Island Size Distribution Research Articles

Formation and coarsening of epitaxially-supported metal nanoclusters

This mini-review describes developments over the last ∼30 years in characterizing the nucleation & growth of epitaxially-supported metal nanoclusters (NCs) or islands during vapor deposition, as well as their post-deposition coarsening. A beyond-mean-field treatment for homogeneous nucleation & growth corrects the deficiencies of traditional treatments in describing, e.g., the island size distribution, but also necessitates consideration of the spatial distribution of islands and their capture zones. We discuss advances in modeling capabilities, including those based upon on an ab-initio level treatment of periphery diffusion kinetics, for description of the non-equilibrium growth shapes of these NCs, focusing on 2D NCs. For post-deposition coarsening of arrays of NCs, there is generally a competition between Ostwald Ripening (OR) and Smoluchowski Ripening (SR). SR is also known as Particle Migration & Coalescence. For 2D NCs in homoepitaxial systems, conventional OR is observed on pristine fcc(111) surfaces, dramatically enhanced OR in the presence of even trace amounts of chalcogens for Cu(111) and Ag(111), and anomalous OR on anisotropic fcc(110) surfaces. The unexpected discovery of SR for fcc(100) homoepitaxial systems prompted extensive analysis of the underlying diffusivities of 2D NCs as a function of size, as well as of NC coalescence dynamics. A comprehensive understanding of these processes is now available. Self-assembly of 3D NCs during deposition, issues related to heterogeneous nucleation, directed assembly, NC growth structure selection, and coarsening are addressed. For SR of 3D epitaxial NCs, recent insights into the size-dependence of diffusivity are described.

Coarsening of Quasi Two-Dimensional Emulsions Formed by Islands in Free-Standing Smectic Films.

We study the coarsening behavior of assemblies of islands on smectic A freely suspended films in ISS microgravity experiments. The islands can be regarded as liquid inclusions in a two-dimensional fluid in analogy to liquid droplets of the discontinuous phase of an emulsion. The coarsening is effectuated by two processes, predominantly by island coalescence, but to some extend also by Ostwald ripening, whereby large islands grow at the expense of surrounding smaller ones. A peculiarity of this system is that the continuous and the discontinuous phases consist of the same material. We determine the dynamics, analyze the self-similar aging of the island size distribution and discuss characteristic exponents of the mean island growth.

Microscopic moisture localisation in unsaturated materials using nuclear magnetic resonance relaxometry

Due to the detrimental effects of moisture in the built environment, there is a continuous interest in non-destructive experimental techniques that quantify and/or localise moisture in materials. Most existing experimental techniques, however, typically focus on macroscopic moisture contents in samples rather than the microscopic distribution of water in the individual pores of building materials. For the latter, a popular method such as X-ray computed tomography is not readily applicable, due to the gap between its spatial resolution limit and the typical pore sizes of building materials. Nuclear magnetic resonance (NMR) relaxometry is capable of measuring water in pores of both the nanometer and micrometer scale and is therefore an interesting possibility. While most NMR research focusses on water-saturated materials or overall moisture contents, this study determines the size distributions of the water islands in unsaturated materials with NMR, and compares results to X-ray computed tomography (XCT) images and pore network model (PNM) simulations. Results on unsaturated materials show that NMR focusses on the biggest water islands (i.e. in capillary filled pores) and disregards the hydrogen nuclei in smaller water islands (i.e. stored in pore corners). NMR relaxometry is therefore only adept at providing very rough estimates of the size of water-filled pores, especially since post-processing of the NMR experiments to obtain these water island size distributions involves a lot of uncertainty.

Moisture localisation in unsaturated materials using nuclear magnetic resonance experiments, X-ray computed tomography and pore network modeling

Due to the detrimental effects of moisture in the built environment, there is continuous interest in non-destructive experimental techniques that localize and/or quantify moisture in materials. To this aim, nuclear magnetic resonance (NMR) experiments, X-ray computed tomography (XCT) and pore network modelling (PNM) are heavily researched. Since these techniques are all based on different physical principles and assumptions, comparing their results is not only necessary, but can provide valuable insights as well. Since most research, centered around these three approaches, solely focuses on water-saturated materials, in this study, these approaches are used to determine the size distributions of the water islands in unsaturated materials. By comparing the results of all three methods, it can be concluded that NMR mainly focuses on the biggest water islands/columns (i.e. large pore corners and filled pores) while the other techniques are capable of representing all water islands. PNM and XCT imaging provide similar results with the exception that PNM slightly overestimates both size as well as quantity of the water islands trapped in pore corners. Nevertheless, due to PNM being by far the fastest approach, it remains a valuable first estimation of the distribution of moisture in unsaturated materials.

Development of Desirable Fine Ferrite Grain Size and Random Second Phase Dual-Phase Steel Microstructures Using Composition and/or Processing Modifications

Microstructural morphology is known to have a significant impact on the mechanical properties of dual-phase steels. A fine ferrite grain size and random distribution of small second phase islands are desirable to provide superior isotropic properties compared to the banded second phase distribution that is typical for this type of steel. A rapid alloy prototyping (RAP) facility has been used to investigate three different DP 800 variants by systematically varying the compositions and/or process parameters compared to the ‘standard’ DP800 composition and processing that gives a banded microstructure. For Variant 1, the heating rate during the annealing cycle after cold rolling varied between 0.65 and 30 °C/s for the 45%, 60% and 75% cold reduction samples. It was found that a cold reduction of 75% and heating rate of 15 °C/s resulted in the microstructure that can give the best combination of strength and ductility because of the fine grain size and high martensite volume fraction. For Variant 2, the effect of changing the hot rolled (HR) microstructure (ferrite–pearlite, ferrite–bainite or martensite) on the final microstructure was investigated. Both the ferrite–50% bainite and fully martensite/bainite HR materials for all cold reductions resulted in annealed microstructures with necklace martensite morphology and finer ferrite grains compared to the ferrite–pearlite HR material, which gave a typical banded ferrite–martensite microstructure with a coarser ferrite grain size. For Variant 3, the Mn content was reduced, and increased Nb was used to achieve higher pancaking during the hot rolling stage, which refined ferrite grains in the HR condition with the same hardness. After annealing with the standard parameters only the 45% cold-reduced material produced a finer ferrite grain size than the standard material, whereas the 60% and 75% cold-reduced samples required a higher heating rate to achieve finer ferrite grain sizes due to rapid recrystallisation and growth kinetics.

Island and lake size distributions in gradient percolation

The well known problem of gradient percolation has been revisited to study the probability distribution of island sizes. It is observed that like the ordinary percolation, this distribution is also described by a power law decaying function but the associated critical exponents are found to be different. Because of the underlying gradient for the occupation probability, the average value of the island sizes also has a gradient. The variation of the average island size with the probability of occupation along the gradient has been studied together with its scaling analysis. Further, we have introduced and studied the gradient bond percolation and on studying the island size distribution statistics, we have obtained very similar results. We have also studied the characteristics of the diffusion profile of the particle system on a lattice which is initially half filled and half empty. Here also we observe the same value for the island size probability distribution exponent. Finally, the same study has been repeated for the nonlinear gradient percolation and the value of the island size distribution exponent is found to be a function of the strength of the nonlinear parameter.

Island Growth of Poly(chloro-p-xylylene) Coatings

The evolution of the morphology of island poly(chloro-p-xylylene) films formed on silicon substrates by vapor deposition polymerization is investigated by atomic force microscopy. The dependences of the effective thickness of the island coating, the number density of polymer islands, and their average size on the surface coverage are studied. The maximal density of polymer islands and the surface coverage corresponding to the transition to the coalescence regime are estimated. Within the framework of the theory of dynamic scaling, the size distribution of islands and the size distribution of their “capture zones” are analyzed. It is shown that, at low degrees of filling of the substrate, before the coalescence of islands, these distributions are described by scaling functions corresponding to the model of reaction-limited aggregation. The size of the critical nucleus is estimated from the size distributions of the “capture zones” of polymer islands.

Solid-State Dewetting Dynamics of Amorphous Ge Thin Films on Silicon Dioxide Substrates.

We report on the dewetting process, in a high vacuum environment, of amorphous Ge thin films on SiO2/Si (001). A detailed insight of the dewetting is obtained by in situ reflection high-energy electron diffraction and ex situ scanning electron microscopy. These characterizations show that the amorphous Ge films dewet into Ge crystalline nano-islands with dynamics dominated by crystallization of the amorphous material into crystalline nano-seeds and material transport at Ge islands. Surface energy minimization determines the dewetting process of crystalline Ge and controls the final stages of the process. At very high temperatures, coarsening of the island size distribution is observed.

Atomic Layer Epitaxy of III-Nitrides: A Microscopic Model of Homoepitaxial Growth.

We develop a microscopic theoretical model of AlN, GaN, and InN film growth by atomic layer epitaxy. To make the model realistic, we take into account the atomic hydrogen that is created by the hydrogen plasma commonly used in plasma-assisted atomic layer epitaxy. This growth technique relies on separate deposition steps for nitrogen and the group-III cation. Our model addresses the processes that occur after a complete monolayer of nitrogen has formed, that is, the deposition, adsorption, surface diffusion, island nucleation, and island growth of group-III cations. According to our model, the three nitrides grow in a standard and qualitatively similar manner: during a brief nucleation phase, a modest attractive interaction leads to stable island nuclei consisting of just a few atoms. These then grow in place at a nearly constant island density and with an island size distribution which obeys an expected universal scaling relationship that depends only on the critical island size.

Remodeling mechanisms determine size distributions in developing retinal vasculature.

The development of retinal blood vessels has extensively been used as a model to study vascular pattern formation. To date, various quantitative measurements, such as size distribution have been performed, but the relationship between pattern formation mechanisms and these measurements remains unclear. In the present study, we first focus on the islands (small regions subdivided by the capillary network). We quantitatively measured the island size distribution in the retinal vascular network and found that it tended to exhibit an exponential distribution. We were able to recapitulate this distribution pattern in a theoretical model by implementing the stochastic disappearance of vessel segments around arteries could reproduce the observed exponential distribution of islands. Second, we observed that the diameter distribution of the retinal artery segment obeyed a power law. We theoretically showed that an equal bifurcation branch pattern and Murray’s law could reproduce this pattern. This study demonstrates the utility of examining size distribution for understanding the mechanisms of vascular pattern formation.

Raman microscopy and infrared optical properties of SiGe Mie resonators formed on SiO2 via Ge condensation and solid state dewetting

All-dielectric photonics is a rapidly developing field of optics and material science. The main interest at visible and near-infrared frequencies is light management using high-refractive-index Mie-resonant dielectric particles. Most work in this area of research focuses on exploiting Si-based particles. Here, we study monocrystalline Mie-resonant particles made of Ge-rich SiGe alloys with refractive index higher than that of Si. These islands are formed via solid state dewetting of SiGe flat layers by using two different processes: (i) dewetting of monocrystalline SiGe layers (60%–80% Ge content) obtained via Ge condensation of SiGe on silicon on insulator; and (ii) dewetting of a SiGe layer deposited via molecular beam epitaxy on silicon on insulator and ex situ Ge condensation, forming a Ge-rich shell surrounding a SiGe-core. Using high-spatial-resolution Raman microscopy we monitor Ge content x and strain ϵ of flat layers and SiGe-islands. We observe strain relaxation associated with formation of trading dislocations in the SiGe islands compared to the starting SiGe layers, as confirmed by TEM images. For initial high Ge concentration in the flat layers, the corresponding Ge content in the dewetted islands is lower, owing to diffusion of Si atoms from Si or SiO2 into SiGe islands. The Ge content also varies from particle to particle on the same sample. Size and shape of the dewetted particles depend on the fabrication process: thicker initial SiGe layers lead to larger particles. Samples with narrow island size distribution display rather sharp Mie resonances in the 1000–2500 nm spectral range. Larger islands display Mie resonances at longer wavelength. Positions of the resonances are in agreement with the theoretical calculations in the discrete dipole approximation.

One-dimensional island size distribution: From non-equilibrium to equilibrium

We present a critical view of the analysis of experimental one-dimensional island size distribution as a function of time. We study the processes of island growth using large-scale kinetic Monte Carlo simulations with diffusion barriers calculated within the framework of the density functional theory. We have shown that one-dimensional island size distribution depends significantly on the time of the experiment. Our model predicts that during annealing or cooling, the transition from one state of thermodynamical equilibrium to another occurs through a non-equilibrium state. This transition consists of Ostwald ripening and decay of one-dimensional islands. The results of our work demonstrate that considering experimental one-dimensional island size distribution as an equilibrium is a big misconception.

Evolution of Morphology in the Process of Growth of Island Poly(p-xylylene) Films Obtained by Vapor Deposition Polymerization

Using atomic force microscopy, the evolution of the morphology of island poly(p-xylene) films formed on silicon substrates by vapor deposition polymerization at two deposition temperatures of +23 and 0°C and a fixed monomer flow is studied. The dependences of the surface coverage, the effective thickness of the island coating, and the density and average size of the polymer islands on the deposition time are investigated. Within the framework of the dynamic scaling theory, the size distribution of islands and the size distribution of their capture zones are analyzed. It is shown that the observed features of the evolution of the morphology of island poly(p-xylylene) films cannot be fully described in the framework of classical models based on diffusion-limited aggregation. However, they can be explained by the reversibility of aggregation, which is a specific feature of the polymeric nature of the island coatings being formed.

Neutral island statistics during reionization from 21-cm tomography

Abstract We present the prospects of extracting information about the epoch of reionization by identifying the remaining neutral regions, referred to as islands, in tomographic observations of the redshifted 21-cm signal. Using simulated data sets we show that at late times the 21-cm power spectrum is fairly insensitive to the details of the reionization process but that the properties of the neutral islands can distinguish between different reionization scenarios. We compare the properties of these islands with those of ionized bubbles. At equivalent volume-filling fractions, neutral islands tend to be fewer in number but larger compared to the ionized bubbles. In addition, the evolution of the size distribution of neutral islands is found to be slower than that of the ionized bubbles and also their percolation behaviour differs substantially. Even though the neutral islands are relatively rare, they will be easier to identify in observations with the low frequency component of the Square Kilometre Array due to their larger size and the lower noise levels at lower redshifts. The size distribution of neutral islands at the late stages of reionization is found to depend on the source properties, such as the ionizing efficiency of the sources and their minimum mass. We find the longest line of sight through a neutral region to be more than 100 comoving Mpc until very late stages (90–95 per cent reionized), which may have relevance for the long absorption trough at z = 5.6–5.8 in the spectrum of quasar ULAS J0148+0600.

Impact of size distributions of Ge islands as etching masks for anisotropic etching on formation of anti-reflection structures

The impact of the size distributions of Ge islands on the structural and optical characteristics of anti-reflection structures was investigated. The variation of island size distribution was achieved through the variation of growth temperature in gas-source molecular beam epitaxy at 700 °C–800 °C. Ge islands were utilized as etching masks to form the anti-reflection structures. By using lower growth temperature of 700 °C and subsequent etching, larger texture without many hollows was formed in contrast to that using 800 °C. Broader size distribution of islands formed at 700 °C was found to lead to larger texture size. Smaller texture is formed by smaller islands and short etching, whereas larger texture is formed by erosion of smaller texture during long etching. A potential short-circuit current density of 36.75 mA cm−2 was obtained for the sample by the islands grown at 700 °C with reduced etching margins, comparable to that of conventional pyramid textures.

Islands growth control in adsorptive multilayer plasma-condensate systems

A model for adsorbate islands growth is proposed to simulate pattern formation in multilayer plasma-condensate system. It was shown that morphology of surface patterns and mean island size can be effectively controlled by adsorption rate (pressure of gaseous atmosphere), interaction strength of adsorbate and external electrical field, managing anisotropic diffusion of atoms between layers. Dynamics of patterns formation is analyzed by considering statistical properties of growing surface on each formed layer and mean island size having size from third up to two diffusion lengths of adatoms. It was shown that island growth relates to modified Ostawald ripening scenario with universal island size distribution. Obtained data relates well to experimental observation of adsorbate island formation at condensation of metals and semiconductors. Described model and results are general and can be used to describe real experimental observations of surface nanopatterning at condensation in plasma-condensate devices.

Characterisation of size distribution and positional misalignment of nanoscale islands by small-angle X-ray scattering

Highly ordered arrays of nanoscale magnetic structures form the basis of artificial spin ices, uniform particles for bio-medical applications, and data storage as Bit Patterned Media. We demonstrate that small-angle X-ray scattering (SAXS) allows the size distribution and the positional alignment of highly ordered arrays to be determined with high spatial and statistical accuracy. The results obtained from the SAXS measurements are compared to an analysis of Scanning Electron Microscopy images and found to be in excellent agreement. This confirms the validity of the technique and demonstrates its potential as a fast, accurate, and statistically reliable method for characterising arrays of ordered nanostructures.

The Aftermath of Petermann Glacier Calving Events (2008–2012): Ice Island Size Distributions and Meltwater Dispersal

AbstractThree large calving events occurred at Petermann Glacier in northwest Greenland between 2008 and 2012 that generated ice islands (large tabular icebergs) that ranged from ~30 to 300 km2in areal extent. Ice islands are known to deteriorate, via fracture and melt, during their drift through regional water bodies where they pose a potential risk to offshore resource extraction operations and disperse freshwater from the Greenland Ice Sheet. This study presents the first analysis of the deterioration occurring across the flux of ice islands that travel between Nares Strait and the North Atlantic after Petermann Glacier calving events. The evolution of Petermann ice island size distributions was evaluated, and the spatial dispersal of meltwater was quantified, through analyses that utilized the newly developed Canadian Ice Island Drift, Deterioration and Detection Database. Size‐frequency distributions remained relatively consistent, both spatially and temporally, and were well fit by power law models with slopes of approximately −1.7. This suggested that fracture was an important process by which the Petermann ice islands deteriorated, regardless of elapsed time or distance from the glacier. Ice island meltwater fluxes into the Baffin Island and Labrador currents were not large enough to slow down the Atlantic Meridional Overturning Circulation by weakening deep‐water convection in the Labrador Sea. However, augmented meltwater input was calculated within Petermann Fjord (2.0 mSv) and in the vicinity of grounding locations (0.4 mSv). Further research is necessary to better understand how this freshwater alters fjord circulation and influences the composition of local ocean waters.

Phase-field method for epitaxial kinetics on surfaces.

We present a procedure for simulating epitaxial growth based on the phase-field method. We consider a basic model in which growth is initiated by a flux of atoms onto a heated surface. The deposited atoms diffuse in the presence of this flux and eventually collide to form islands which grow and decay by the attachment and detachment of migrating atoms at their edges. Our implementation of the phase-field method for this model includes uniform deposition, isotropic surface diffusion, and stochastic nucleation (in both space and time), which creates islands whose boundaries evolve as the surface atoms "condense" into and "evaporate" from the islands. Computations using this model in the submonolayer regime, prior to any appreciable coalescence of islands, agree with the results of kinetic Monte Carlo (KMC) simulations for the coverage-dependence of adatom and island densities and island-size distributions, for both reversible and irreversible growth. The scaling of the island density, as obtained from homogeneous rate equations, agrees with KMC simulations for irreversible growth and for reversible growth for varying deposition flux at constant temperature. For reversible growth with varying temperature but constant flux, agreement relies on an estimate of the formation energy of the critical cluster. Taken together, our results provide a comprehensive analysis of the phase-field method in the submonolayer regime of epitaxial growth, including the verification of the main scaling laws for adatoms and island densities and the scaling functions for island-size distributions, and point to the areas where the method can be extended and improved.

Irreversible island nucleation and growth with anomalous diffusion in [formula omitted

Recently, there has been significant interest in the effects of anomalous diffusion on island nucleation and growth. Of particular interest are the exponents χ and χ1 which describe the dependence of the island and monomer density on deposition rate as well as the dependence of these exponents on the anomalous diffusion exponent μ and critical island size. While most simulations have been focused on growth on a 2D and/or quasi-1D substrate, here we present simulation results for the irreversible growth of ramified islands in three-dimensions (d=3) for both the case of subdiffusion (μ<1) and superdiffusion (1<μ≤2). Good agreement is found in both cases with a recently developed theory (Amar and Semaan, 2016) which takes into account the critical island-size i, island fractal dimension df, substrate dimension d, and diffusion exponent μ. In addition, we confirm that in this case the critical value of μ is given by the general prediction μc=2∕d=2∕3. We also present results for the irreversible growth of point-islands in d=3 and d=4 for both monomer subdiffusion and superdiffusion, and good agreement with RE predictions is also obtained. In addition, our results confirm that for point-islands with d≥3 one has μc=1 rather than 2∕d. Results for the scaling of the capture-number distribution (CND), island-size distribution (ISD), and average capture number for the case of irreversible growth with monomer superdiffusion in d=2 are also presented. Surprisingly, we find that both the scaled ISD and CND depend very weakly on the monomer diffusion exponent μ. These results indicate that – in contrast to the scaling of the average capture number which depends on the monomer diffusion exponent μ – both the scaled ISD and CND are primarily determined by the capture-zone distribution, which depends primarily on the “history” of the nucleation process rather than the detailed mechanisms for monomer diffusion.