Multifractal behavior of crystallization on Au/Ge bilayer films

The relationship between the distribution and the dimension of fractal patterns in annealed Au/Ge bilayer films has been investigated. The variation of the single-fractal branch width can be shown by using a simple fractal dimension. The nonuniform distribution of multiple-fractal patterns can be described quantitatively by using the multifractal spectra. It has been demonstrated that, when the fractals are fewer, they exhibit the greater nonuniform distribution and the multifractal spectrum is wider. We found that a few fractal patterns distribute nonuniformly in film annealed at 100 degreesC for 60 min, and that many fractal patterns distribute uniformly in whole film annealed at 120 degreesC for 60 min. Correspondingly, the width Delta alpha of multifractal spectra decreases from 3.70 to 0.23.