Stability and Kinetics of Step Motion on Crystal Surfaces

TL;DR

This paper analytically investigates the stability, kinetics, and fluctuations of monoatomic steps on crystal surfaces, introducing models that describe their collective motion and morphological behaviors under various conditions.

Contribution

It develops a Green's function approach, stability analysis, Langevin formalism, and phase field model to comprehensively study step dynamics on crystal surfaces.

Findings

Derived integro-differential equations for step motion

Analyzed stability of moving steps under perturbations

Modeled collective step behavior including bunching and spreading

Abstract

The kinetics of monoatomic steps in diffusion-controlled crystal growth and evaporation processes are investigated analytically using a Green's function approach. Integro-differential equations of motion for the steps are derived; and a systematic linear stability analysis is carried out treating simultaneously perturbations both along and perpendicular to the steps. Morphological fluctuations of steadily moving steps in response to ambient thermodynamic noises are also studied within a general Langevin formalism. Finally, a phase field model is developed to investigate the time-dependent, collective motion of steps. An application of the model to a finite step train recovers a variety of kinetic behaviors such as the bunching and spreading of steps.