Singularity spectra of rough growing surfaces from wavelet analysis

TL;DR

This paper introduces a wavelet-based method to analyze the singularity spectra of simulated rough surfaces from molecular beam epitaxy, revealing multiaffine properties and effects of desorption on surface morphology.

Contribution

It applies the WTMM method to surface analysis, providing a complete singularity spectrum and insights into the effects of desorption on surface roughness.

Findings

Wide spectrum of Hoelder exponents indicating multiaffinity

Desorption shifts the spectrum towards smaller exponents

Mathematical foundation for anomalous scaling

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.