PHYSICAL REVIEW B 83, 245419 (2011) Ab initio study of edge smoothing, atom attraction, and downward funneling in Ag/Ag(100) Yunsic Shim and Jacques G. Amar Department of Physics and Astronomy, University of Toledo, Toledo, Ohio 43606, USA (Received 21 July 2010; revised manuscript received 11 May 2011; published 22 June 2011) The results of density-functional theory (DFT) calculations of the energy barriers for three low-barrier relaxation processes in Ag/Ag(100) growth—edge-zipping, atom attraction, and downward funneling—are presented and compared with embedded atom method (EAM) calculations. In general, we find good agreement between the DFT values for these processes and the values assumed in recent simulations of low-temperature Ag/Ag(100) growth [Shim and Amar, Phys. Rev. B 81, 045416 (2010)]. We also find reasonable agreement between our DFT results and the results of EAM calculations, although in a few specific cases there is a noticeable disagreement. In order to investigate the effects of long-range interactions, we have also carried out additional calculations for more complex configurations. While our EAM results indicate that long-range interactions such as “pinning” can significantly enhance the energy barriers for edge-zipping and atom attraction, these effects can be significantly weaker in our DFT calculations due to the redistribution of the electron density. DOI: 10.1103/PhysRevB.83.245419 PACS number(s): 68.43.Jk, 31.15.A−, 81.15.Aa I. INTRODUCTION Recently, there has been a great deal of progress in un- derstanding the morphological evolution in epitaxial thin-film growth (for a recent review see Ref. 1), and a variety of effects and processes have been shown to play an important role. One case of particular interest is that of Ag/Ag(100) growth, for which an unusually complex dependence of the surface roughness on deposition temperature has been observed over the temperature range T = 55–300 K. 2 In particular, as the temperature was reduced below 300 K, the roughness of 25-monolayer (ML) films was found to first increase—with a peak at approximately 220 K—and then decrease as the temperature was further reduced. As the temperature was decreased below 135 K, the roughness again increased—with a second low-temperature peak at approximately 90 K—and then decreased again as the temperature was further reduced to 55 K. While the high-temperature behavior (T = 135–300 K) has been quantitatively explained using a simplified model 2 that assumes instantaneous island restructuring and also takes into account the effects of an Ehrlich-Schwoebel barrier to interlayer diffusion, 3 such a model leads to poor agreement with experiment at lower temperatures. Recently we have shown 4 that by explicitly taking into account a variety of low-barrier processes for edge smoothing and interlayer diffusion at kinks, as well as for downward funneling 5 (DF) of atoms deposited at threefold hollow sites, the low-temperature behavior may be qualitatively explained. These include the process of edge-zipping, which tends to regularize (110) step edges and corresponds to the “attraction” of a monomer to two next-nearest-neighbor atoms [which may or may not have additional nearest-neighbor bonds; see Figs. 1(a)–1(c)] as well as the process of atom attraction corresponding to the attraction of a monomer to a single next-nearest-neighbor atom or a nearby island [see Figs. 1(d)–1(f)]. The barriers for DF of atoms deposited at nonfourfold-hollow sites [see Figs. 4(a)– 4(c)] were also found to play an important role in determining the temperature dependence of the surface roughness. By including barriers for these processes obtained primarily from embedded atom method 6 (EAM) calculations, along with the effects of short-range attraction of depositing atoms to microprotrusions, 7–10 excellent quantitative agreement with experiment was obtained over the entire temperature range T = 55–180 K. In particular, our results indicated that the non- monotonic temperature dependence of the surface roughness below 110 K is primarily determined by a competition between the process of edge-zipping and DF at threefold hollow sites (see Fig. 4). Our results also indicated that at somewhat higher temperatures (T> 110 K) the processes of atom attraction 4 and edge diffusion 11 also play an important role since they tend to suppress interlayer diffusion. In the kinetic Monte Carlo (KMC) simulations carried out in Ref. 4, activation barriers for these processes obtained using the embedded atom method 6 (EAM) were primarily used since these are considered to be relatively accurate for metals, while density-functional theory (DFT) 12 calculations were only available for a few higher-barrier processes, 11,13–15 such as monomer diffusion on a flat terrace, single-bond edge diffusion along an infinitely long step edge, and interlayer diffusion at a (110) step edge. Therefore it is of interest to carry out ab initio calculations in order to determine more accurately the energy barriers for these key processes. In addition, we note that our KMC simulations 4 indicated that the value (0.16 eV) of the energy barrier for edge-zipping calculated by Mehl et al. 16 using the Adams, Foiles, and Wolfer (AFW) EAM potential 17 leads to good agreement 4 with the ex- perimentally observed temperature (T ≃ 90 K) corresponding to the low-temperature peak in surface roughness. However, the Voter-Chen (VC) EAM potential 18 leads to a barrier for edge-zipping, which is significantly lower (0.09 eV) thus leading to a peak in the surface roughness as a function of temperature, which occurs at a significantly lower temperature than in experiment. A similar but smaller discrepancy occurs between the AFW and VC barriers for atom attraction. Here we present the results of DFT calculations of the barriers for edge-zipping, DF at 3 + 0, 3 + 1, and 3 + 2 sites (where 3 + x denotes a threefold hollow site with x in-plane lateral bonds), and atom attraction. In general, we find that the local-density approximation (LDA) leads to barriers which are somewhat higher than those obtained using the generalized 245419-1 1098-0121/2011/83(24)/245419(6) ©2011 American Physical Society