Damping of Growth Oscillations in Molecular Beam Epitaxy: A Renormalization Group Approach

TL;DR

This paper models homoepitaxial crystal growth using a conserved Sine-Gordon equation with shot noise, revealing a transition from layer-by-layer to rough growth through renormalization group analysis.

Contribution

It introduces a renormalization group approach to analyze growth oscillations and identifies a transition in pinning potential behavior during epitaxial growth.

Findings

Pinning potential shifts from strong to weak with coverage

Identifies length and time scales consistent with scaling theories

Heuristically derives a nonlinear term under renormalization

Abstract

The conserved Sine-Gordon Equation with nonconserved shot noise is used to model homoepitaxial crystal growth. With increasing coverage the renormalized pinning potential changes from strong to weak. This is interpreted as a transition from layer-by-layer to rough growth. The associated length and time scales are identified, and found to agree with recent scaling arguments. A heuristically postulated nonlinear term $\nabla^2 (\nabla h)^2$ is created under renormalization.