Stochastic and fractal properties of silicon and porous silicon rough surfaces

In this paper, we investigate the stochastic properties and fractal behavior of Si and porous silicon (PS) rough surfaces to characterize the complexity of their morphology. To this end, height fluctuations of these rough surfaces are determined by Atomic Force Microscopy (AFM) and then roughness and correlation length of the surfaces are calculated. The generalized Hurst exponent, h(q) and singularity spectrum, f(α) are obtained by using two dimensional MF-DFA method for both rough surfaces; Our results show that both mentioned surfaces are multifractal and have different scaling exponents. To investigate the reason of the observed multifractality behavior, we determine height distribution, skewness and kurtosis measures and show that the deviation from the Gaussian distribution for the height fluctuations of the surfaces can be a reason for the observed multifractality behavior