Competing growth processes induced by next-nearest-neighbor interactions: Effects on meandering wavelength and stiffness

Abstract

In this paper we explore the meandering instability of vicinal steps with a kinetic Monte Carlo simulations (kMC) model including the attractive next-nearest-neighbor (NNN) interactions. kMC simulations show that increase of the NNN interaction strength leads to considerable reduction of the meandering wavelength and to weaker dependence of the wavelength on the deposition rate F. The dependences of the meandering wavelength on the temperature and the deposition rate obtained with simulations are in good quantitative agreement with the experimental result on the meandering instability of Cu(0 2 24) [T. Maroutian et al., Phys. Rev. B 64, 165401 (2001)]. The effective step stiffness is found to depend not only on the strength of NNN interactions and the Ehrlich-Schwoebel barrier, but also on F. We argue that attractive NNN interactions intensify the incorporation of adatoms at step edges and enhance step roughening. Competition between NNN and nearest-neighbor interactions results in an alternative form of meandering instability which we call ``roughening-limited'' growth, rather than attachment-detachment-limited growth that governs the Bales-Zangwill instability. The computed effective wavelength and the effective stiffness behave as ${\ensuremath{\lambda}}_{\mathrm{eff}}\ensuremath{\sim}{F}^{\ensuremath{-}q}$ and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\beta}}}_{\mathrm{eff}}\ensuremath{\sim}{F}^{\ensuremath{-}p}$, respectively, with $q\ensuremath{\approx}p/2$.