Multifractal spectra of atomic force microscope images of ZnO film

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