Surface Kinetics and Generation of Different Terms in a Conservative Growth Equation

TL;DR

This paper develops a kinetic-based method to derive local growth equations for epitaxial surface growth, identifying key terms and their effects on surface stability in different dimensions, applicable to experimental growth models.

Contribution

It introduces a kinetic approach to derive closed-form growth equations from adatom surface kinetics, including symmetry-breaking and curvature-dependent terms, extending to higher dimensions.

Findings

Derived growth equations for (1+1) and (2+1) dimensions.

Identified key kinetic processes contributing to growth terms.

Showed stabilizing effect of dissociation on surface growth.

Abstract

A method based on the kinetics of adatoms on a growing surface under epitaxial growth at low temperature in (1+1) dimensions is proposed to obtain a closed form of local growth equation. It can be generalized to any growth problem as long as diffusion of adatoms govern the surface morphology. The method can be easily extended to higher dimensions. The kinetic processes contributing to various terms in the growth equation (GE) are identified from the analysis of in-plane and downward hops. In particular, processes corresponding to the (h -> -h) symmetry breaking term and curvature dependent term are discussed. Consequence of these terms on the stable and unstable transition in (1+1) dimensions is analyzed. In (2+1) dimensions it is shown that an additional (h -> -h) symmetry breaking term is generated due to the in-plane curvature associated with the mound like structures. This term is independent of any diffusion barrier differences between in-plane and out of-plane migration. It is argued that terms generated in the presence of downward hops are the relevant terms in a GE. Growth equation in the closed form is obtained for various growth models introduced to capture most of the processes in experimental Molecular Beam Epitaxial growth. Effect of dissociation is also considered and is seen to have stabilizing effect on the growth. It is shown that for uphill current the GE approach fails to describe the growth since a given GE is not valid over the entire substrate.