Fluctuations, line tensions, and correlation times of nanoscale islands on surfaces

TL;DR

This study investigates nanoscale island fluctuations on crystal surfaces, revealing how anisotropy affects fluctuation modes, and provides quantitative line tensions and kinetic insights consistent with experimental data.

Contribution

It introduces an analytical framework for understanding fluctuation modes and coupling in nanoscale islands, and derives absolute line tensions and kinetic parameters from simulations.

Findings

Fourier modes couple due to crystal anisotropy.

Eigenmodes are linear combinations of Fourier modes.

Correlation times scale with wavelength, indicating step-edge diffusion as rate-limiting.

Abstract

We analyze in detail the fluctuations and correlations of the (spatial) Fourier modes of nano-scale single-layer islands on (111) fcc crystal surfaces. We analytically show that the Fourier modes of the fluctuations couple due to the anisotropy of the crystal, changing the power spectrum of the fluctuations, and that the actual eigenmodes of the fluctuations are the appropriate linear combinations of the Fourier modes. Using kinetic Monte Carlo simulations with bond-counting parameters that best match realistic energy barriers for hopping rates, we deduce absolute line tensions as a function of azimuthal orientation from the analyses of the fluctuation of each individual mode. The autocorrelation functions of these modes give the scaling of the correlation times with wavelength, providing us with the rate-limiting kinetics driving the fluctuations, here step-edge diffusion. The results for the energetic parameters are in reasonable agreement with available experimental data for Pb(111) surfaces, and we compare the correlation times of island-edge fluctuations to relaxation times of quenched Pb crystallites.