The effect of dimer mobility on thin film nucleation kinetics

Dimer mobility and dissociation energies of small clusters have been incorporated into a set of rate equations to study the extent of the cluster mobility effect on thin film nucleation kinetics. The numerical analysis results showed that total cluster density and condensation coefficient both increase with increasing dimer dissociation energy and decrease with increasing dimer mobility. By comparison of theoretical calculations with the experimental results of Velfe et al. for Au deposition on NaCl [Thin Solid Films 98 (1982) 15], it is suggested that for this system at 150°C the dimer dissociation energy is low and dimer mobility has little effect on the nucleation kinetics.     

Kinetics of formation of discrete nanostructures during vacuum condensation from a single-component vapor

The kinetics of cluster formation during the vacuum condensation of thin films from a single-component vapor is investigated by numerically solving the system of kinetic equations. The size distributions of clusters containing from a few atoms to several hundred atoms are obtained. The regions of dominant nucleation on active centers (point defects of the crystal substrate) and random nucleation are determined in the “condensation rate-temperature” coordinates. It is demonstrated that the regions corresponding to the pseudolayer and three-dimensional (rough) growth mechanisms can be separated in the condensation rate-temperature coordinates. The inference is made that the experimentally observed bimodal size distributions of islands can be associated with the difference between the growth rates of clusters at the stage preceding the coalescence.     

Bonding of gold nanoclusters to oxygen vacancies on rutile TiO2(110)

Through an interplay between scanning tunneling microscopy (STM) and density functional theory (DFT) calculations, we show that bridging oxygen vacancies are the active nucleation sites for Au clusters on the rutile TiO2(110) surface. We find that a direct correlation exists between a decrease in density of vacancies and the amount of Au deposited. From the DFT calculations we find that the oxygen vacancy is indeed the strongest Au binding site. We show both experimentally and theoretically that a single oxygen vacancy can bind 3 Au atoms on average. In view of the presented results, a new growth model for the TiO2(110) system involving vacancy-cluster complex diffusion is presented.     

Growth and characterization of Au,Ni and Au–Ni nanoclusters on 6H-SiC(0001) carbon nanomesh

The nucleation and thermal stability of Au, Ni, and Au–Ni nanoclusters on 6H-SiC(0001) carbon nanomesh as well as the interaction between Au–Ni bimetallic clusters and reactive gases have been studied by X-ray photoelectron spectroscopy (XPS) and scanning tunneling microscopy (STM). Both Au and Ni atoms grow as three-dimensional (3D) clusters. Annealing the Au/carbon nanomesh surface up to 1150 °C leads to complete desorption of the Au clusters, while interfacial reaction occurs between Ni clusters and the substrate surface when the Ni clusters are subjected to the same annealing process. The nucleation of Au–Ni clusters depends critically on the deposition sequence. Au atoms preferentially nucleate on the existing Ni clusters, leading to the formation of bimetallic clusters with Au enriched on the surface. If the deposition sequence is reversed, a part of Ni atoms nucleate between the Au clusters. The thermal stability of the Au–Ni clusters resembles that of the Ni/carbon nanomesh surface, irrespective of the deposition sequence. XPS characterization reveals that Ni atoms in Au–Ni bimetallic clusters are oxidized upon exposure to 5.0 × 10^? 7 mbar O₂ for 5 min at room temperature while negligible structure change can be detected when the bimetallic clusters are exposed to CO gas under the similar conditions.     

Kinetic Monte Carlo simulations of Au clusters on Si(111)-7 × 7 surface

Self-assembled growth of Au nanoclusters on the Si(111)-7 × 7 surface has been studied using kinetic Monte Carlo simulations. A model considering various atomic processes of deposition, adsorption, diffusion, nucleation, and aggregation is introduced, and the main energetic parameters are optimized based on the experimental results. The evolution of surface morphology during Au growth is simulated in real time, from which the atomic behaviors of Au could be really captured. Most of Au atoms diffuse on the substrate in the very early stage of growth, and Au clusters nucleate and grow with the increasing coverage. The competition among various atomic processes results in the distinct distribution of Au clusters under different coverages. The growth conditions are further optimized, showing that the higher uniformity of Au clusters would be obtained at a low deposition rate and an optimal substrate temperature of about 380 K.     

Support effects on the nucleation, growth, and morphology of gold nano-clusters

The nucleation, growth, and morphology of gold (Au) clusters on an irreducible oxide (SiO₂), highly reduced TiO_x (x ∼ 1), and less reduced TiO_x (x ∼ 2) were investigated by scanning tunneling microscopy (STM) with the goal of understanding the relationship between the nucleation, growth, and morphology of Au clusters and the reducibility of the oxide support. Au clusters show preferential nucleation and growth on a TiO_x surface compared to a SiO₂ surface. In addition, higher densities of Au clusters were found on highly reduced TiO_x, suggesting that reduced Ti sites play a role as an active site for the nucleation and growth of Au clusters.     

Homogeneous and heterogeneous clustering in the accretion regime

Condensation of nano-droplets in a supersaturating vapor decomposes in two steps: the formation of a nucleation center, also called critical nuclei or nucleation seed, and the growth sequence, by accretion of further atoms on the nucleation center. These two steps have been investigated separately through the clustering of homogeneous particles Na_n and heterogeneous particles Na_nX in a helium buffer gas (X = (Na₂O)₂ or (NaOH)₂). The growth sequence is analyzed with preformed molecules X injected in a supersaturating sodium vapor and driving production of Na_nX clusters. Cluster distribution mean sizes are controlled by sodium concentration and by the condensation cell effective length. The signal intensities observed for homogeneous and heterogeneous clusters are proportional to the homogeneous and heterogeneous nucleation center numbers respectively. We can measure the efficiency for the homogeneous nucleation center production versus sodium concentration. This process is the onset of the condensation phase transition.     

Study of nanoclusters growth at initial stages of ultrathin film deposition by kinetic modeling

Comparative analysis of Au, Cu, Pt, Ni and Fe nanoclusters growth on amorphous carbon substrate by proposed kinetic model based on rate equations is present. Partial sticking coefficients introduced into the model let to discriminate elementary processes such as adatom adsorption and diffusion on bare substrate and on top of islands, nucleation and mobility of islands and its coalescence, 2-d and 3-d island growth modes. The quantitative fittings of experimental time dependencies of surface coverage, clusters density, cluster size are performed by solving model equations. From the best fittings the values of phenomenological coefficients defining elementary processes are found for different materials. Comparative analysis of those coefficients let to discover mechanisms of nanoclusters formation and growth of different materials. It is shown that clusterization for Cu and Au is more favorable than for Pt and Ni. Diffusivity for Pt and Ni on amorphous carbon (a-C) substrate is significantly less than for Au and Cu. In opposite, diffusivity on the top of islands for Ni and Pt is significantly higher than for Au and Cu. The mobility of islands for Au and Cu is much higher than for Ni and Pt. The fitting of experimental curves of Fe deposition on a-C at different temperatures showed that temperature mainly influences sticking process but not diffusion.     

Excimer laser ablation of gold-loaded inverse polystyrene-block-poly (2-vinylpyridine) micelles

Diblock-copolymers (PS(1700)-b-P2VP(450) or PS(1350)-b-P2VP(400)) forming spherical micelles, can be loaded with a Au-salt and deposited on top of various substrates. Such polymer films have been exposed to a pulsed ArF excimer laser in order to remove the polymer matrix and, in parallel, to chemically reduce the salt into metallic Au nanodots. To analyze this process in detail, it was subdivided into three steps: (a) laser ablation of thick and thin diblock-copolymer films; (b) laser irradiation of Au-salt loaded diblock-copolymer films; and (c) laser irradiation of arrays of metallic Au nanodots. In (a) it was found that a complete removal of the polymer by laser ablation is only possible in air under ambient conditions while identical laser irradiations under vacuum result in a residual layer of approximately 14 nm. Substep (b) revealed a nucleation process of the resulting metallic Au within the micellar core leading to clusters of small Au dots. Furthermore, this substep provided evidence for an asymmetric interplay between the macroscopic temperature of a polymer film during laser treatment and the energy density per laser pulse. In (c) it could be demonstrated that metallic Au nanodots on mica are stable against laser irradiation under conditions leading to a polymer removal. Received: 7 August 2000 / Accepted: 2 November 2000 / Published online: 3 April 2001     

Simulation of supersaturated vapor nucleation on molecular condensation nuclei

The results of model calculations of nucleation of di(2-ethylhexyl)sebacate (DEHS) supersatu-rated vapor on FeO molecules based of the simplest structural models of clusters are considered. The earlier conclusion that the allowance for the escape of a molecular condensation nucleus (MCN) from a cluster weakly affects the results of analysis of nucleation on a MCN is confirmed. It is found that the interaction of electric charges of the FeO molecule and the ester groups of the DEHS molecule plays the important role in the DEHS nucleation. The importance of the strength of the bond between the MCN and the first condensate molecule is established. The strength of this bond considerably affects the coefficient of conversion of the MCN into aerosol particles as well as the form of the dependence of this quantity on the spontaneous condensation background.     

Thermodynamics of supersaturated vapor nucleation on molecular condensation nuclei

A key problem in the theory of a supersaturated vapor nucleation on molecular condensation nuclei (namely, the work of formation and the equilibrium concentrations of clusters) is considered. To calculate these quantities using the structural models of clusters, which are better suited for this purpose than the classical droplet model, we derive the equation connecting the work of transfer of a molecular condensation nucleus from the gas phase to a homogeneous cluster with a change in the number of contacts between molecules, occurring in the course of this transfer, and with the work of rupture of individual contacts.     

Surface nucleation and growth in the system of interacting particles

Recent experiments on epitaxial growth of metals on graphene have shown a strong dependence of island densities on coverage. These investigations cannot be explained by the standard mean-field nucleation theories. To understand them, we extend to higher coverage the former theory of rate equations developed for the initial state of nucleation, in a system where adsorbate interaction is included. We account for that, in the case of high coverage, the repulsive interaction influences both the attachment of monomers to clusters and the mobility of atoms. In our work we analyze the modification of the dependence of the island density on coverage, temperature and F/D ratio. In some regimes our theory results in the experimentally observed substantial growth of island density with coverage for a high deposited amount and a weak dependence on deposition rate F. We also find out the local maxima in temperature dependence of island density, as a consequence of long-range repulsive interactions.     

Heterogeneous nucleation on cleavage steps: I. Theory

A theory of the nucleation kinetics of clusters formed on the cleavage steps of a substrate surface during metal deposition is presented. The spatial distribution of clusters along steps is shown to evolve with time in a shape-preserving way. As a consequence it has been possible to derive an expression for the linear number density of clusters as a function of substrate temperature, deposition rate and the duration of the deposition.     

CLUSTER NUCLEATION LIMITED BY GROWTH PATTERN COVERAGE IN THIN FILM PREPARATION FROM VAPOR

In the early stage of thin film preparation from vapor, growth patterns consisting of stable clusters will gradually cover almost the entire substrate surface. During this process, the density of single atoms is zero on growth patterns and the nucleation of clusters will proceed in the substrate parts uncovered by these patterns. The influence of growth pattern coverage on the nucleation of thin films has not been considered wholly in the classical theory of thin films. We will systematically study the influence of growth pattern coverage and give some correction formulas for the widely used classical theory of thin films. It was found that the classical nucleation rate is proportional to the square of the uncovered area. The corrected formulas are of particular importance in the dominant coverage case.     

Homogeneous nucleation and growth of droplets in vapours

The theory of homogeneous nucleation of liquid drops in supersaturated vapours is reviewed. A new kinetic treatment which accounts for the heating of the growing clusters due to the latent heat of condensation is presented, and the irreversible thermodynamics of non-isothermal nucleation discussed. It is found that growing clusters are generally colder than the surrounding vapour during their sub-critical growth period.

Time dependent nucleation is discussed and a simple estimate for the time-lag in establishing the steady state is given. The nucleation in cloud chambers expanding with constant speed is discussed in detail, and the number of droplets formed and their final mean size is calculated as a function of the terminal expansion ratio. Re-evaporation of nucleated clusters is discussed. Numerical results are given for a number of typical situations in experiments on water-vapour. These results for the nucleation rate as corrected by Lothe and Pound predict much lower ‘critical’ expansion ratios than indicated by the limited experimental data available, even when the non-isothermal theory is used.

To restore agreement between theory and experiments the surface tension for small droplets (?100 molecules) could be increased some 15% above that of the bulk liquid, or the pre-exponential in the nucleation rate could be decreased by some 10^?15. This latter expedient roughly corresponds to use of the ‘classical’ instead of the Lothe-Pound nucleation rate. These two alterations would, however, affect the theoretical curves in different manners and careful experiments could possibly distinguish between them.     

Oscillatory regimes of vapor condensation

The problem of the condensation of supersaturated vapor in an open system at a constant rate of production of a monomer and a continuous flow of a carrier gas that removes the products of condensation from the system is considered. It is shown both analytically and by numerical experiment that with a decreasing rate of the carrier gas to below a critical magnitude, the condensation regime becomes oscillatory; namely, time oscillations of the cluster-size distribution in the vapor to be condensed are set in. The cause of the phenomenon is in the suppression of the rate of nucleation and the presence of large clusters.     

Cluster diffusion and dissociation in the kinetics of layer growth: An atomic view

Data on diffusion and dissociation of single Pt clusters on Pt(111), available for the first time from field ion microscope observations, are used to make predictions about nanoscale phenomena by solving the mean-field differential equations for growth. In the submonolayer regime, cluster dissociation is found to be much more important than diffusion of clusters in reducing the saturation island density. Cluster dissociation also significantly affects the nucleation of a second layer on top of existing clusters and must be considered on an equal footing with interlayer transport over cluster edges.     

Computer simulation of cluster decay

Lennard-Jones metastable clusters consisting of 5 to 1030 atoms have been studied by molecular-dynamics simulation. Evaporation rate constants and caloric equations of state have been obtained in the microcanonical ensemble and with the use of RRK theory of unimolecular reactions and a local harmonicity approximation the canonical rate constants have been evaluted. The comparison with classical nucleation theory, specifically with the liquiddrop model, shows that the calculated equilibrium vapour pressure is significantly higher than theoretical one for small clusters, whereas the microcanonical results agree with theory.     

Kinetics and energy states of nanoclusters in the initial stage of homogeneous condensation at high supersaturation degrees

The condensation of metal vapor in an inert gas is studied by the molecular dynamics method. Two condensation regimes are investigated: with maintenance of partial pressure of the metal vapor and with a fixed number of metal atoms in the system. The main focus is the study of the cluster energy distribution over the degrees of freedom and mechanisms of the establishment of thermal equilibrium. It is shown that the internal temperature of a cluster considerably exceeds the buffer gas temperature and the thermal balance is established for a time considerably exceeding the nucleation time. It is found that, when the metal vapor concentration exceeds 0.1 of the argon concentration, the growth of clusters with the highest possible internal energy occurs, the condensation rate being determined only by the rate of heat removal from clusters.     

Revision of single atom local density and capture number varying with coverage in uniform depletion approximation and its effect on coalescence and number of stable clusters

In vapour deposition,single atoms (adatoms) on the substrate surface are the main source of growth.The change in its density plays a decisive role in the growth of thin films and quantum size islands.In the nucleation and cluster coalescence stages of vapour deposition,the growth of stable clusters occurs on the substrate surface covered by stable clusters.Nucleation occurs in the non-covered part,while the total area covered by stable clusters on the substrate surface will gradually increase.Carefully taking into account the coverage effect,a revised single atom density rate equation is given for the famous and widely used thin-film rate equation theory,but the work of solving the revised equation has not been done.In this paper,we solve the equation and obtain the single-atom density and capture number by using a uniform depletion approximation.We determine that the single atom density is much lower than that evaluated from the single atom density rate equation in the traditional rate equation theory when the stable cluster coverage fraction is large,and it goes down very fast with an increase in the coverage fraction.The revised equation gives a higher value for the ’average’ capture number than the present equation.It also increases with increasing coverage.That makes the preparation of single crystalline thin film materials difficult and the size control of quantum size islands complicated.We also discuss the effect of the revision on coalescence and the number of stable clusters in vapour deposition.