Scale decomposition of molecular beam epitaxy

TL;DR

This paper applies wavelet analysis to study the dynamic scaling and coarsening behavior in molecular beam epitaxy, revealing exact scaling functions and a power-law growth of mound sizes during nonlinear growth phases.

Contribution

It introduces a wavelet-based methodology for analyzing epitaxial growth, providing exact scaling functions and characterizing mound coarsening with a new scale growth law.

Findings

Existence of a dynamic scaling form in wavelet-discriminated MBE equations.

Wavelet methodology accurately models epitaxial growth dynamics.

Mound coarsening follows a power law with exponent approximately 1/3.

Abstract

In this work, a study of epitaxial growth was carried out by means of wavelets formalism. We showed the existence of a dynamic scaling form in wavelet discriminated linear MBE equation where diffusion and noise are the dominant effects. We determined simple and exact scaling functions involving the scale of the wavelets when the system size is set to infinity. Exponents were determined for both, correlated and uncorrelated noise. The wavelet methodology was applied to a computer model simulating the linear epitaxial growth; the results showed a very good agreement with analytical formulation. We also considered epitaxial growth with the additional Ehrlich$-$Schwoebel effect. We characterized the coarsening of mounds formed on the surface during the nonlinear phase using the wavelet power spectrum. The latter have an advantage over other methods in the sense that one can track the coarsening in both frequency (or scale) space and real space simultaneously. We showed that the averaged wavelet power spectrum (also called scalegram) over all the positions on the surface profile, identified the existence of a dominant scale $a^*$, which increases with time following a power law relation of the form $a^* \sim t^n$, where $n\simeq 1/3$.