Session R52: Thin Film nucleation, growth, and morphology

Introducing open boundary conditions in modeling nonperiodic materials and interfaces

Simulations are essential to accelerate the discovery of new materials. We introduce the first method of open boundary conditions in material and interface modeling. The new method, which we named ROBIN (recursive open boundary and interfaces) allows for discretizing millions of atoms in real space, thereby avoiding any symmetry or order of the atom distribution. The computational costs are limited to solving quantum properties in a focus area. It is verified in detail that the impact of the infinite environment on that area is included exactly. Calculations of graphene with the same amount of 1) periodic (currently available methods) and 2) randomly distributed silicon atoms shows that assuming periodicity elevates a small perturbation into a strong impact on the material property prediction. Graphene was confirmed to produce a band gap with periodic substitution of 3% carbon with silicon in agreement with published periodic boundary condition calculations. Instead, 3% randomly distributed silicon in graphene only shifts the energy spectrum. The predicted shift agrees quantitatively with published experimental data. Periodic boundary conditions can be applied on truly periodic systems only. Other systems should apply an open boundary method.   

Morphology and Mechanical Response of a Compressed Cylindrical Shells

Uniaxially compressed cylindrical shells are common in our daily life, such as rolled-up sleeves and retreated package of drinking straws. The deformations are complex and unpredictable, but often contain arrays of diamond. Is there any other modes of pattern? How does the cylinder respond mechanically when these modes transit? To clarify these problems, we perform both experiments and Molecularly Dynamics simulation. A rod is inserted inside and coaxial to the cylindrical shell in both approaches to avoid folding. It turns out that there are five more different patterns, besides the famous Yoshimura diamonds. These six modes of deformation are respectively spiral, ladder, diamond, wrinkle, ridge, and sagging. Phase diagram is drawn in a 3D plot with the spacing between shell and rod, compression strain and compression rate as axes. Material properties are incorporated to render these three parameters dimensionless. Two main features that worth noting are that different modes are allowed to mix and mode transitions are always accompanied by the absorption or release of latent heat. Simulation reveals that plasticity may disrupt and cause nonuniformity of the pattern.   

Up against a wall: interfacial free energies at curved surfaces

Interfacial free energies drive diverse physical phenomena, from wetting and capillarity to dendrite growth in crystal systems. While the interfacial free energy, γ, is largely controlled by the microscopic interactions between different phases, the geometry of the interface also plays a role in tuning the interfacial free energy. Although several analytic theories that try to include these geometric effects on γ have been proposed, experimental and simulation studies of curvature dependence of γ are few. Here we present simulation results for the 2-dimensional hard-disk fluid model at curved, hard, structureless walls and use the simulation results to test the limits of currently available analytical theories for interfacial free energy, including Morphometric Thermodynamics.   

Two-step Unconventional Protocol for Epitaxial Growth in One Dimension with Hindered Reactions

We study the effect of hindered aggregation and/or nucleation on the island formation process in a two-step (rather than the conventional one-step) growth protocol. In the proposed model, the attachment of monomers to islands and/or other monomers is hindered by additional energy barriers which decrease the hopping rate of monomers to occupied sites. For zero and weak barriers, the attachment is limited by diffusion while for strong barriers it is limited by reaction. We describe the time evolution of the system in terms of the monomer and island densities, N₁ and N. We also calculate the gap length, capture zone, and island-size distributions. For all sets of barriers considered, we compare the results from this analytical model with those from kinetic Monte Carlo simulations. The behavior of the system depends on the ratio of the nucleation barrier to the aggregation barrier. The two-step growth protocol gives more control and understanding of the island formation mechanism by intrinsically separating the nucleation and aggregation processes into different times regimes. We discuss experimental implications   

Foamability of oil mixtures

In the absence of stabilization mechanism of films of pure liquids, foams do not form in pure liquids. Froth formation is observed in liquid mixtures, among which, oil mixtures, and that effect is well documented in the literature. The higher film lifetimes has however not been understood in non-volatile liquids and in the absence of surface-active molecules. We have experimentally studied the foaming of binary mixtures of liquids, and found the foam lifetime depends not only on the nature of the liquids but also on the proportions of the two liquids. We suggest a stabilizing mechanism of thin films of liquid mixtures based on non-linear variations of the mixture’s surface tension with its composition, analogous to Gibbs’ elasticity defined for surfactant solutions. We show that the variations of foam lifetime with mixture composition is quantitatively described by the model. Finally, we define an effective disjoining pressure for thin films that can be fully computed from the variations of the surface tension of any liquid mixture which surface tension does not vary linearly with composition.   

Coupled Sublattice Melting and Charge-Order Transition in Two Dimensions

Two-dimensional melting is one of the most fascinating and poorly understood phase transitions in nature. Theoretical investigations often point to a two-step melting scenario involving unbinding of topological defects at two distinct temperatures. Here we report on a novel melting transition of a charge-ordered K-Sn alloy monolayer on a silicon substrate. Melting starts with short-range positional fluctuations in the K sublattice while maintaining long-range order, followed by longer-range K diffusion over small domains, and ultimately resulting in a molten sublattice. Concomitantly, the charge-order of the Sn host lattice collapses in a multi-step process with both displacive and order-disorder transition characteristics. Our combined experimental and theoretical analysis provides a rare insight into the atomistic processes of a multi-step melting transition of a two-dimensional materials system.   

Quantification of multiple crystallite orientations in complex thin film materials

As thin films and interfaces have become more intricate, the morphological and structural information also grows in complexity. An increasing amount of studies have focused on understanding correlations between crystallite orientation and electronic structure. Crystallite orientation within thin films is studied using grazing incidence wide-angle X-ray scattering (GIWAXS) patterns, where the Miller indices of a crystal structure are related to the scattering reflections. GIWAXS can be used to elucidate crystallite orientations within a thin film by comparing the azimuthal distribution of specific miller indices. However, as thin film technologies advance, there is a growing need to quantify the orientational distribution of similar thin films or also for multiple orientations within a single thin film in a comparative manner. Herein, we present a new method for quantifying the orientational distribution of crystallites, dubbed the Mosaicity Factor (MF). The efficacy of this method will first be studied using a model system consisting of Gaussian distributions. We will highlight the strengths and capabilities of MF when characterizing multiple gaussian shapes and overcoming signal noise. Case studies will be used to show the range of applications available and the strengths of MF.   

The role of He and H on the structural evolution of He- and H-irradiated 6H-SiC

The behavior of irradiated H and He ions in the 6H-SiC lattice was rather different. H irradiated with low fluence at RT, blisters were formed after annealing at 1100°C, while at high irradiation fluence no blister cavities were observed due to the formation of an amorphous layer. At an irradiation temperature of 450 and 900°C, amorphization of 6H-SiC did not occur and hydrogen-containing microcracks grew laterally below the surface. Thus blisters appeared on the surface of the samples irradiated at 900°C even without annealing. For He irradiation, regardless of the fluence and irradiation temperature, blisters did not form. The presented results are well supported by density functional theory calculations. The coalescence between two small bubbles is an exothermic process when the H₂-bubbles contain an unpaired hydrogen and endothermic process when the H₂-bubbles contain paired H atoms, but it is energetically cheap. On the other hand, activation of the coalescence of He bubbles is endothermic and energetically very expensive.   

Epitaxial growth of cubic WCy(001) thin films

Tungsten carbide films were sputter-deposited onto MgO(001) substrates at 400 °C in 5 mTorr Ar-CH₄ gas mixtures as a function of the CH₄ fraction f_CH4= 0.4 - 6%. High resolution transmission electron microscopy (TEM) and x-ray diffraction ω-2θ scans, ω-rocking curves, and reciprocal space maps on d = 10 nm thick layers indicate epitaxial growth of rock-salt WC_y with a cube-on-cube epitaxial relationship: (001)_WC || (001)_MgO and [100]_WC || [100]_MgO. The measured out-of-plane coherence length matches the film thickness for d = 10 nm but remains nearly unaffected by a 60-fold increase in layer thickness to d = 600 nm. This suggests a critical thickness for epitaxial breakdown of ~ 10 nm, associated with the nucleation of misoriented grains as also observed by TEM. The relaxed lattice constant increases monotonically from 0.419 to 0.425 nm with increasing f_CH4. Comparing these measured lattice parameters with first-principle predictions indicates a C-to-W ratio y = 0.47 - 0.68. However, composition measurements using energy-dispersive x-ray spectroscopy and Rutherford backscattering spectrometry yield measured C-to-W ratios of 0.57-1.25, suggesting that a considerable fraction (18 – 46 %) of C does not incorporate in the cubic phase but likely forms amorphous carbon.   

InAs(111) Homoepitaxy with Molecular Beam Epitaxy

In this study we have mapped the growth parameters for optimal homoepitaxy of InAs on InAs(111)A substrates using molecular beam epitaxy. Increasing the substrate temperature reveals a transition from 2D flat island growth to step-flow. The optimized parameters we established (substrate temperature = 500° C, growth rate = 0.12ML/s and V/III ratio = 48) produce an atomically flat surface, free of 3D imperfections. We study material quality using photoluminescence and have established a relationship between InAs(111)A surface smoothness and light emission intensity. This work paves the way for integrating the 6.1 A family of materials with the desirable properties of semiconductors with a (111) orientation. In addition, we will present preliminary results demonstrating the self-assembly of InGaAs quantum dots on these smooth InAs(111) surfaces, strongly indicating new paths towards ultra-low bandgap tunable light emitters for infrared optoelectronics.   

Droplet spreading on a surface exhibiting solid-liquid interface premelting

We study, using molecular-dynamics simulation, the spreading kinetics and equilibrium shape of liquid Pb droplets on an Al(111) substrate. The Al-Pb solid-liquid interface (SLI) was found previously to exhibit interfacial premelting at temperatures below the Al melting point [1]. We examine here how premelting affects the spreading and compare with both hydrodynamic (viscosity dominated) and kinetic (interfacial friction dominated) spreading mechanisms. For premelted surfaces, kinetic spreading is observed at intermediate times, in contrast to low temperatures near the Pb melting point where the surface is faceted and the hydrodynamic mechanism dominates. We conclude that the presence of the premelting layer has a significant effect on the thermodynamics of the Al(111)/Pb SLI and that the induced surface disorder gives rise to a kinetic spreading mechanism. We also observe that the structure of the droplet contact line with the premelted surface resembles that seen in reactive wetting.

[1] Y. Yang, M.D. Asta and B.B. Laird, Phys.Rev. Lett, 110, 096102 (2013)]   

Visualization of Nanorod Assembly and Dynamics on Liquid Surfaces

The two-dimensional phase behavior of rod-like particles was studied by dispersing silica-coated gold nanorods on a liquid surface. Nanorods with aspect ratio ranging from 3 to 6 were synthesized, coated with silica, functionalized with polyethylene glycol (PEG), and then dispersed in ionic liquid 1-ethyl 3-methylimidazolium ethyl sulfate ([EMIM][EtSO4]). The dispersed rods, driven to the surface by the low surface energy of PEG, were observed directly on the surface of an ionic liquid droplet by scanning electron microscopy. Rod diffusion coefficients were calculated in dilute systems by tracking position and orientation of single nanorods. In concentrated systems, the nanorod packing was studied using an in-situ liquid cell to control volume and surface area of the droplet. The 2D packing was characterized by pair correlation function, translational order parameter, orientational order parameter, and Voronoi tessellation. Order parameters were calculated as a function of areal density and nanorod aspect ratio. An increase in local orientational order was observed at higher areal densities but a liquid crystalline phase was not observed due to low aspect ratio.   

Effects of short-range repulsive barriers on island nucleation

A variety of effects such as strain and surfactants can lead to attachment barriers in thin-film growth. While several studies of the effects of attachment barriers on submonolayer growth have been carried out, the emphasis has been on rate-equations which do not take into account island geometry or coalescence and are primarily applicable to point-islands. Here we present the results of kinetic Monte Carlo simulations for the case of extended 2D islands with critical island-size i = 1 which were carried out to determine the dependence of the exponent χ (describing the dependence of the peak island density on deposition rate) on barrier strength and ratio R = D/F of the monomer hopping rate D to deposition rate F. In particular, we have studied two different cases, one with a barrier to island nucleation and attachment as well as the case with an island attachment barrier but no nucleation barrier. Our results indicate that in both cases - and in contrast to the case of no barrier for which χ is equal to 1/3 - the asymptotic (large R) value of χ increases continuously with barrier strength, reaching a value close to ½ in the limit of a very strong barrier and very large R. The effects of attachment barriers on island morphology and coalescence will also be discussed.   

X-ray Photon Correlation Spectroscopy Studies of Ion Beam Nanopatterning Kinetics and Dynamics

Solid surfaces can be ultra-smoothened or patterned on the nanoscale by irradiating with a broad beam of energetic ions. Different nano-patterns can be achieved by varying target-ion combination, the energy of ions, ions’ incident angle or the temperature of the solid target. There are several theories that seek to explain nanopatterning processes, but a definitive fundamental understanding has not been reached. In this study, the surface sensitive X-ray technique of Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) is used to do real-time investigations of nano-pattern formation on Silicon and Germanium due to Ar⁺ and Kr⁺ bombardment. The coherent X-ray beam that is utilized in these GISAXS experiments enables us to study not only the kinetics, but also the fluctuations around the average kinetics, i.e. the dynamics of the nanopatterning process. The X-ray Photon Correlation Spectroscopy (XPCS) two-time correlation function shows a novel behavior in the early stage, with memory stretching back to the beginning of the bombardment. During the late stage, the stationary intensity auto-correlations are computed to determine the correlation times as a function of length-scale.   

Recent Applications of Voronoi Tesselation and Analysis of Their Size Distributions with the Generalized Wigner Surmise

While Voronoi tessellation has long been applied in spatial studies, analysis of their cell-size distribution using the single-adjustable-parameter generalized Wigner surmise, P_β(s) = as^βexp(-bs², has only been done in the last decade. Here we discuss some intriguing examples: Mitko et al. (2019) consider the evolution of morphology during growth of island films of low-e dielectric films via vapor deposition polymerization. Löbl et al. (2019) probe infilling Al-droplet-etched nanoholes in an AlGaAs surface. In both cases, estimates of the critical nucleus size were extracted from the value of the exponenet β determined from a fit to P_β(s). We discuss the results and their implications. In other tantalizing examples, the Voronoi cell-size was not [yet] analyzed using P_β(s). Brookes (2017) uses Voronoi analysis of cells on the outer layer of eye-banked corneas to assess their viability before transplanting. Konishi et al. (2017) studied the growth-rate dependence of the spatial distribution of self-assembled 2D quantum dots on InAs-GaAs. They also consider the influence of modest array size.