Time-lapse STM images that illustrate ripening mechanisms of 2D Ag islands. (A) A small island, noted by the arrow, diminishes due to OR on Ag(111) at 300 K. 2 min after the last image, the island disappears. Image sizes are . (B) Islands coalesce due to diffusion (SR) on Ag(100) at 300 K. Image sizes are . Islands that will merge before a following image are linked by black bars. This analysis is based upon inspection of many sequential images in between the ones shown.
(Color online) Log-log plots of the coarsening rate, , vs island radius, , for (A) Ag islands on Ag(100) and (B) Ag islands on Ag(111). The units of are the surface lattice constant, , and the units of K are . Curves are based on the analysis in Ref. 42 .
Schematic illustration of the possible potential energy surface for a metal adatom near a step edge. Reproduced from Ref. 31 with permission from Elsevier.
Comparison of OR rates on low-index surfaces of Ag. Experimental data are shown as individual points. (a) shows decay of single Ag islands on (110) and (111) surfaces at 225 K. For both data sets, the initial island area is . For the (111), the average initial island area is , and the island is close to an extended step edge and larger islands (atom sinks), so the driving force for coarsening is strong. The (110) data were kindly provided by . Morgenstern. (b) shows the increase in average area of (111) and (100) island ensembles at 300 K. Note the different ordinates for the (111) and (100). The straight lines show how the rates were estimated. The data for (100) reflect SR, not OR, but the rate of SR can be taken as an upper limit on the rate of OR.
Two sequences of STM images, following deposition of 0.3 ML Ag on Ag(100). Image size: . Panels A–C show coarsening of the clean surface at 250 K, at various times after deposition. (A) 25 min, (B) 89 min, and (C) 160 min. Panels D–F show the coarsening of the surface at 250 K, after exposure to 20 l oxygen. (D) 9 min after deposition, (E) 77 min, and (F) 167 min. Note that the total times elapsed in panels C and F are similar. Reproduced from Ref. 62 with permission. Copyright 2009 Elsevier.
Semilog plot of the ratio of decay rates (inverse lifetimes) for Cu islands on Cu (111) in the presence and absence of sulfur, as a function of . The data derives from both STM and LEEM experiments at 488 K. The data have been replotted from Fig. 2 of Ref. 34 , with permission from the authors. Copyright 2004 by the American Physical Society.
Semilog plot of the ratio of decay rates (inverse lifetimes) for Ag islands on Ag(111) in the presence and absence of sulfur, as a function of . At 0.035, decay is so rapid that a quantitative analysis is not possible, and the horizontal bar represents the lower limit. Adapted from Ref. 30 with permission.
Illustration of the formation of a Ag adatom (labeled Ag) on a terrace, starting from (A) a kink site at a clean step edge and (B) a kink site at a step edge decorated with an adsorbed sulfur or oxygen atom (black circle).
Illustration of the formation of a cluster on a terrace, starting from Ag atoms at a kink site at a clean step edge, and S atoms on terraces (black circles).
Schematic of an cluster on Ag(111). The Ag atom is in a bridge site, and the S atoms are in hollow sites. Reproduced from Ref. 30 with permission. Copyright 2009 American Institute of Physics.
STM images of Ag(111) after S adsorption at 200 K, showing the evolution of dot-rows and pits with increasing coverage. In the left column [(A)–(C)], each image is , and in the right column each image is . Values of are [(A) and ] 0.03, [(B) and ] 0.1, and [(C) and ] 0.3. Reproduced from Ref. 62 with permission. Copyright 2008 American Chemical Society.
STM images of Ag(111), showing temporal changes in dot-row domains at 200 K. The image size is , acquisition time is 200 s/image, and . There is no time lapse between images. Reproduced from Ref. 62 with permission. Copyright 2008 American Chemical Society.
Sequence of STM images of Ag(111). (A) After deposition of 1.2 ML Ag at 135 K, and then heating to 200 K. (B) Follows (A), after 120 min in ultrahigh vacuum at 200 K. (C) After deposition of 0.12 ML S at 200 K. (D) Same as (C), but higher magnification so that dot rows are visible. (E) Same as (d), after 45 min in vacuum at 200 K. Image size in (A)–(C) is , and in (D) and (E) it is . Reproduced from Ref. 31 with permission. Copyright 2009 Elsevier.
Schematic illustration of the consumption of Ag atoms during formation of clusters. White circles are Ag atoms, and black circles are S atoms. (A) At low S coverage, clusters form from Ag adatoms that are on the terrace and in equilibrium with the step edge. The net result is that the step edge recedes. (B) At higher S coverage, diffusion of Ag on the terrace is impeded, so the source of Ag becomes the terrace itself. A pit results.
Schematic representations of two cluster-based mechanisms for accelerated coarsening. For clarity, only processes and species involved in net mass transfer between the edge of the small island, and the edge of the large island or terrace, are shown. In (A), a shuttle-pair consisting of and detach and attach intact at step edges, as proposed in Ref. 29 . In (B), a single type of cluster, , is involved, as proposed in Ref. 34 . Metal adatoms attach and detach at step edges, forming clusters on the terraces. Adapted from Ref. 31 with permission. Copyright 2009 Elsevier.
Values of and in eV, for isolated metal atoms on different low-index surfaces. The origin of the values is noted as DFT, effective medium theory (EMT), embedded atom method (EAM), Rosato–Guillope–Legrand (RGL) potential (Refs. 72 and 73 ), or experiment (EXP). The sum is the barrier for OR, if coarsening kinetics are TD limited. This condition is met for most surfaces under most conditions. An exception is noted in Sec. II . If unlabeled, a value of the sum in the right-hand column is derived from theory—preferentially from within a single calculation.
Values of and in eV, calculated with DFT, for Ag–S, Cu–S, and Au–S clusters on the corresponding unreconstructed (111) metal surfaces. The error estimates reflect numerical uncertainties arising from insufficient -points, slab thickness, etc. They do not reflect inherent theoretical limitations. The far-right column shows values reproduced from Table I , to facilitate comparison between clusters and metal atoms as agents of mass transport in the case of TD-limited OR. is calculated from Eq. (1) , with for TD-limited kinetics, and with no contribution from if .
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