Relaxation kinetics of nano-ripples on Cu(001) surface

Abstract

The relaxation of nano-ripples on Cu(001) is studied over a range of temperatures experimentally. Numerical simulations of relaxation of ripples are also carried out using a nonlinear continuum approach that accounts for the formation and interaction energies of surface steps and the Schwoebel barrier at the step edges. The total activation energy of the relaxation process is measured to be $1.18\ifmmode\pm\else\textpm\fi{}0.14\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ experimentally and $0.95\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ numerically. From these activation energies, it is clear that the system is in the regime where the relaxation kinetics is determined by attachment and detachment of atoms at step edges. Ripples are seen to decay with the formation of step-free regions or facets which indicates that the line tension of the steps plays an important role in the decay behavior. Although the ripples have a dominant spatial frequency or wavelength, our studies find that the decay behavior is not the same as that of a sinusoid of a single wavelength. The inherent nonlinearity of the evolution equations leads to significant coupling between the modes in the vicinity of the dominant wavelength. Numerical calculations that account for these coupling effects are in very good agreement with the experimental observations.