Finite Islands Research Articles

Polarization-dependent effects in vibrational absorption spectra of 2D finite-size adsorbate islands on dielectric substrates.

In the last few years, infrared reflection-absorption spectroscopy (IRRAS) has become a standard technique to study vibrational excitations of molecules. These investigations are strongly motivated by potential applications in monitoring chemical processes. For a better understanding of the adsorption mechanism of molecules on dielectrics, the polarization-dependence of an interaction of infrared light with adsorbates on dielectric surfaces is commonly used. Thus, the peak positions in absorption spectra could be different for s- and p-polarized light. This shift between the peak positions depends on both the molecule itself and the dielectric substrate. While the origin of this shift is well understood for infinite two-dimensional adsorbate layers, finite-size samples, which consist of 2D islands of a small number of molecules, have never been considered. Here, we present a study on polarization-dependent finite-size effects in the optical response of such islands on dielectric substrates. The study uses a multi-scale modeling approach that connects quantum chemistry calculations with Maxwell scattering simulations. We distinguish the optical response of a single molecule, a finite number of molecules, and a two-dimensional adsorbate layer. We analyze CO and CO2 molecules deposited on CeO2 and Al2O3 substrates. The evolution of the shift between the polarization-dependent absorbance peaks is first studied for a single molecule, which does not exhibit any shifting at all, and for finite molecular islands, where it increases with increasing island size, as well as for an infinite two-dimensional adsorbate layer. In the latter case, the agreement between the obtained results and the experimental IRRAS data and more traditional three/four-layer model theoretical studies supports the predictive power of the multi-scale approach.

Modelling the size of nitrogen c(2x2) islands on Cu(001) with elastic multisite interactions

An extended elastic eigenvector approach for adatom interactions is applied to model nitrogen c(2x2) atom islands on Cu(001). Oscillating interactions between adatom monomers or dimers are considered. Attractive pair interactions of adatoms are able to describe agglomeration but fail to explain the size of islands. Multisite interactions created by dimers, however, can explain the size of islands if an interaction parameter is adjusted properly. Finite size islands are formed when repulsive monomer interactions are balanced by attractive monomer-dimer interactions.A simple model of nearest neighbor attraction and s−3 repulsion is used as an example for the interaction parameter search.Previous experimental studies have shown that in the low coverage region nitrogen atoms agglomerate to isolated square islands of about 5 nm × 5 nm size with a c(2x2) structure. With increasing coverage those islands form regular patterns but do not touch below about 0.4 monolayers. Previous experiments and calculations have shown that the square island pattern show significant elastic effects.Different adatom structures within the nitrogen islands have been analyzed, a dimer step model is able to reproduce the experimentally found island size. This model requires a molecular bond between nitrogen adatoms forming dimers. The model is also used to compute elastic interactions between islands and to check it against the experimentally found island pattern.Shortcomings and limitations of the model are discussed and open questions are formulated.

Analytical description of the nonlinear plasmonic response in nanographene

Graphene exhibits a remarkably high intrinsic nonlinearity that can be pushed even further when the optical frequency is tuned to the plasmon resonances of the material. Atomistic simulations provide an accurate description of these phenomena, although their computational cost is prohibitive for large graphene nanostructures. An alternative formalism consists in relying on classical electromagnetism, using the local nonlinear conductivities extracted from extended graphene. We show that both of these approaches are in excellent agreement for sufficiently large structures (10s nm lateral size) when describing second- and third-harmonic generation, as well as Kerr nonlinearities. Additionally, we exploit an eigenmode decomposition of the optical field in the classical formalism to obtain analytical expressions for the plasmon-driven resonant response of graphene ribbons and finite islands, in excellent agreement with full numerical calculations. This analytical description constitutes a valuable asset to explore nonlinear phenomena in the context of graphene plasmonics and is equally useful to model nonlinearities in other planar plasmonic materials, such as thin metal layers and exfoliated chalcogenides.

Modified Traffic Cellular Automaton for the Density Classification Task

The density classification task asks to design a cellular automaton that converges to the uniform configuration that corresponds to the state that is in majority in the initial configuration. We investigate connections of this problem to state-conserving cellular automata. We propose a modified traffic CA that washes out finite islands in the same way as the Gacs, Kurdyumov and Levin automaton, but is also guaranteed to converge to a uniform configuration on rings of odd size. We find experimentally several good classifiers that are close to state-conserving cellular automata, and we observe that the best performing known density classifier by Wolz and de Oliveira is only a simple swap away from a state-conserving automaton.

Cooperative Effects in Molecular Conduction

Current experimental and theoretical studies on the effect of intermolecular interactions on molecular conduction appear to be in conflict with each other. In particular, some experimental results, e.g., the observation of 2-dimensional free-particle character for interface bound electrons indicate strong intermolecular interactions while other observations indicate an additive character of conduction properties. In this paper we use a generic tight binding model with a physically motivated choice of parameters in order to examine this issue. The model encompasses direct intermolecular interactions as well as through-metal interactions and can be solved exactly to yield spectral properties (surface density of states) and transport characteristics (transmission coefficients and current-voltage behaviors) for single molecule junctions, molecular islands and molecular layers. We find linear scaling of conduction properties with the number of conducting molecules in junctions characterized by molecular layers when the probe (STM tip) addresses different numbers of molecules; however, the conduction per molecule can differ significantly from that of an isolated single molecule. When a junction involves finite molecular islands of varying sizes, linear scaling sets in only beyond a certain molecular island size, of the order of a few tens of molecules. Implications for current observation of linear scaling behaviors are discussed.

First-Principles Theory of Quantum Well Resonance in Double Barrier Magnetic Tunnel Junctions

Quantum well (QW) resonances in Fe(001)/MgO/Fe/MgO/Fe double barrier magnetic tunnel junctions are calculated from first principles. By including the Coulomb blockade energy due to the finite size islands of the middle Fe film, we confirm that the oscillatory differential resistance observed in a recent experiment [T. Nozaki, Phys. Rev. Lett. 96, 027208 (2006)10.1103/PhysRevLett.96.027208] originates from the QW resonances from the Delta1 band of the Fe majority-spin channel. The primary source of smearing at low temperatures is shown to be the variation of the Coulomb blockade energy.

On the Yang–Lee edge singularity for Ising model on nonhomogeneous structures

We studied distribution of zeros of the partition function of ferromagnetic Ising model near the Yang–Lee edge on two self-similar structures. We have shown that the nature of associated critical behavior crucially depends on the local lattice structure: If the sites of higher coordination number make an infinite connected cluster then we find an usual power-law behavior, while a logarithmic divergence of the correlation length develops near the edge in the case that these sites make only finite islands. We reveal also a close connection between Yang–Lee edge critical behavior and critical behavior of a simple zero-field Gaussian model on the same structures.

Dynamics of Grain Boundaries in Two‐Dimensional Hydrogen‐Bonded Molecular Networks

The temporal evolution of domain boundaries of hydrogen-bonded molecular monolayers at the liquid-solid interface is evaluated by recording series of subsequent scanning tunneling microscopy (STM) images. Comparison of dissimilar benzene carboxylic acids reveals a clear distinction between one- and two-dimensional H-bonded network structures. Trimesic acid forms a two-dimensionally H-bonded networked structure, whereas terephthalic acid organizes in a dense packing of H-bonded linear chains on a graphite surface. In addition, TMA forms a sixfold lattice on a threefold graphite substrate, whereas TPA exhibits only a twofold lattice, causing a high grain-boundary line energy for the latter. In the case of TMA the nanostructure was mostly stable during the observation time. For TPA, Ostwald ripening-that is, the growth of larger islands at the expense of smaller islands-was observed. To explain the various experimentally observed timescales of the dynamics occurring at grain boundaries, molecular mechanics simulations were applied to calculate the binding energy of edge molecules, that is, the line energy, of finite islands of both trimesic and terephthalic acid on a graphite substrate.

Island-density and size dynamics in ion-assisted atomic deposition

The mutation rate equations for island nucleation and growth during atomic deposition in the presence of congruent ion irradiation are solved for a point-island model. The irradiation is considered to sputter monomer adatoms and atomic clusters or islands and to dissociate islands into adatoms. It is shown that adatom sputtering alone can decrease island density and, in the late stage of island aggregation, increase island size while island sputtering and dissociation processes can lead to island density increase. Comparison with the limited experimental data available shows good qualitative agreement with the analytic predictions in terms of the model parameters. Suggestions for a more exact approach in which finite size islands are considered are made.

Formation of cracks in epitaxial overlayers

The one-dimensional model of epitaxial interfaces developed by Frank and van der Merwe and refined to account for the anharmonic and non-convex character of the interatomic bonding is used to study the formation of cracks in epitaxial films. In our model, the force which keeps the atoms together displays a maximum (the theoretical tensile strength of the material), and the chemical bonds become distorted, i.e. long (weak) and short (strong) bonds alternate in expanded overlayers. In compressed overlayers, the bonds in the cores of the misfit dislocations are expanded and can break along the dislocation lines at small misfits. In expanded overlayers, the bonds in the core of the misfit dislocations are compressed and cannot break. However, due to the anharmonicity of the potential and the distortion of the chemical bonds, coupled kink-antikink configurations could replace single kinks beyond the metastability limit of the latter. The bonds in the cores of the antikinks are strongly elongated. They can easily break as the force which keeps the atoms together is several orders of magnitude weaker than the theoretical tensile strength of the material and the overlayer can crack along the dislocation lines at large absolute values of the misfit. Therefore compressed overlayers can crack at small positive misfits, whereas expanded overlayers are more prone to crack at large absolute values of the negative misfit. Finite 2D islands crack easier than infinite overlayers when compressed and more difficult when under tensile stress.

Nonlinear destabilization of linearly stable tearing modes with multiple rational surfaces

The stability of finite size magnetic islands is analyzed in configurations with multiple resonant magnetic surfaces. It is demonstrated that there are configurations that are linearly stable which can be unstable to finite size perturbations. Two different examples of single helicity double tearing are given for configurations with two q=2 surfaces. In the first case the destabilization is due to the extension of magnetic separatrices out to regions of destabilizng current gradients. For the second case the modes are linearly stabilized by the suppression of the linear coupling of the rational surfaces by differential plasma rotation, which essentially decouples the perturbations around the different rational surfaces. A finite size magnetic island will interact quasilinearly with initial plasma rotation. The plasma rotation is then equilibrated and the mode destabilized.

Size dependence of the orientational disorder and melting transitions of finite N2 islands deposited on graphite

The orientational order–disorder and melting transition temperatures for quasi two-dimensional islands of N2 molecules deposited on graphite are calculated for sizes 1≤N≤256 molecules, using a Monte Carlo procedure with free surface boundary conditions. These transition temperatures are strong functions of N, and the values for 256 molecules are close to those measured experimentally for fractional macroscopic monolayers. Calculated results show that the two sublattice herringbone orientational structure persists up to the orientational transition temperature, above which hindered planar rotation occurs. The registered √3×√3 mass center structure exists until melting, where the islands disassociate. These features are consistent with experiment. Below melting, the root mean square fluctuations of the mass centers away from their √3×√3 equilibrium values are substantially larger than for bulk N2 or for small three-dimensional rare gas clusters. The fluctuations are also substantially larger for edge molecules than for those in the center.

Kinetically Controlled Aggregation in Reactive Adsorbate Overlayers

AbstractThe kinetics of surface chemical reactions depend critically on the lateral distribution of the adsorbed reactants. In some cases, the adsorbates are aggregated into islands and the rate of reaction is strongly influenced by the structural (sizes and shapes) and energetic (lateral interaction potentials) characteristics of the aggregated overlayer. Adsorbate aggregation or segregation on surfaces may be induced by a variety of mechanisms, three important types of which are briefly discussed here. The first process is driven by strong lateral interactions between the adsorbed particles, which favor their organization in an ordered two‐dimensional phase, but because of kinetic constraints the system only reaches a long‐lived metastable state characterized by finite islands with highly ramified edges. A somewhat more complex aggregation‐segregation process, in a system comprised of two interacting adsorbate species, is also described, and the consequences with respect to surface reaction kinetics are demonstrated. The second aggregation process reflects (Eden‐type) island formation during adsorption of molecules from the gas phase. More specifically, these islands result from the so‐called (extrinsic) precursor‐mediated chemisorption mechanism. Finally, we discuss the segregation of adsorbed reactants induced by the bimolecular annihilation reaction A + B → 0, under steady‐state conditions. Unlike in the first example, this segregation process takes place even in the absence of adsorbate interactions (except for the reactive A‐B interaction) and is most pronounced in the absence of particle diffusion.

The effect of realistic forces in finite epitaxial islands: Equilibrium structure, stability limits and substrate-induced dissociation of migrating clusters

The behaviour of finite epitaxial islands in the periodic field of the substrate is theoretically investigated. The harmonic interactions, traditionally adopted in the model of Frank and Van der Merwe, are replaced by Toda and Morse potentials and sets of difference recursion equations, governing the equilibrium properties of the system, are derived and solved numerically. It is shown that allowing for anharmonicity in the interactions in the deposit reveals several qualiatively new effects, such as: (1) The existence of substrate-induced rupture of anharmonic clusters which migrate on the substrate. It is predicted that such dissociation should be enhanced, if (a) the energy barrier for surface diffusion is increased, (b) the natural incompatibility between substrate and deposit is decreased, and (c) the size of the clusters grows. (2) A split in the misfit stability limits for pseudomorphism and for spontaneous generation of misfit dislocations with respect to the sign of the misfit. The limits corresponding to negative misfit rapidly increase while the positive misfit limits decrease (in absolute terms) with growing degree of anharmonicity. (3) A marked asymmetry in the magnitude of various properties of the clusters, such as adhesion to the substrate, activation energy for surface diffusion, mean strain, dislocation lengths, etc., with respect to the sign of the mismatch between surface and deposit.

The effect of realistic forces in finite epitaxial islands: Equilibrium structure, stability limits and substrate-induced dissociation of migrating clusters

The effect of realistic forces in finite epitaxial islands: Equilibrium structure, stability limits and substrate-induced dissociation of migrating clusters

The effect of anharmonicity in epitaxial interfaces: I. Substrate-induced dissociation of finite epitaxial islands

The behaviour of finite epitaxial islands in the periodic field of the substrate is theoretically investigated whereby the role of anharmonicity in the interatomic forces of the deposit is examined. The harmonic potential, traditionally adopted in the model of Frank and van der Merwe, is replaced by Toda and Morse potentials and sets of difference recursion equations, governing the static properties of such a system, are derived and solved numerically. Thus a new effect of substrate-induced rupture of anharmonic chains migrating on the surface, is found. It is shown that dissociation of migrating clusters is enhanced, if: (i) The substrate potential becomes increasingly modulated, (ii) the natural misfit between deposit and substrate is decreased (in absolute value), (iii) the misfit is negative, rather than positive (with the same absolute value) and (iv) the size of the cluster increases. A relation between dislocations in the chain and rupture appears to exist, suggesting dilatons (enormously stretched interatomic bonds) as the origin for destruction. The influence of anharmonicity on the equilibrium structure of the overgrowth is considered in Part II.

The effect of anharmonicity in epitaxial interfaces: I. Substrate-induced dissociation of finite epitaxial islands

The effect of anharmonicity in epitaxial interfaces: I. Substrate-induced dissociation of finite epitaxial islands

A one-dimensional model for the mobility of small epitaxial islands II: Sinusoidal potential

A one-dimensional model of finite epitaxial islands assuming a sinusoidal representation of the substrate potential field is considered. The equilibrium solutions, both stable and unstable, are obtained numerically. The activation energies for surface diffusion of entities composed of chains of atoms connected by springs are calculated as a function of the misfit, chain length (island size) and the energy parameters assuming that plastic deformations in solids can be explained by the dislocation slip mechanism suggested by Frenkel and Kontorova. It is found that the activation energies oscillate around a nearly constant value which is lower than that for a single atom if the natural misfit is greater than the critical misfit, above which misfit dislocations can be spontaneously introduced at the free ends. In the opposite case the activation energies increase monotically with the chain length after reaching a minimum value which is connected with the appearance of the first dislocation as a lowest energy state. It is concluded that an observable mobility is only to be expected in the first case. In the second case mobility can only be expected for very small clusters. The critical misfit is calculated as a function of the energy parameters and it is found that it deviates considerably from that estimated by Frank and van der Merwe who considered a continuum sinusoidal model only for very deep potential troughs and small elastic moduli of the overgrowth.

The size dependence of equilibrium elastic strain in finite epitaxial islands

The equilibrium elastic strain in epitaxial islands of small size is shown to have a sawtooth dependence on island width by minimizing the systems energy as calculated from a periodic interaction potential between substrate and overgrowth. Such a sawtooth variation is consistent with Vincent's observations and idea that a given misfit between island and substrate may not be entirely accommodated by an integral number of identical misfit dislocations, and hence, the remaining misfit, which depends in part on island width, will be accommodated by residual elastic strain. The present calculations of mechanical equilibrium support these ideas and further reveal that in some cases misfit dislocations may over compensate for the misfit, thereby introducing an elastic strain of opposite sign to that normally expected. Other results of the calculations are in agreement with earlier theoretical and experimental observations.