Ab Initio Thermodynamics and Kinetics for Coalescence of Two-Dimensional Nanoislands and Nanopits on Metal (100) Surfaces

Abstract

Postdeposition coalescence or sintering of pairs of lowstrain two-dimensional nanoislands and nanopits on unreconstructed metal (100) surfaces is typically mediated by diffusion along step edges, and is highly sensitive to the associated kinetics. Thus, for selected systems, we provide an ab initio density functional theory (DFT) level description of both system thermodynamics and kinetics. Specifically, we assess lateral pair and trio interactions both conventionally with adatoms at 4-fold hollow adsorption sites, and unconventionally with one adatom at the bridge-site transition state for hopping. Rather than use standard cluster expansion algorithms, these interactions are determined subject to the constraint that key step-edge properties are recovered exactly. Together, both classes of interactions determine barriers for edge diffusion processes for any local step configuration, including diffusion along close-packed ⟨110⟩ edges, kink rounding, meandering processes at kinked ⟨100⟩ steps, and extraction processes at pit corners. Our formalism applies for homoepitaxial systems, and also for several lattice-matched heteroepitaxial systems. The barriers provide input for stochastic models of nanocluster evolution, which are analyzed by kinetic Monte Carlo simulation. Such modeling with DFT energetics from the PBEsol functional recovers extensive experimental observations of both the time scale and the island-size dependence for sintering of Ag islands on Ag(100). Description of pit sintering on Ag(100) is more delicate, being sensitive to specific unconventional trio interactions.

Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes

“…It is generally accepted that cluster diffusion is mediated by periphery diffusion (PD), also described as edge diffusion, of adatoms along the steps at the periphery of the cluster. The STM studies prompted extensive atomistic lattice-gas modeling starting in the 1990's of epitaxial cluster diffusion [4][5][6][7][8][9][10][11] and of related reshaping phenomena [12][13][14][15][16][17][18][19]. This work supplemented limited earlier studies [20][21][22].…”

“…E eff also reflects thermodynamic parameters determined by adatom interactions, particularly the formation energy, E form , to create a step edge atom from a kink atom. It was previously suggested that long-range cluster diffusion is limited by creation of edge atoms through their extraction from the core of the cluster or "core breakup" [1,20], so that E eff = E e + δ + E form [19]. This perspective is consistent with the predictions of the mesoscale continuum Langevin theory where the activation energy for cluster diffusion corresponds to that for mobility of edge atoms, E PD , where σ PD ~ exp[-E PD /(k B T)] with E PD = E e + δ + E form [23,24].…”

Communication: Diverse nanoscale cluster dynamics: Diffusion of 2D epitaxial clusters

“…[1][2][3]5,6 Note also that reshaping of 2D epitaxial clusters and pits, or 3D clusters and voids in bulk crystals, is equivalent on the macroscale, 16 but not on the nanoscale. 11,12 The size-dependence of diffusivity of supported metal nanoclusters was also found to deviate from macroscale predictions. [17][18][19][20][21][22] Refined continuum treatments with multiple order parameters might describe such anomalous scaling of diffusion.…”

“…6 Differences occur when linear nanocluster sizes, L, decrease below various characteristic lengths. [1][2][3][9][10][11][12] For L < L k , the characteristic separation between kinks on close-packed step edges, 2D clusters become effectively faceted and reshaping is controlled by inhibited nucleation of new edges. 9 Similar anomalies have been discussed for 3D nanoclusters, but here facets can be macroscopic and nucleation of new layers becomes prohibitive above nanoscale.…”

Modeling of Diffusivity for 2D Vacancy Nanopits and Comparison with 2D Adatom Nanoislands on Metal(100) Surfaces Including Analysis for Ag(100)

“…For metal(100) systems, one generally expects 2NN pair attractions and bent trio repulsions to be ~10% of the strength of NN interactions (and weaker longer range pair and many-body interactions also exist). [28][29][30] However, in Appendix B, we argue that our simpler model with just NN attractions recovers the appropriate near-square equilibrium shape of clusters at least for Ag(100). The actual hopping dynamics in metal(100) systems is also more complicated than our prescription, as has been determined by a comprehensive DFT analysis of energetics at both the initial site and the transition state for hopping for general step edge configurations.…”