Sintering of Metal(100) Homoepitaxial Islands: Kink Rounding Barriers, Modified Size Scaling, and Experimental Behavior
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Sintering of Metal(100) Homoepitaxial Islands: Kink Rounding Barriers, Modified Size Scaling, and Experimental Behavior
Da-Jiang Liu1 , C. R. Stoldt2∗ , P. A. Thiel1,2 , and J. W. Evans1,3 1 Ames Laboratory – USDOE, 2 Department of Chemistry, 3 Department of Mathematics, Iowa State University, Ames, Iowa 50011 ABSTRACT Near-square islands form during sub-monolayer homoepitaxial growth on metal (100) surfaces. Diffusion of these islands after deposition leads to collision of island pairs, typically corner-to-corner creating dumbbell-shaped clusters. Subsequent coalescence (or sintering) recovers a near-square equilibrium shape. This process is mediated by periphery diffusion (PD) and its study can provide detailed insight into the underlying dynamic processes and energetics. Atomistic modeling reveals that the size scaling of the characteristic relaxation time, τ , depends on the detailed energy barriers of various hopping processes that contribute to PD. Simulations without an extra kink or corner rounding barrier for PD reveals τ ∼ L4 , while behavior approaching τ ∼ L3 is observed with a significant extra kink rounding barrier for PD. The latter is consistent with experimental observations for Ag/Ag(100) at 300 K. INTRODUCTION For submonolayer homoepitaxial systems, where the substrate is “completely wet” by the 2D islands, the natural and traditional expectation was that post-deposition coarsening of the adlayer would occur via Ostwald Ripening (OR) [1]. The remarkable discovery first made for the Ag/Ag(100) system at 300 K was that large 2D clusters or islands of 100’s to 1000’s of adatoms have significant diffusive mobility [2]. Furthermore, cluster diffusion and subsequent coalescence, i.e., Smoluchowski Ripening (SR) rather than OR actually dominates the coarsening process at 300 K (which occurs on the time-scale of hours) [3]. The diffusion coefficient of a cluster with linear size ∼ L scales like D(s) ∼ L−α , with α ≈ 2.2 for L =10-20 at T = 300 K, and the mechanism was proposed to be periphery diffusion (PD) [4]. In fact, these and related studies have prompted much theoretical analysis of cluster diffusion (and, specifically, of the size scaling) via both atomistic [5–7] and continuum [8] models. More recently, the subsequent coalescence or sintering process through the same PD mechanism has been studied both experimentally and theoretically [9–13]. In this paper, using Ag(100) as an example, we show that one can reveal details of periphery diffusion (and specifically kink rounding) through realistic modeling of the sintering process. ATOMISTIC MODELING OF PERIPHERY DIFFUSION For simplicity, our atomistic model of PD assumes that configuration energies can be determined by counting nearest-neighbor (NN) bonds with strength φ. The four key elementary ∗
Current Address: Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309
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Figure 1: Bird’s eye view of key periphery diffusion (PD) processes and the associated barriers assuming NN interactions φ: straight edge dif
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