Multifractal spectra of atomic force microscope images of ZnO film

The surface topographies of Si-substrate and ZnO films as-deposited and annealed were measured by atomic force microscope (AFM). Five methods (variance from average height,absolute deviation from average height, height based on the minimum height of the rough surface, height based on a depth from the surface, height based on the bottom of the film) for determining height distribution probability are used to calculate the multifractal spectra of AFM images. It is found that the former three methods could not satisfy the scaling law well when the smaller probability subsets provide the main contribution to the partition function. On the other hand,the latter two methods can satisfy the scaling law close to 3 orders of magnitude and can be used to compare roughness between different rough surface quantitatively.