Kinetically driven island morphology in growth on strained Cu(100).

We study the effects of strain on the monomer and dimer diffusion mechanisms and island morphology during the growth of Cu on a biaxially strained Cu(100) substrate. We find an approximately linear dependence of the activation barriers on strain. In particular, while hopping is favored for compressive and/or small (<2%) tensile strain, for greater than 2% tensile strain, the exchange mechanism is favored. We then present the results of temperature-accelerated dynamics simulations of submonolayer growth at 200 K. For the case of 2% compressive strain we find that, as in previous kinetic Monte Carlo simulations of Cu/Ni(100) growth, the competition between island growth and multi-atom relaxation ("pop-out") events leads to an island morphology with a mixture of open and closed steps. At slightly higher coverage, island coalescence then leads to elongated islands. However, annealing leads to a significant decrease in the number of open steps. In contrast, for the case of 8% tensile strain, only one large strongly anisotropic island is formed. Surprisingly, we find that despite the large strain, the island anisotropy is not due to energetics but is instead due to anisotropic attachment barriers that favor the exchange-mediated attachment of monomers to corners over close-packed step-edges. An explanation for the asymmetry in attachment barriers is provided. Our results provide a new general kinetic mechanism for the formation of anisotropic islands in the presence of isotropic diffusion and tensile strain.

Improved scaling of temperature-accelerated dynamics using localization.

While temperature-accelerated dynamics (TAD) is a powerful method for carrying out non-equilibrium simulations of systems over extended time scales, the computational cost of serial TAD increases approximately as N(3) where N is the number of atoms. In addition, although a parallel TAD method based on domain decomposition [Y. Shim et al., Phys. Rev. B 76, 205439 (2007)] has been shown to provide significantly improved scaling, the dynamics in such an approach is only approximate while the size of activated events is limited by the spatial decomposition size. Accordingly, it is of interest to develop methods to improve the scaling of serial TAD. As a first step in understanding the factors which determine the scaling behavior, we first present results for the overall scaling of serial TAD and its components, which were obtained from simulations of Ag/Ag(100) growth and Ag/Ag(100) annealing, and compare with theoretical predictions. We then discuss two methods based on localization which may be used to address two of the primary "bottlenecks" to the scaling of serial TAD with system size. By implementing both of these methods, we find that for intermediate system-sizes, the scaling is improved by almost a factor of N(1/2). Some additional possible methods to improve the scaling of TAD are also discussed.

Critical island size, scaling, and ordering in colloidal nanoparticle self-assembly.

In order to obtain a better understanding of short-range (SR) and long-range (LR) nanoparticle (NP) interactions during the self-assembly of dodecanethiol-coated Au NPs in toluene via drop drying, we have investigated the dependence of the island density, scaled island-size distribution (ISD), and scaled capture-zone distribution (CZD) on coverage, deposition flux, and NP size. Our results indicate that, while the critical island size is larger than 1 for all NP sizes studied, due to the increase in the strength of the SR attraction between NPs with increasing NP size, both the exponent describing the dependence of the island density on deposition flux and the critical island-size decrease with increasing NP size. We also find that, despite the existence of significant cluster diffusion and coalescence, the ISD is sharply peaked as in epitaxial growth. In particular, for large NP size, we find good agreement between the scaled ISD and epitaxial growth models as well as good agreement between the scaled CZD and scaled ISD. However, for smaller NPs the scaled ISD is less sharply peaked despite the fact that the critical island size is larger. This latter result suggests that in this case additional effects such as enhanced island coalescence or NP detachment from large islands may play an important role. Results for the ordering of NP islands are also presented which indicate the existence of LR repulsive interactions. One possible mechanism for such an interaction is the existence of a small dipole moment on each NP which arises as a result of an asymmetry, driven by surface tension, in the thiol distribution for NPs adsorbed at the toluene-air interface. Consistent with this mechanism, we find good agreement between experimental results for the nearest-neighbor island-distance distribution and simulations which include dipole repulsion.

Localized saddle-point search and application to temperature-accelerated dynamics.

We present a method for speeding up temperature-accelerated dynamics (TAD) simulations by carrying out a localized saddle-point (LSAD) search. In this method, instead of using the entire system to determine the energy barriers of activated processes, the calculation is localized by only including a small chunk of atoms around the atoms directly involved in the transition. Using this method, we have obtained N-independent scaling for the computational cost of the saddle-point search as a function of system size N. The error arising from localization is analyzed using a variety of model systems, including a variety of activated processes on Ag(100) and Cu(100) surfaces, as well as multiatom moves in Cu radiation damage and metal heteroepitaxial growth. Our results show significantly improved performance of TAD with the LSAD method, for the case of Ag/Ag(100) annealing and Cu/Cu(100) growth, while maintaining a negligibly small error in energy barriers.

Shape transitions in strained Cu islands on Ni(100): kinetics versus energetics.

We examine the ramified islands observed in submonolayer Cu/Ni(100) growth. Our results indicate that the strain-energy contribution to the dependence of island energy on shape is surprisingly weak. In contrast, our accelerated dynamics simulations indicate that unexpected concerted popout processes occurring at step edges may be responsible. Kinetic Monte Carlo (KMC) simulations which include these processes produce island shapes which are very similar to those observed in experiment. These results suggest that the shape transition is of kinetic origin but is strongly mediated by strain.

Adaptive temperature-accelerated dynamics.

We present three adaptive methods for optimizing the high temperature T(high) on-the-fly in temperature-accelerated dynamics (TAD) simulations. In all three methods, the high temperature is adjusted periodically in order to maximize the performance. While in the first two methods the adjustment depends on the number of observed events, the third method depends on the minimum activation barrier observed so far and requires an a priori knowledge of the optimal high temperature T(high)(opt)(E(a)) as a function of the activation barrier E(a) for each accepted event. In order to determine the functional form of T(high)(opt)(E(a)), we have carried out extensive simulations of submonolayer annealing on the (100) surface for a variety of metals (Ag, Cu, Ni, Pd, and Au). While the results for all five metals are different, when they are scaled with the melting temperature T(m), we find that they all lie on a single scaling curve. Similar results have also been obtained for (111) surfaces although in this case the scaling function is slightly different. In order to test the performance of all three methods, we have also carried out adaptive TAD simulations of Ag/Ag(100) annealing and growth at T = 80 K and compared with fixed high-temperature TAD simulations for different values of T(high). We find that the performance of all three adaptive methods is typically as good as or better than that obtained in fixed high-temperature TAD simulations carried out using the effective optimal fixed high temperature. In addition, we find that the final high temperatures obtained in our adaptive TAD simulations are very close to our results for T(high)(opt)(E(a)). The applicability of the adaptive methods to a variety of TAD simulations is also briefly discussed.

Effects of substrate rotation in oblique-incidence metal(100) epitaxial growth.

The effects of substrate rotation on the surface morphology in oblique-incidence metal(100) epitaxial growth are studied via kinetic Monte Carlo simulations of a simplified model, and compared with previous results obtained without rotation. In general, we find that substrate rotation leads to two main effects. At high deposition angles with respect to the substrate normal, rotation leads to a significant change in the surface morphology. In particular, it leads to isotropic mounds and pyramids with (111) facets rather than the anisotropic ripples and rods observed in the absence of rotation. Due to the existence of rapid transport on these facets, the lateral feature size increases approximately linearly with film thickness. Due to the fact that substrate rotation tends to reduce the effects of shadowing, the surface roughness is also decreased compared to the roughness in the absence of rotation. While this leads to a moderate reduction in the roughness for the case of ballistic deposition, the effect is significantly larger in the case of deposition with attraction. In the case of ballistic deposition, we also find that the surface roughness increases with rotation rate Omega for Omega<1 rev/monolayer (ML) before saturating at larger rotation rates ( Omega>1 rev/ML). In contrast, for the case of attraction the surface roughness exhibits a negligible dependence on rotation rate for finite rotation rate.

Capture-zone areas in submonolayer nucleation: effects of dimensionality and short-range interactions.

Simulation results for the asymptotic scaled capture-zone distribution (CZD) for the case of irreversible nucleation and growth of point islands are presented for substrate dimension d=1 , 2, 3, and 4 and compared with a recent conjecture based on the Wigner distribution. Poor agreement is found between the predicted Wigner distributions and the asymptotic CZD in the limit of infinite DF (corresponding to the ratio of monomer hopping rate D to deposition rate F ). Our results also indicate that for d=2 and 3 the asymptotic CZD for point islands is independent of model details and dimension. However, for d=1 and d=4 the resulting distribution is significantly more sharply peaked. We also find that in contrast to the island-size distribution, for which mean-field-like behavior is observed in d=3 and above, the asymptotic CZD is significantly broadened by fluctuations even in d=4 .

Parallel kinetic Monte Carlo simulations of Ag(111) island coarsening using a large database.

The results of parallel kinetic Monte Carlo (KMC) simulations of the room-temperature coarsening of Ag(111) islands carried out using a very large database obtained via self-learning KMC simulations are presented. Our results indicate that, while cluster diffusion and coalescence play an important role for small clusters and at very early times, at late time the coarsening proceeds via Ostwald ripening, i.e. large clusters grow while small clusters evaporate. In addition, an asymptotic analysis of our results for the average island size S(t) as a function of time t leads to a coarsening exponent n = 1/3 (where S(t)∼t(2n)), in good agreement with theoretical predictions. However, by comparing with simulations without concerted (multi-atom) moves, we also find that the inclusion of such moves significantly increases the average island size. Somewhat surprisingly we also find that, while the average island size increases during coarsening, the scaled island-size distribution does not change significantly. Our simulations were carried out both as a test of, and as an application of, a variety of different algorithms for parallel kinetic Monte Carlo including the recently developed optimistic synchronous relaxation (OSR) algorithm as well as the semi-rigorous synchronous sublattice (SL) algorithm. A variation of the OSR algorithm corresponding to optimistic synchronous relaxation with pseudo-rollback (OSRPR) is also proposed along with a method for improving the parallel efficiency and reducing the number of boundary events via dynamic boundary allocation (DBA). A variety of other methods for enhancing the efficiency of our simulations are also discussed. We note that, because of the relatively high temperature of our simulations, as well as the large range of energy barriers (ranging from 0.05 to 0.8 eV), developing an efficient algorithm for parallel KMC and/or SLKMC simulations is particularly challenging. However, by using DBA to minimize the number of boundary events, we have achieved significantly improved parallel efficiencies for the OSRPR and SL algorithms. Finally, we note that, among the three parallel algorithms which we have tested here, the semi-rigorous SL algorithm with DBA led to the highest parallel efficiencies. As a result, we have obtained reasonable parallel efficiencies in our simulations of room-temperature Ag(111) island coarsening for a small number of processors (e.g. N(p) = 2 and 4). Since the SL algorithm scales with system size for fixed processor size, we expect that comparable and/or even larger parallel efficiencies should be possible for parallel KMC and/or SLKMC simulations of larger systems with larger numbers of processors.

Vacancy formation and strain in low-temperature Cu/Cu(100) growth.

The development of compressive strain in metal thin films grown at low temperature has recently been revealed via x-ray diffraction and explained by the assumption that a large number of vacancies were incorporated into the growing films. The results of our molecular dynamics and parallel temperature-accelerated dynamics simulations suggest that the experimentally observed strain arises from an increased nanoscale surface roughness caused by the suppression of thermally activated events at low temperature combined with the effects of shadowing due to off-normal deposition.

Parallel kinetic Monte Carlo simulations of two-dimensional island coarsening.

The results of parallel kinetic Monte Carlo (KMC) simulations of island coarsening based on a bond-counting model are presented. Our simulations were carried out both as a test of and as an application of the recently developed semirigorous synchronous sublattice (SL) algorithm. By carrying out simulations over long times and for large system sizes the asymptotic coarsening behavior and scaled island-size distribution (ISD) were determined. Our results indicate that while cluster diffusion and coalescence play a role at early and intermediate times, at late times the coarsening proceeds via Ostwald ripening. In addition, we find that the asymptotic scaled ISD is significantly narrower and more sharply peaked than the mean-field theory prediction. The dependence of the scaled ISD on coverage is also studied. Our results demonstrate that parallel KMC simulations can be used to effectively extend the time scale over which realistic coarsening simulations can be carried out. In particular, for simulations of the late stages of coarsening with system size L=1600 and eight processors, a parallel efficiency larger than 80% was obtained. These results suggest that the SL algorithm is likely to be useful in the future in parallel KMC simulations of more complicated models of coarsening.

Effects of shadowing in oblique-incidence metal (100) epitaxial growth.

The effects of shadowing in oblique-incidence metal (100) epitaxial growth are studied using a simplified model. We find that many of the features observed in Cu(100) growth, including the existence of a transition from anisotropic mounds to ripples perpendicular to the beam, can be explained primarily by geometrical effects. We also show that the formation of (111) facets is crucial to the development of ripples at large angles of incidence. A second transition to "rods" with (111) facets oriented parallel to the beam is also found at high deposition angles and film thicknesses.

Upper critical dimension for irreversible cluster nucleation and growth in the point-island regime.

We compare the results of kinetic Monte Carlo (KMC) simulations of a point-island model of irreversible nucleation and growth in four dimensions (4D) with the corresponding mean-field (MF) rate-equation predictions for the monomer density, island density, island-size distribution (ISD), capture-number distribution (CND), and capture-zone distribution (CZD), in order to determine the critical dimension d(c) for mean-field behavior. The asymptotic behavior is studied as a function of the fraction of occupied sites (coverage) and the ratio DF of the monomer hopping rate D to the (per site) monomer creation rate F. Excellent agreement is found between our KMC simulation results and the MF rate equation results for the average island and monomer densities. For large D/F, the scaled CND and CZD do not depend on island size, in good agreement with the MF prediction, while the scaled ISD also agrees well with the MF prediction except for a slight difference at the peak values. Coupled with previous results obtained in d = 3 , these results indicate that for growth in the point-island regime, the upper critical dimension for irreversible cluster nucleation and growth is equal to 4.