Coarsening mechanisms in a metal film: From cluster diffusion to vacancy ripening.

Coarsening of Ag films on Ag(100) at room temperature occurs primarily via diffusion-mediated coalescence of two-dimensional adatom clusters, rather than by Ostwald ripening, up to a coverage of 0.65 monolayer. Above 0.8 monolayer, vacancy clusters coarsen primarily via Ostwald ripening, due to their much lower diffusivity. An asymmetric transition region separates these two regimes, characterized by a near-percolating structure which undergoes self-similar coarsening. Disciplines Mathematics | Physical Chemistry Comments This article is from Physical Review Letters 76, no. 4 (1996): 652–655, doi:10.1103/PhysRevLett.76.652. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/chem_pubs/79 VOLUME 76, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 22 JANUARY 1996 Coarsening Mechanisms in a Metal Film: From Cluster Diffusion to Vacancy Ripening J.-M. Wen, J. W. Evans, M. C. Bartelt, J. W. Burnett,* and P. A. Thiel Departments of Chemistry and Mathematics, and Ames Laboratory, Iowa State University, Ames, Iowa 50011 (Received 17 April 1995) Coarsening of Ag films on Ag(100) at room temperature occurs primarily via diffusion-mediated coalescence of two-dimensional adatom clusters, rather than by Ostwald ripening, up to a coverage of 0.65 monolayer. Above 0.8 monolayer, vacancy clusters coarsen primarily via Ostwald ripening, due to their much lower diffusivity. An asymmetric transition region separates these two regimes, characterized by a near-percolating structure which undergoes self-similar coarsening. PACS numbers: 68.35.Fx, 61.16.Ch, 66.30.Fq, 68.60.–p The evolution and control of film morphology is of fundamental and technological interest. Typically, during deposition a film is driven far from equilibrium, and thus can be potentially “trapped” in a variety of manifestly nonequilibrium configurations [1–3]. While this allows control of morphology by intelligent manipulation of deposition parameters, one must recognize that a nonequilibrium structure is always prone to rearrangement. Understanding the mechanisms and kinetics of such rearrangement is necessary to predict film stability, and presents a key challenge in nonequilibrium physics. Below a critical temperature for two-dimensional (2D) phase separation, the equilibrium structure of a partially filled layer consists of a single large domain or “island” of a condensed phase coexisting with a dilute 2D gas phase [4]. Since nucleation and growth of islands during deposition produces a distribution of “smaller” islands [5,6], subsequent temporal evolution toward the equilibrium state must involve coarsening, i.e., an increase in the lengthscale characteristic of the dominant structure [7]. Current discussions of coarsening in adlayers primarily invoke Ostwald ripening (OR) [7,8], at least for low coverages, u. During OR, atoms tend to detach from smaller islands and reattach to larger islands, driven by a gradient in the vapor pressure of the surrounding 2D gas. This process results in asymptotically self-similar growth, with the characteristic linear dimension L increasing with time as L , t1y3 (the Lifshitz-Slyozov law) [9]. It has also been recognized that another mechanism can control coarsening at moderate u, where the adlayer has an interconnected and interpenetrating structure [8]. This is the edge running mechanism, which involves long-range diffusion of adatoms along the domain boundary of the condensed phase. A substantial body of generic 2D lattice-gas modeling of coarsening phenomena exists [10], which might be expected to apply to adlayer evolution. However, in the absence of information on activation barriers for adatom hopping rates in various configurations, these studies invariably use simple Metropolis or Kawasaki rate choices [10]. While this approach might reasonably describe equilibrium behavior (for a suitably chosen Hamiltonian), it cannot correctly predict competition between different kinetic pathways during coarsening of nonequilibrium structures. The primary goal here is to determine the coarsening mechanism and kinetics for various u, for Ag/Ag(100) at 300 K. This is the first comprehensive analysis of adlayer coarsening in such a system. We are even able to assess the relative contributions to coarsening of OR and a competing mechanism, cluster diffusion (CD) and subsequent coalescence, both for adatom clusters at low u and for vacancy clusters at high u. While CD was recognized in older studies of coarsening of 3D metal (adatom) clusters on nonmetallic surfaces [11,12], it has been overlooked in 2D metal-on-metal systems, presumably because of an expectation that diffusion of large 2D adatom or vacancy clusters is insignificant. Previously, the coarsening of vacancy islands has received only cursory attention [13,14]. We find, in fact, that CD of adatom islands dominates coarsening for low u, and present detailed modeling of this behavior. A dramatic asymmetry between behavior at low and high u is revealed. We also determine the transition region where interconnected domains, necessary to support edge running, occur, and apply appropriate concepts from correlated percolation theory to explain why this region occurs well above 0.5 monolayer (ML). Scanning tunneling microscopy (STM) allows direct determination of the mechanism of coarsening (see Fig. 1). We use an Omicron STM housed in a UHV chamber, as described previously [15]. Evaporation of submonolayer coverages, with the sample held at room temperature, generates the “initial” nonequilibrium 2D structures, whose features are then monitored quantitatively as a function of time, to observe coarsening over a period of several hours. Precautions are taken to eliminate tip-induced effects [15]. The nucleation, growth, and subsequent coalescence of 2D islands during deposition is fairly well understood [5]. Nucleation of stable islands occurs only at very low u, after which existing islands grow, and the island density per unit area N remains constant until the onset of growth-induced coalescence around 0.4 ML. Percolation occurs much later, around 0.7–0.8 ML [6]. We can tailor the initial configuration created by deposition, simply by changing the deposition flux R: At fixed u and temperature, N decreases, and the mean island area or size, Sav ø uyN , increases with decreasing R. For the low u (adatom island) regime, we label this initial configuration only with u 652 0031-9007y96y76(4)y652(4)$06.00 © 1996 The American Physical Society VOLUME 76, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 22 JANUARY 1996 FIG. 1. STM images obtained following deposition of Ag on Ag(100) at room temperature. In each row, the left frame shows the starting point, and the right frame shows the surface several hours later. Full horizontal scale is 1500 Å. Bright areas are the deposited film, one atom deep; dark areas are substrate. Each frame shows a single terrace of the substrate, except (b) where bunched steps are visible at the edges. Conditions are (a) 0.11 ML, N0 ­ 4.9 3 1025 Å22, tf ­ 520 min; (b) 0.69 ML, tf ­ 400 min; and (c) 0.87 ML, N0 ­ 1.5 3 1025 Å22, tf ­ 390 min. N0 is the initial island density. and Sav (or, equivalently, u and N), although the full size and separation distributions provide a more complete description. A similar prescription applies to the high u (vacancy cluster) regime. In the transition range of u, where the film constitutes a near-percolating network, an appropriate measure of characteristic linear dimension is the mean chord length or terrace length (in a specified direction). We now examine experimental data for coarsening in the three different u regimes. The low-u (adatom-island) regime illustrated in Fig. 1(a) encompasses the majority of the first layer, since it extends up to about 0.65 ML. Here, we choose four initial configurations, labeled a –d in Fig. 2(a), and show N vs t for each point in Fig. 2(b). In each case, the total decrease in N is broken down into two components: one due to OR, and one due to CD (each component representing N values that would occur if only one of the coarsening mechanisms was active). The contribution of each is determined directly from the STM images. OR is taken to occur when a cluster disappears without an obvious collision, and also without a marked increase in size of any single neighbor. This is often preceded by a gradual shrinkage. CD, on the other hand, can usually be discerned clearly by following the clusters’ trajectories, and by confirming the growth of a single neighbor when a cluster disappears. (A cluster which disappears via OR contributes to the minuscule growth of several neighbors.) Also, after collision, the overlapping, near-square shapes of the two original clusters sometimes remain visible for a time. By applying these criteria in examining the STM images, there is an ambiguity in determining the mechanism of cluster disappearance in ,5% of cases. Surprisingly, in the entire low-u region, coarsening is dominated by CD, rather than by the traditionally pictured OR. Focusing on the part of this regime specified by Fig. 2(a), for instance, OR is insignificant at the two points, a and b, which are characterized by large Sav . OR is measurable for both the lower Sav points, g and d, but even there it only competes significantly with CD at d. See Fig. 2(b). These are reasonable observations, given the recent discovery [15] that large 2D adatom islands on Ag(100) undergo significant diffusion at 300 K on the time scale of equilibration. Within a range of island sizes S of 100– 700 atoms, the diffusion coefficient D ø 10217 cm2 s21 varies little with island size (by a factor of 2 at most), suggesting that cluster diffusion is dominated by evaporationcondensation (EC) processes [15]. Given the weak dependence of D on S, one expects that increasing the average initial island size [e.g., going from g-d to a-b in Fig. 2(a)] does not diminish the effectiveness of the CD process. However, absolute rates for island shrinkage FIG. 2. Coarsening in the low-coverage regime. (a) The sizecoverage space spanned by the four points studied. Initial conditions are (a) 0.27 ML, N0 ­ 6.7 3 1025 Å22; (b) 0.07 ML, N0 ­ 2.6 3 1025 Å22; (g) 0.05 ML, N0 ­ 5.8 3 1025 Å22; (d) 0.03 ML, N0 ­ 3.7 3 1025 Å22. (b) Island densities as functions of time, for the four data points in (a), normalized to the initial density. (c) Rate-equation results (solid lines) for data corresponding to a and b.