Free Adatoms Research Articles

Modeling of Al and Ga Droplet Nucleation during Droplet Epitaxy or Droplet Etching.

The temperature dependent density of Al and Ga droplets deposited on AlGaAs with molecular beam epitaxy is studied theoretically. Such droplets are important for applications in quantum information technology and can be functionalized e.g., by droplet epitaxy or droplet etching for the self-assembled generation of quantum emitters. After an estimation based on a scaling analysis, the droplet densities are simulated using first a mean-field rate model and second a kinetic Monte Carlo (KMC) simulation basing on an atomistic representation of the mobile adatoms. The modeling of droplet nucleation with a very high surface activity of the adatoms and ultra-low droplet densities down to 5 × 10 cm is highly demanding in particular for the KMC simulation. Both models consider two material related model parameters, the energy barrier for surface diffusion of free adatoms and the energy barrier for escape of atoms from droplets. The rate model quantitatively reproduces the droplet densities with = 0.19 eV, = 1.71 eV for Al droplets and = 0.115 eV for Ga droplets. For Ga, the values of are temperature dependent indicating the relevance of additional processes. Interestingly, the critical nucleus size depends on deposition time, which conflicts with the assumptions of the scaling model. Using a multiscale KMC algorithm to substantially shorten the computation times, Al droplets up to 460 °C on a 7500 × 7500 simulation field and Ga droplets up to 550 °C are simulated. The results show a very good agreement with the experiments using = 0.19 eV, = 1.44 eV for Al, and = 0.115 eV, = 1.24 eV ( 300 °C) or = 1.24 + 0.06 (T[°C] − 300)/100 eV ( °C) for Ga. The deviating is attributed to a re-nucleation effect that is not considered in the mean-field assumption of the rate model.

Real-time insight into nanostructure evolution during the rapid formation of ultra-thin gold layers on polymers.

Ultra-thin metal layers on polymer thin films attract tremendous research interest for advanced flexible optoelectronic applications, including organic photovoltaics, light emitting diodes and sensors. To realize the large-scale production of such metal-polymer hybrid materials, high rate sputter deposition is of particular interest. Here, we witness the birth of a metal-polymer hybrid material by quantifying in situ with unprecedented time-resolution of 0.5 ms the temporal evolution of interfacial morphology during the rapid formation of ultra-thin gold layers on thin polystyrene films. We monitor average non-equilibrium cluster geometries, transient interface morphologies and the effective near-surface gold diffusion. At 1 s sputter deposition, the polymer matrix has already been enriched with 1% gold and an intermixing layer has formed with a depth of over 3.5 nm. Furthermore, we experimentally observe unexpected changes in aspect ratios of ultra-small gold clusters growing in the vicinity of polymer chains. For the first time, this approach enables four-dimensional insights at atomic scales during the gold growth under non-equilibrium conditions.

Impact of boron on the step-free area formation on Si(111) mesa structures

We report about the influence of boron (B) on surface morphology of Si layers grown by molecular beam epitaxy on Si(111) mesas. Dimension of step-free mesa areas is reduced in comparison to pristine Si and scales with the B-coverage. This can be explained by a reduced mass transport on the Si surface in the presence of B-induced √3 × √3 surface structure which is due to a reduced Si equilibrium free adatom density. We demonstrate that a suitable combination of initial B coverage and Si layer thickness results in large step free areas and B doping concentration up to 4 × 1018 cm−3.

Scaling in reversible submonolayer deposition

The scaling of island and monomer density, capture zone distributions (CZDs), and island size distributions (ISDs) in reversible submonolayer growth was studied using the Clarke-Vvedensky model. An approach based on rate-equation results for irreversible aggregation (IA) models is extended to predict several scaling regimes in square and triangular lattices, in agreement with simulation results. Consistently with previous works, a regime I with fractal islands is observed at low temperatures, corresponding to IA with critical island size i=1, and a crossover to a second regime appears as the temperature is increased to \epsilon R^{2/3} ~ 1, where \epsilon is the single bond detachment probability and R is the diffusion-to-deposition ratio. In the square (triangular) lattice, a regime with scaling similar to IA with i=3 (i=2) is observed after that crossover. In the triangular lattice, a subsequent crossover to an IA regime with i=3 is observed, which is explained by the recurrence properties of random walks in two dimensional lattices, which is beyond the mean-field approaches. At high temperatures, a crossover to a fully reversible regime is observed, characterized by a large density of small islands, a small density of very large islands, and total island and monomer densities increasing with temperature, in contrast to IA models. CZDs and ISDs with Gaussian right tails appear in all regimes for R ~ 10^7 or larger, including the fully reversible regime, where the CZDs are bimodal. This shows that the Pimpinelli-Einstein (PE) approach for IA explains the main mechanisms for the large islands to compete for free adatom aggregation in the reversible model, and may be the reason for its successful application to a variety of materials and growth conditions.

Structure and properties of pure and mixed transition metal dimers on graphene

Small Fe, Co and Ni clusters are known to exhibit high magnetic moments and are therefore investigated rather intensely for the purpose of developing novel magnetic materials with high magnetisation densities. The reduced bond density of these clusters compared to their respective bulk states, results in them being particularly sensitive to their environment. The choice of a substrate for these clusters is therefore of particular importance. Graphene has been shown to exhibit many novel phenomena and it is therefore interesting to investigate the suitability of using graphene as a support material for these metal clusters and if this would allow for an integration of technologies. In this paper, we report the results of plane–wave density functional theory (DFT) calculations of Fe, Co and Ni adatoms, and homonuclear and heteronuclear dimers, including mixing with Pt, adsorbed on graphene. We investigated the adsorption site structure, and stability, the projected density of states and electron populations, and magnetic moments. Calculations were performed using the Perdew–Burke–Ernzerhof (PBE) functional for the wavefunction with energy cutoffs of 40Ry and 480Ry for the wavefunction and density respectively. Brillouin zone sampling was performed with a Monkhorst–Pack grid of (8 ? 8 ? 1). We find that the adatoms bind weakly to graphene and that the magnetic moment of the most stable adatom configuration (the hole site configuration) is reduced by 2 ?B compared to the free adatom, and that the most stable dimer configuration is one where the dimer bond axis is oriented perpendicular to the graphene plane. The stability of the adatoms and dimers on graphene can be explained by considering the electronic interconfigurational energy change that accompanies the desorption of these clusters as well as the amount of charge transferred from cluster to graphene. Therefore, the accuracy of these calculations will depend rather strongly on how adequately the 3d–4s exchange correlation inter–action is treated.

A Level Set Approach to Anisotropic Surface Evolution with Free Adatoms

We variationally derive a thermodynamically consistent model for surface evolution under the influence of free adatoms. The resulting system of nonlinear partial differential equations couples a diffusion equation on a surface to the evolution of the surface. A numerical approach based on a finite element discretization of a level set equation is described for an anisotropic evolution, with nonconvex anisotropy functions. Various simulation examples in two and three dimensions demonstrate the applicability of the method.

Surface diffusion including adatoms

The aim of this paper is to study continuum models for surface diffusion taking into account free adatoms on the surface, which is of particular importance in the (self-assembled) growth of nanostructures. The extended model yields a coupled system of parabolic differential equations for the surface morphology and the adatom density, involving a cross-diffusion structure. We investigate two different situations, namely the growth of a film on a substrate and the growth of a crystal-like structure (a closed curve or surface). An investigation of the equilibrium situation, which can be phrased as an energy minimization problem subject to a mass constraint, shows a different behaviour in both situations: for the film the equilibrium is attained when all atoms are attached to the surface, while for a crystal the adatom density does not vanish on the surface. The latter is also a deviation from the usual equilibrium theory, since the equilibrium shape will be strictly included in the Wulff shape. Moreover, it turns out that the total energy is not lower semicontinuous and non-convex for large adatom densities and rough surfaces. The dynamics of the adatom surface diffusion model is investigated in detail for situations close to a flat surface in the film case and the situation close to a radially symmetric curve, both with an almost spatially homogeneous adatom density, where the cross-diffusion structure of the model and the decay to equilibrium can be studied in detail. Finally, we discuss the numerical solution of the adatom surface diffusion model in the film case and provide various simulation results.

Effect of atomic diagonal motion on cluster diffusion coefficient and its scaling behavior

Abstract The effect of atomic diagonal motion on the cluster diffusion and its size dependence is simulated by kinetic Monte Carlo method. The diffusion coefficient D(N) of a cluster with size N satisfies a power law D(N)∝N−α, where the scaling exponent α decreases with the increase of additive diagonal motion barrier Ed. When Ed is very small, the cluster diffusion is dominantly controlled by periphery diffusion mechanism and α is found to be about 1.5. On the contrary, when Ed is very large, the cluster diffusion is mainly controlled by the correlation evaporation and condensation (CEC) mechanism and α approaches 1.0. Furthermore, a threshold Edt∼0.4E0 (E0 is the diffusion barrier for a free adatom), corresponding to the transition of different dominant mechanisms for the cluster diffusion, is found existing in the relationship between D and Ed. When Ed Edt, the CEC mechanism is more important, and D is nearly independent of Ed. Additionally, the temperature dependent of D is found to be D∼ exp (− E a k B T ) and the active energy Ea is found to ∼1.42E0.

First-layer island growth during epitaxy.

We study the growth of first-layer islands making use of a mean-field model to describe the diffusion of free adatoms on the uncovered substrate. Model parameters are determined from recent experimental results for the growth of metals. The growth law is found using the quasi-steady-state approximation and we show that this result is consistent, at short times where this approximation may be questioned, with the exact asymptotic result. \textcopyright{} 1996 The American Physical Society.

Concentration profiles of surface atoms during epitaxial growth on vicinal surfaces

Concentration profiles of surface atoms have been obtained from Monte Carlo simulations of epitaxial growth and compared with predictions based upon the original Burton–Cabrera–Frank (BCF) theory and with a modified BCF theory. The modification is a BCF-type equation for a quantity that involves the concentrations of surface atoms in each of the possible environments and accounts for the fact that all atoms, not simply free adatoms, can participate in surface diffusion. Even at temperatures beyond those where growth becomes dominated by step advancement, the modified BCF equation provides a more accurate description of the adatom concentration profiles than that obtained using only the free adatom concentration, which is the central quantity in the original BCF theory. This is due to step detachment processes combined with the meandering of the steps, which leads to an effective source of free adatoms that is not taken into account in the original BCF approach.

Adatom Concentration Profiles on Simulated Vicinal Surfaces During Epitaxial Growth

ABSTRACTConcentration profiles of surface atoms have been obtained from Monte Carlo simulations of epitaxial growth with anisotropic nearest-neighbor bonding on two different vicinal GaAs(001) surfaces which are misoriented toward [110] (denoted asA) and [110] (denoted asB). These profiles are compared with predictions based upon the original Burton-Cabrera-Frank (BCF) theory and with a modified BCF theory which accounts for the fact that all atoms, not simply free adatoms, can participate in surface diffusion. On both surfaces the modified BCF equation provides a more accurate description of the adatom concentration profiles than that obtained using only the free adatom concentration. This is due to step detachment processes which leads to an effective source of free adatoms that is not taken into account in the original BCF approach. Above the temperature where the growth becomes dominated by step advancement, the curvature of the concentration profile of potentially active atoms on both surfaces are similar but the concentrations differ due to the difference of the capture efficiency of the two types of step edges.