Strain-dependence of Te interstitial diffusion in CdTe.

While the dominant defects which control non-radiative recombination and long-range interstitial diffusion in CdTe correspond to Cd vacancies and Te anti-sites, the short-range diffusion of Te and Se interstitials between these defects is also of interest, since they both play a role in defect passivation. In addition, since CdTe thin films are typically polycrystalline and may also involve interfaces with materials with different lattice constants, the effects of strain are also of interest. Here we present the results of molecular dynamics (MD) simulations of Te interstitial diffusion in zincblende CdTe for values of the triaxial strain ranging from -2% (compressive) strain to +2.8% (tensile) strain. By carrying out MD simulations of Te interstitial diffusion over a range of temperatures, and then carrying out Arrhenius fits, we have determined the effective activation barrier E_a and prefactor D_0 for each value of the global strain. We find that both E_a and D_0 exhibit non-monotonic behavior, increasing with both compressive and tensile strain. We also present an analysis of the key diffusion pathways for 3 different values of the strain which explains the non-monotonic strain dependence obtained in our simulations. Our results also indicate that in each case, the diffusion of interstitial Te involves a variety of concerted events with a wide range of activation barriers. .

Island density scaling in reversible submonolayer growth with attachment barriers.

Island nucleation and growth play an important role in thin-film growth. One quantity of particular interest is the exponent χ, which describes the dependence of the saturation island density N_{sat}∼(D_{h}/F)^{-χ} on the ratio D_{h}/F of the monomer hopping rate D_{h} to the deposition rate F. While standard rate equation (RE) theory predicts that χ=i/(i+2) (where i is the critical island size), more recently it has been predicted that in the presence of a strong barrier to the attachment of monomers to islands, a significantly larger value χ=2i/(i+3) may be observed. While this prediction has recently been tested using kinetic Monte Carlo simulations for the case of irreversible growth corresponding to i=1, it has not been tested for the case of reversible island growth corresponding to i>1. Here we present a mean-field self-consistent RE method which we have used to study the dependence of the effective value of χ on D_{h}/F and barrier-strength for i=1,2,3, and 6. Both the no-nucleation-barrier case in which there exists a barrier for monomers to attach to islands larger than the critical island size (but not to smaller islands) and the nucleation-barrier case in which there is a barrier for monomers to attach to islands of all sizes are studied. In all cases, we find that the existence of attachment barriers significantly increases the effective value of χ for a given barrier strength. In addition, for i=1 we find good agreement between our extrapolated asymptotic value of χ and the theoretical strong-barrier prediction both with and without a nucleation barrier. In contrast, for i>1 the value of χ is significantly larger in the presence of a nucleation barrier than in its absence. In particular, while an asymptotic analysis of our results for i>1 also leads to excellent agreement with the strong barrier prediction in the presence of a nucleation barrier, in the absence of a nucleation barrier the asymptotic values are significantly lower.

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.

Intracellular detection of singlet oxygen using fluorescent nanosensors.

Detection of singlet oxygen is of great importance for a range of therapeutic applications, particularly photodynamic therapy, plasma therapy and also during photo-endosomolytic activity. Here we present a novel method of intracellular detection of singlet oxygen using biocompatible polymeric nanosensors, encapsulating the organic fluorescent dye, Singlet Oxygen Sensor Green (SOSG) within its hydrophobic core. The singlet oxygen detection efficiency of the nanosensors was quantified experimentally by treating them with a plasma source and these results were further validated by using Monte Carlo simulations. The change in fluorescence intensity of the nanosensors serves as a metric to detect singlet oxygen in the local micro-environment inside mammalian cancer cells. We used these nanosensors for monitoring singlet oxygen inside endosomes and lysosomes of cancer cells, during cold plasma therapy, using a room-temperature Helium plasma jet.

Island nucleation and growth with anomalous diffusion in one-dimension.

Recently a general rate-equation (RE) theory of submonolayer island nucleation and growth was developed [J. G. Amar and M. Semaan, Phys. Rev. E 93, 062805 (2016)] which takes into account the critical island-size i, island fractal dimension df, substrate dimension d, and diffusion exponent µ, and good agreement with simulations was found for the case of irreversible growth corresponding to a critical island-size i=1 with d = 2. Here we present the results of simulations carried out in 1D (corresponding to d = 1) of island nucleation and growth with anomalous diffusion which were carried out for both the case of superdiffusion (µ>1) and subdiffusion (µ<1). Excellent agreement is found with the general RE theory for both irreversible growth (i=1) and reversible growth with i=2 for all 0≤µ≤2.

Island nucleation and growth with anomalous diffusion.

While most studies of submonolayer island nucleation and growth have been based on the assumption of ordinary monomer diffusion corresponding to diffusion exponent µ=1, in some cases either subdiffusive (µ<1) or superdiffusive (µ>1) behavior may occur. Here we present general expressions for the exponents describing the flux dependence of the island and monomer densities as a function of the critical island size i, substrate dimension d, island fractal dimension d_{f}, and diffusion exponent µ, where 0≤µ≤2. Our results are compared with kinetic Monte Carlo simulations for the case of irreversible island growth (i=1) with 0≤µ≤2 and d=2 as well as simulation results for d=1, 3, and 4, and excellent agreement is found.

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, stability, and morphology of 2D colloidal Au nanoparticle islands.

The critical island-size, stability, and morphology of 2D colloidal Au nanoparticle islands formed during drop-drying are studied using an empirical potential which takes into account core-core, ligand-ligand, and ligand-solvent interactions. Good agreement with experiment is obtained for the dependence of the critical island-size on nanoparticle diameter. Our results for the critical length-scale for smoothing via edge-diffusion are also consistent with the limited facet size and island-relaxation observed in experiments. In addition, the relatively high rate of monomer diffusion on an island as well as the low barrier for interlayer diffusion are consistent with experimental observations that second-layer growth does not occur until after the first layer is complete.

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.

Adsorption and diffusion of colloidal Au nanoparticles at a liquid-vapor interface.

Motivated by recent drop-drying experiments of Au nanoparticle (NP) island self-assembly, we investigate the structure, diffusion, and binding of dodecanethiol-coated Au NPs adsorbed at the toluene-vapor interface using molecular dynamics (MD) simulations as well as analytical calculations. For a 6 nm core diameter NP our results indicate the existence of significant intermixing between the ligands and the solvent. As a result, the NP lies primarily below the interface with only a portion of the ligands sticking out, while the toluene-vapor interface is significantly higher in the region above the NP core than away from the NP. These results are consistent with a competition between the negative free energy of mixing of toluene and the dodecanethiol ligands, which tends to keep the NP below the interface, and the effects of surface tension which keeps the NP near the interface. Consistent with this result, we find that the coefficient for nanoparticle diffusion along the interface is close to the Stokes-Einstein prediction for three-dimensional bulk diffusion. An analysis of the ligand arrangement surrounding the NP also indicates that there is relatively little asymmetry in the ligand-coating. We then consider the effects of van der Waals interactions on the adsorption energy. In particular, we derive an analytical expression for the van der Waals interaction energy between a coated nanoparticle and the surrounding solvent along with a closed-form expression for the van der Waals corrections to the binding energy at the interface due to the long-range core-solvent interaction. Using these results along with the results of our MD simulations, we then estimate the van der Waals corrections to the adsorption energy for dodecanethiol-coated Au nanoparticles at the toluene-vapor interface as well as for decanethiol-coated nanoparticles at the water-vapor interface. In both cases, we find that the long-range core-solvent interaction may significantly reduce the binding energy. Based on these results, we conclude that in many cases, the core-solvent van der Waals interaction is likely to have a significant effect on the binding energy and interface position of Au NPs. Our results also indicate that the competition between the van der Waals interaction and the short-range attraction to the interface leads to the existence of well-defined activation barriers for nanoparticle adsorption from the solvent as well as for interfacial desorption.

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.

Rate-equation approach to irreversible island growth with cluster diffusion.

A self-consistent rate-equation (RE) approach to irreversible island growth and nucleation is presented which takes into account cluster mobility. As a first application, we consider the irreversible growth of compact islands on a two-dimensional surface in the presence of monomer deposition (with rate F) and monomer diffusion (with rate D(1)) while the mobility of an island of size s is assumed to satisfy D(s)=D(1)s(-µ) where µ>0. Results are obtained for the dependence of the island-density and island-size distribution (ISD) on the parameters D(1)/F, µ, and coverage θ. For all values of µ, we find excellent agreement between our self-consistent RE results and simulation results for the island and monomer densities, up to and even somewhat beyond the coverage corresponding to the peak island density. We also find good agreement between our self-consistent RE and simulation results for the portion of the ISD corresponding to island sizes less than the average island-size S. However, for larger island sizes the effects of correlations become important and as a result the agreement is not as good. Using our self-consistent RE approach we also demonstrate that the discrepancies between simulations and recent mean-field predictions for the exponent τ(µ) describing the power-law size dependence of the ISD for µ<1 can be explained almost entirely by geometric effects. Our results are also compared with those obtained using a simpler mean-field Smoluchowski approach. In general, we find that, except for the case µ=1/2 (for which the island and monomer densities are reasonably well predicted), such an approach leads to results which are in poor agreement with the simulations.

Effects of cluster diffusion on the island density and size distribution in submonolayer island growth.

The effects of cluster diffusion on the submonolayer island density and island-size distribution are studied for the case of irreversible growth of compact islands on a 2D substrate. In our model we assume instantaneous coalescence of circular islands, while the cluster mobility is assumed to exhibit power-law decay as a function of island size with exponent µ. Results are presented for µ=1/2,1, and 3/2 corresponding to cluster diffusion via Brownian motion, correlated evaporation condensation, and edge diffusion respectively, as well as for higher values including µ=2,3, and 6. We also compare our results with those obtained in the limit of no cluster mobility (µ=∞). In agreement with theoretical predictions of power-law behavior of the island-size distribution (ISD) for µ<1, for µ=1/2 we find N(s)(θ)~s(-τ) [where N(s)(θ) is the number of islands of size s at coverage θ] up to a crossover island-size S(c). However, the value of the exponent τ obtained in our simulations is higher than the mean-field (MF) prediction τ=(3-µ)/2. Similarly, the measured value of the exponent ζ corresponding to the dependence of S(c) on the average island-size S (e.g., S(c)~S(ζ)) is also significantly higher than the MF prediction ζ=2/(µ+1). A generalized scaling form for the ISD [N(s)(θ)=θ/S(1+τζ)f(s/S(ζ))] is also proposed for µ<1, and using this form excellent scaling is found for µ=1/2. However, for finite µ≥1 neither the generalized scaling form nor the standard scaling form N(s)(θ)=θ/S(2)f(s/S) lead to scaling of the entire ISD for finite values of the ratio R of the monomer diffusion rate to deposition flux. Instead, the scaled ISD becomes more sharply peaked with increasing R and coverage. This is in contrast to models of epitaxial growth with limited cluster mobility for which good scaling occurs over a wide range of coverages.

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.

Island-size distribution and capture numbers in three-dimensional [corrected] nucleation: dependence on island morphology.

The scaling of the monomer and island densities, island-size distribution (ISD), and capture-number distribution (CND) as a function of the fraction of occupied sites (coverage) and ratio D(h)/F of the monomer hopping rate D(h) to the (per site) monomer creation rate F are studied for the case of irreversible nucleation and growth of fractal islands in three dimensions (d=3) . We note that our model is a three-dimensional analog of submonolayer growth in the absence of island relaxation and may also be viewed as a simplified model of the early stages of vacancy cluster nucleation and growth under irradiation. In contrast to results previously obtained for point-islands in d=3 , for which mean-field behavior corresponding to a CND which is independent of island size was observed, our results indicate that for fractal islands the scaled CND increases approximately linearly with island size in the asymptotic limit of large D(h)/F . In addition, while the peak height of the scaled ISD for fractal islands appears to diverge with increasing D(h)/F , the dependence on D(h)/F is much weaker than for point-islands in d=3 . The results of a self-consistent rate-equation calculation for the coverage and D(h)/F dependence of the average island and monomer densities are also presented and good agreement with simulation results is obtained. For the case of point-islands, the value of the exponent chi describing the D(h)/F dependence of the island density at fixed coverage, e.g., N(sat) approximately (D(h)/F)-chi , is in good agreement with the value (chi=1/3) expected for irreversible growth. However, for both compact and fractal islands in d=3 , our results indicate that the value of chi (chi approximately 0.42) is significantly larger. In order to explain this behavior, an analytical expression [e.g., chi=d(f)/(3d(f)-2) ] for the dependence of chi on island fractal dimension d(f) in d=3 is derived and found to give reasonable agreement with our simulation and rate-equation results for the case of point-islands (d(f)=infinity) , compact islands (d(f)=3) , and fractal islands (d(f) approximately 2.5) . A general expression for the exponent chi , valid for d>or=2 , as a function of the critical island size i and d(f) is also derived.

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.