分形基底上刻蚀模型动力学标度行为的 数值模拟研究

为探讨分形基底结构对生长表面标度行为的影响, 本文采用Kinetic Monte Carlo(KMC)方法模拟了刻蚀模型(etching model)在谢尔宾斯基箭头和蟹状分形基底上刻蚀表面的动力学行为. 研究表明,在两种分形基底上的刻蚀模型都表现出很好的动力学标度行为, 并且满足Family-Vicsek标度规律. 虽然谢尔宾斯基箭头和蟹状分形基底的分形维数相同, 但模拟得到的标度指数却不同, 并且粗糙度指数 α与动力学指数z也不满足在欧几里得基底上成立的标度关系α+z=2. 由此可以看出, 标度指数不仅与基底的分形维数有关, 而且和分形基底的具体结构有关.

Numerical simulations of dynamic scaling behavior of the etching model on fractal substrates

In order to investigate the effect of the structure of fractal substrates on dynamic scaling behavior of the surfaces,the etching model growing on the Sierpinski arrowhead and crab fractal substrates is simulated by means of Kinetic Monte Carlo(KMC).It is found that the etching model evolving on two kinds of fractal substrates can exhibit dynamic scaling behavior,and can still be described by the Family-Vicsek scaling relation.Although the Sierpinski arrowhead and crab fractal substrates have the same fractal dimension,the obvious different values of roughness exponentαand dynamic exponent z,however,are obtained on these two substrates,and they neither of them satisfy the scaling relationα+z = 2,which is satisfied in the usual Euclid space.It can be seen from the results obtained here that the scaling exponents of the etching model growing on fractal substrate are determined by not only the fractal dimension but also the fractal structure.