Singularity spectra of rough growing surfaces from wavelet analysis

Abstract

We apply the wavelet transform modulus maxima (WTMM) method to the analysis of simulated MBE-grown surfaces. In contrast to the structure function approach commonly used in the literature, this new method permits an investigation of the complete singularity spectrum. We focus on a kinetic Monte-Carlo model with Arrhenius dynamics, which in particular takes into consideration the process of thermally activated desorption of particles. We find a wide spectrum of Hoelder exponents, which reflects the multiaffine surface morphology. Although our choice of parameters yields small desorption rates (< 3 %), we observe a dramatic change in the singularity spectrum, which is shifted towards smaller Hoelder exponents. Our results offer a mathematical foundation of anomalous scaling: We identify the global exponent alpha_g with the Hoelder exponent which maximizes the singularity soectrum.