Surface diffusion during decay of nano-island on Si(1 0 0) at high temperature

Surface diffusion during decay of a two-dimensional nano-island formed on Si(1 0 0) surface at 750-800 K is studied using STM and a kinetic Monte Carlo simulation. From a surface diffusion point of view, decay proceeds so that the total diffusion rate of atoms on a surface decreases. Atoms at step edges move more frequently than terrace atoms, which results in decay from step edges of the island. In addition, a terrace atom takes part in surface diffusion in the same way as an atom from steps of the island once it hops up on a terrace leaving a vacancy. The mass transport is not a specific atom process but terrace atoms and vacancies on the terrace are involved. Repeated upward and downward hops of atoms and their difference are combined with surface diffusion, which leads to the mass transport. Some tracks of atom using simulation show random walk with preferential diffusion along step edges, re-entering to the island, exchange of diffusing atom and filling in a vacancy on the terrace. The motion of the center of the island to the upper side of the terrace observed by STM is also well reproduced in the simulation.     

A Monte Carlo simulation study of Nitrogen on LiF(0 0 1)

The adsorption of N₂ gas on the LiF(0 0 1) surface is studied by canonical Monte Carlo (CMC) computer simulation. These results show that N₂ forms an ordered structure where the molecules are arranged in a unit cell of symmetry at temperatures below 23 K with 50% coverage. The nitrogen molecules are tilted by 53° from the surface normal and have the same azimuthal orientation along diagonals, with diagonals alternating their orientation. Beyond 23 K, the molecules become azimuthally disordered but with residual short-range order. No change in the position of the peak of the polar (tilt) angle distribution was observed above the transition temperature. This transition is purely of the order-disorder type.     

Usage of pattern recognition scheme in kinetic Monte Carlo simulations: Application to cluster diffusion on Cu(1 1 1)

We have invoked a simple pattern recognition scheme in kinetic Monte Carlo simulations of post-deposition evolution of two dimensional islands on fcc(1 1 1) surfaces. On application of the technique to the diffusion of small Cu clusters (8-100 atoms) on Cu(1 1 1) we find that, at room temperature, clusters with certain magic numbers show stick-slip type of motion with striking patterns rather than the random paths followed by the others. At higher temperatures all clusters display random motion. The calculated diffusion coefficients show dependence on size and temperature with an effective barrier ranging between 0.62 eV and 0.84 eV. Small asymmetries in diffusion barriers lead to a large difference in the frequencies of adatom diffusion along the two types of micro-facetted steps on Cu(1 1 1) leading to consequences in their shape evolution. The pattern recognition scheme revealed 49 basic periphery single atom diffusion processes whose activation energy barriers were calculated using the nudged elastic band technique and interatomic potentials from the embedded atom method.     

Stress modifications induced by dimer vacancies in the Si(0 0 1) surface: Monte Carlo simulations

By means of Monte Carlo simulations, we investigate the local stress modifications induced by dimer vacancies (DVs) in the Si(0 0 1) subsurface layers. In presence of n isolated compact DVs, the sites located below these defect rows are under clearly compressive stress in the third layer and under more and more tensile stress, as n increases, in the fourth layer. At higher DVs densities, analogous trends are observed, but the stress modifications are then slightly extended between the dimer rows. Applying our results to the Ge penetration in Si(0 0 1), we show how the knowledge of the local stress may allow predictions of a given impurity behaviour in the vicinity of the surface, provided that the impurity-defect and impurity-impurity interactions do not play a major role compared to the local stress modification induced by the presence of DVs.     

A multi-scale Monte Carlo study of oxide structures on the Cu(1 0 0) surface

We present a multi-scale Monte Carlo study of the oxidation of the Cu(1 0 0) surface based on the Bortz-Kalos-Lebowitz model with the equilibrium energetics obtained from ab initio calculations. The radial and island size distribution functions are examined and Cu-O structures are analyzed at different temperatures and coverages. We concentrate on the coverages of 0.3 monolayer O or less, with variable sub-monolayer coverages of Cu. The results show that even though the ab initio calculations yield a higher barrier for O than for Cu adatom diffusion on Cu(1 0 0), the stability of Cu structures causes the O adatoms to be more mobile on the Cu(1 0 0) surface than the Cu adatoms. We are able to reproduce the c(2 × 2)-O domains seen in the experiments. However, we give an alternative explanation based on the repulsive interactions of O that, on one hand, cause the local ordering and, on the other hand, prohibits large well-ordered domains. We also give interpretation on the formation of the R45°-O reconstruction of Cu(1 0 0) above the O coverages of 0.3 monolayer based on the ab initio energetics.     

A kinetic Monte Carlo/UBI-QEP model of O2 adsorption on fcc (1 1 1) metal surfaces

The previously developed kinetic Monte Carlo model of molecular oxygen adsorption on fcc (1 0 0) metal surfaces has been extended to fcc (1 1 1) surfaces. The model treats uniformly all elementary steps of the process—O₂ adsorption, dissociation, recombination, desorption, and atomic oxygen hopping—at various coverages and temperatures. The model employs the unity bond index—quadratic exponential potential (UBI-QEP) formalism to calculate coverage-dependent energetics (atomic and molecular binding energies and activation barriers of elementary steps) and a Metropolis-type algorithm including the Arrhenius-type reaction rates to calculate coverage- and temperature-dependent features, particularly the adsorbate distribution over the surface. Optimal values of non-energetic model parameters (the spatial constraint, a travel distance of “hot” atoms, attempt frequencies of elementary steps) have been chosen. Proper modifications of the fcc (1 0 0) model have been made to reflect structural differences in the fcc (1 1 1) surface, in particular the presence of two different hollow sites (fcc and hcp). Detailed simulations were performed for molecular oxygen adsorption on Ni(1 1 1). We found that at very low coverages, only O₂ adsorption and dissociation were effective, while O₂ desorption and O₂ and O diffusion practically did not occur. At a certain O + O₂ coverage, the O₂ dissociation becomes the fastest process with a rate one-two orders of magnitude higher than adsorption. Dissociation continuously slows down due to an increase in the activation energy of dissociation and due to the exhaustion of free sites. The binding energies of both molecular and atomic oxygen decrease with coverage, and this leads to greater mobility of atomic oxygen and more pronounced desorption of molecular oxygen. Saturation is observed when the number of adsorbed molecules becomes approximately equal to the number of desorbed molecules. Simulated coverage dependences of the sticking probability and of the atomic binding energy are in reasonable agreement with experimental data. From comparison with the results of the previous work, it appears that the binding energy profiles for Ni(1 1 1) and Ni(1 0 0) have similar shapes, although at any coverage the absolute values of the oxygen binding energy are higher for the (1 0 0) surface. For metals other than Ni, particularly Pt, the model projections were found to be too parameter-dependent and therefore less certain. In such cases further model developments are needed, and we briefly comment on this situation.     

Selforganized nanopatterning of Si(0 0 1)

The (2 × n) superstructure of Si(0 0 1) consists of elongated (2 × 1) reconstructed stripes separated by a dimer-vacancy line every few nanometers, thus offering a means to obtain a nanopattered Si(0 0 1) surface. Scanning tunneling microscopy (STM) investigations of Si(0 0 1) substrates that were deoxidized at 880-920 °C reveal that the formation of the (2 × n) depends strongly on the Si coverage of the topmost surface layer. It forms only in a narrow coverage window ranging from 0.6 to 0.8 ML. Systematic Monte Carlo simulations by an algorithm that combines the diffusion of monomers and dimers with the simultaneous deposition of Si onto the Si(0 0 1) surface, corroborate the STM results and suggest Si deposition as a viable alternative for introducing dimer vacancies in a well-defined manner.     

Monte Carlo simulation for temperature dependence of Ga diffusion length on GaAs(0 0 1)

Diffusion length of Ga on the GaAs(0 0 1)-(2×4)β2 is investigated by a newly developed Monte Carlo-based computational method. The new computational method incorporates chemical potential of Ga in the vapor phase and Ga migration potential on the reconstructed surface obtained by ab initio calculations; therefore we can investigate the adsorption, diffusion and desorption kinetics of adsorbate atoms on the surface. The calculated results imply that Ga diffusion length before desorption decreases exponentially with temperature because Ga surface lifetime decreases exponentially. Furthermore, Ga diffusion length L along and [1 1 0] on the GaAs(0 0 1)-(2×4)β2 are estimated to be and L_[110]200 nm, respectively, at the incorporation–desorption transition temperature (T860 K).     

The effect of embedded Pb on Cu diffusion on Pb/Cu(1 1 1) surface alloys

We have used scanning tunneling microscopy and low-energy electron microscopy to measure the thermal decay of two-dimensional Cu, Pb-overlayer, and Pb-Cu alloy islands on Pb-Cu(1 1 1) surface alloys. Decay rates covering 6-7 orders of magnitude are accessible by applying the two techniques to the same system. We find that Cu adatom diffusion across the surface alloy is rate-limiting for the decay of both Pb and Pb-Cu islands on the surface alloy and that this rate decreases monotonically with increasing Pb concentration in the alloy. The decrease is attributed to repulsive interactions between Cu adatoms and embedded Pb atoms in the surface alloy. The measured temperature dependences of island decay rates are consistent with first-principles calculations of the Cu binding and diffusion energies related to this “site-blocking” effect.     

Diffusions of small clusters on Pt(1 1 1) and Cu(1 1 1) surfaces

Diffusions of small cluster Pt₆ on Pt(1 1 1) surface and Cu₆ on Cu(1 1 1) are studied by molecular dynamics simulation, respectively. The atomic interaction is modeled by the semiempirical potential. The results show that the diffusion processes in the two systems are far different. For example, on Pt(1 1 1) surface, the hopping of single atom and the shearing of two atoms of hexamer only occur on the adatom(s) adsorbed at B-step, while on Cu(1 1 1) surface they can appear on the adatom(s) either at A-step or B-step. To the concerted translation of the parallelogram hexamer, the anisotropy in the diffusion path is observed in the two systems, the mechanisms and then the preferential paths, however, are completely different. The reasons for these diffusion characteristics and differences are discussed.     

CF interaction with Si(1 0 0)-(2 × 1): Molecular dynamics simulation

In this study, the interaction of CF with the clean Si(1 0 0)-(2 × 1) surface at normal incidence and room temperature was investigated using molecular dynamics simulation. Incident energies of 2, 12 and 50 eV were simulated. C atoms, arising from dissociation, preferentially react with Si to form Si-C bonds. A Si_xC_yF_z interfacial layer is formed, but no etching is observed. The interfacial layer thickness increases with increasing incident energy, mainly through enhanced penetration of the silicon lattice. Silicon carbide and fluorosilyl species are formed at 50 eV, which is in good agreement with available experimental data. The level of agreement between the simulated and experimental results is discussed.     

Energy loss spectra of low primary energy (E0 ? 1 keV) electrons backscattered by silicon dioxide

A Monte Carlo simulation is described and utilized to calculate the energy distribution spectra of the electrons backscattered by silicon dioxide. Spectra are presented for incident energies of 250 eV, 500 eV, and 1000 eV. Spectra interpretation is based on a semiquantitative valence-band structure model for SiO₂ crystals.     

Study of oscillations and pattern formation in the CO + O2 reaction on Pt(1 0 0) surfaces through dynamic Monte Carlo simulation

Oscillations and pattern formation driven by a surface reconstruction are studied for the catalytic oxidation of CO on Pt(1 0 0) single-crystal surfaces through dynamic Monte Carlo simulations at low pressure and relatively high temperatures conditions. Sustained, modulated, irregular and damped oscillations are observed in our analysis as well as the formation of cellular, target, double spiral, spiral wave and turbulent patterns. The effect and the importance of the hex ? 1 × 1 surface phase transition and partial pressure of the reactants in the gas phase on the behavior of the system are discussed.     

A Monte Carlo simulation study of H2 layers on NaCl(0 0 1)

Monte Carlo simulations show that, at one monolayer coverage, H₂ molecules adsorbed on a NaCl(0 0 1) surface occupy all Na⁺ sites and form a commensurate c(2 × 2) structure. If the Cl⁻ sites are occupied as well, a bi-layer p(2 × 1) structure forms. An examination of the H₂ molecules’ rotational motion shows the molecular axes are azimuthally delocalized and so both of the structures acquire (1 × 1) symmetry in accord with experimental observations. These calculations also show that helicoptering o-H₂ (J = 1, m = ±1) prefer to sit on top of Na⁺ sites, while cartwheeling o-H₂ (J = 1, m = 0) prefers to locate over Cl⁻ sites, in agreement with other work.     

Theoretical study of the structures of MgO(1 0 0)-supported Au clusters

A theoretical method, which combines the first-principle calculations and a canonical Monte Carlo (CMC) simulation, was used to study the structures of Au clusters with sizes of 25-54 atoms supported on the MgO(1 0 0) surface. Based on a potential energy surface (PES) fitted to the first-principle calculations, an effective approach was derived to model the Au-MgO(1 0 0) interaction. The second moment approximation to the tight-binding potential (TB-SMA) was used to model the Au-Au interactions in the CMC simulation. It is found that the Au clusters with sizes of 25-54 atoms supported on the MgO(1 0 0) surface possess an ordered layered fcc epitaxial structure.     

Formation of linear structures of Sr and Gd films on the Mo(1 1 2) and W(1 1 2) surfaces

At low coverages, alkaline earth and rare earth layers adsorbed on furrowed transition metal surfaces--such as W(1 1 2) and Mo(1 1 2)--tend to form commensurate linear structures built of monoatomic chains directed across the furrows. Presented Monte Carlo simulations provide insight into parameters of the long-range indirect interaction that, in competition with a dipole-dipole interaction, leads to formation of the linear structures. The most impressive result of the simulations is the revealed repulsive effective interaction between adjacent atoms in linear Sr chains on W(1 1 2) surface. In this case, formation of the linear chains is accomplished due to pronounced minima in the potential of indirect interaction along the surface furrows. This result predicts that a single Sr chain cannot exist on the W(1 1 2) surface.     

Adsorption dynamics of CO2 on Cu(1 1 0): A molecular beam study

Molecular beam scattering measurements have been conducted to examine the adsorption dynamics of CO₂ on Cu(1 1 0). The initial adsorption probability, S₀, decreases exponentially from 0.43 ± 0.03 to a value close to the detection limit (∼0.03) within the impact energy range of E_i = (0.12-1.30) eV. S₀ is independent of the adsorption temperature, T_s, and the impact angle, α_i, i.e., the adsorption is non-activated and total energy scaling is obeyed. The coverage, Θ, dependent adsorption probability, S(Θ), agrees with precursor-assisted adsorption dynamics (Kisliuk type) above T_s ∼ 91 K. However, below that temperature adsorbate-assisted adsorption (S increases with Θ) has been observed. That effect is most distinct at large E_i and low T_s. The S(Θ) data have been modeled by Monte Carlo simulations. No indications of CO₂ dissociation were obtained from Auger Electron Spectroscopy or the molecular beam scattering data.     

Surface mass diffusion and step stiffness on an anisotropic surface; Mo(0 1 1)

Results of step fluctuation experiments for Mo(0 1 1), using low-energy electron microscopy, are re-examined using recently developed procedures that offer accurate coefficients of surface mass diffusion. By these means, surface diffusion D_s is documented at T/T_m ∼ 0.5, while the crossover to relaxation driven by bulk vacancy diffusion is inferred for T/T_m ∼ 0.6. Here, T_m is the melting temperature T_m = 2896 K. We obtain D_s = 4 × 10⁻⁴ exp(−1.13 eV/k_BT) cm²/s for the temperature interval 1080-1680 K. Possible indications of diffusion along step edges appear for T/T_m ∼ 0.4. The same measurements of step fluctuation amplitudes determine also the step stiffness, which by symmetry is anisotropic on Mo(0 1 1). It is shown that three independent procedures yield mutually consistent step stiffness anisotropies. These are (1) step fluctuation amplitudes; (2) step relaxation rate anisotropies; and (3) the observed anisotropies of islands in equilibrium on the Mo(0 1 1) surface. The magnitude of the step stiffness obtained from step edge relaxation is consistent with earlier measurements that determine diffusion from grain boundary grooving.