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Singularity spectra of rough growing surfaces from wavelet analysis
1Institut fur Theoretische Physik, Julius-Maximilians-Universitat Wurzburg, Am Hubland, 97074 Wurzburg, Germany.
Summary
This study uses the wavelet transform modulus maxima method to analyze simulated surfaces grown by molecular-beam epitaxy. The method reveals multiaffine surface morphology and a shift in singularity spectrum due to desorption, providing a foundation for anomalous scaling.
Area of Science:
- Surface science
- Materials science
- Statistical physics
Background:
- Molecular-beam epitaxy (MBE) is a technique for depositing thin films.
- Surface morphology analysis often uses structure function approaches.
- Understanding surface scaling properties is crucial for materials development.
Purpose of the Study:
- To apply the wavelet transform modulus maxima method for analyzing simulated MBE surfaces.
- To investigate the complete singularity spectrum of surface growth.
- To understand the impact of desorption on surface morphology and scaling.
Main Methods:
- Wavelet transform modulus maxima method for singularity spectrum analysis.
- Kinetic Monte Carlo (KMC) model with Arrhenius dynamics.
- Inclusion of thermally activated desorption processes in simulations.
Main Results:
- A wide spectrum of Holder exponents was observed, indicating multiaffine surface morphology.
- Small desorption rates (<3%) caused a dramatic shift in the singularity spectrum towards smaller exponents.
- The global exponent alpha(g) was identified with the maximum Holder exponent.
Conclusions:
- The wavelet transform modulus maxima method provides a comprehensive analysis of surface singularity spectra.
- Thermally activated desorption significantly alters surface scaling behavior, even at low rates.
- The study establishes a mathematical foundation for anomalous scaling in surface growth phenomena.