Effects of next-nearest-neighbor interactions on the orientation dependence of step stiffness: Reconciling theory with experiment for Cu(001)

Abstract

Within the solid-on-solid (SOS) approximation, we carry out a calculation of the orientational dependence of the step stiffness on a square lattice with nearest-and next-nearest-neighbor interactions. At low temperature our result reduces to a simple, transparent expression. The effect of the strongest trio (three-site, nonpairwise) interaction can easily be incorporated by modifying the interpretation of the two pairwise energies. The work is motivated by a calculation based on nearest neighbors that underestimates the stiffness by a factor of 4 in directions away from close-packed directions, and a subsequent estimate of the stiffness in the two highsymmetry directions alone that suggested that inclusion of next-nearest-neighbor attractions could fully explain the discrepancy. As in these earlier papers, the discussion focuses on Cu(001).

Thermal roughening of {001} surfaces

“…At higher temperatures also larger step excursions, such as multiple kinks, need to be taken into account as well. 2,[7][8][9][10] In principle the cubic ͑001͒ Kossel crystal with nearestneighbor interaction can be mapped onto the twodimensional ͑2D͒ spin system. The nearest-neighbor interaction between the atoms can be associated with the Ising parameter.…”

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

“…When NNN interactions just enter in the lattice gas energies, they contribute to the equilibrium stiffness, etc., as in ref. [32].…”

“…Within the solid-on-solid (SOS) approximation, Stasevich et al [32,35] demonstrated the equilibrium dependence of the step stiffness on NNN interactions for Cu (001) . Mehl et al [8] found that energy barriers are not simply the sum of bond energies, so that the NNN bonding energy deduced from a set of such barriers depends on the diffusion path (i.e.…”

Multiscale Studies of the Formation and Stability of Surface-based Nanostructures, DOE Computational Materials Science Network - Final Report

“…This year we are collaborating with an experimental group in Hong Kong to investigate similar effects on structures on Si(111) at hightemperature [1]. b) We completed our theoretical investigation of step stiffness, which weights the response of steps to driving forces and thereby plays a crucial role in the dynamics of nanoscale structures [2]. We have derived analytic expressions for the stiffness anisotropy; though complicated, they can be straightforwardly used as input for finite-element simulations.…”

“…b) Since step stiffness is the "inertial parameter" that weights the response of steps to driving forces, it plays a crucial role in the dynamics of nanoscale structures. We have shown that the typical assumption of isotropy is poor, especially near facet directions, and have developed remarkably simple formulas to describe the angular dependence at most orientations on the two principal faces of fcc metals [2,3]. c) While lattice-gas models have long been invoked to describe the energetics of atoms on surfaces, it has only recently become possible to calculate reliably these energies to verify that phenomenologically-derived parameters correspond to actual values.…”