develops as a result of the asymmetry in step kinetics or of a drift due to an external field. Considering nonlinearity of the growing unstable mode we attributed the appearance of stable periodic pattern and spatiotemporal chaos in the instabilities to the symmetry of the system. Also the chaotic motion of a wandering step can be suppressed by a strong crystal anisotropy.
(b) As a result of the discretness of the lattice, several distinct stages appear in the change of the fluctuation of a step growing from a straight initial state. In the final stage a transition from the linear growth law to the nonlinear growth law has been observed in the simulation.
(c) Growth law and relaxation law of fractal aggregates are controlled not only by growth mechanism but alse by the geometrical fractal dimension of the aggregates.
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