分形理论及其在薄膜微结构研究中的应用

Fractal Theory and Application in Microstructure of Thin Film

介绍分形的基本概念以及几种常用的计算简单分形维数的方法,用分形研究Au-MgF2纳米金属介质复合薄膜中Au颗粒和半连续Ag膜中Ag小岛的分布规律。结果表明:复合薄膜中Au颗粒的分形维数随Au含量的增加由1.5516逐渐增大到1.7671,表明金属介质复合薄膜中Au颗粒的平均尺寸随着Au含量的增加而增大;半连续Ag膜中Ag小岛的分形维数随厚度的增加从1.4051增大到1.7428,说明半连续Ag膜的覆盖率随着其厚度的增加而增大。这一结果与实验结果一致,因此分形可以用来定量表征薄膜显微结构的演化规律。

This paper introduces the basic concept and several calculating methods of fractal dimension of fractal theory. Law of distribution of Au particles of Au-MgF2 nano-metal dielectric composite films and Ag islands of semicontinuous Ag films have been studied by fractal theory. The result shows with the Au vol- ume fraction increasing, the fractal dimension of Au particles increases from 1. 5516 to 1. 7671 gradually, indicating that the mean size of Au particles varies with Au volume fraction the same way as fractal dimension. The fractal dimension of Ag islands increases from 1. 4051 to 1. 7428 as the thickness increases. It shows that area coverage of semicontinuous Ag films also increase. This result is in agreement with the experimental observation.