Multifractal analysis and scaling range of ZnO AFM images

The surface topographies of as-sputtered and annealed ZnO films were measured by atomic force microscope (AFM). Multifractal behavior of AFM images has been analyzed by box-counting method. It is found that the scaling range can be extended from the image size to the smallest pixel (about 3 decades) by selecting an appropriate method for determining height probability and neglecting smallest probabilities (totally <0.2%) in several boxes. Multifractal spectra can be used to characterize the rough surface of thin film quantitatively.