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 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 the monomers to the occupied sites of the lattice. For zero and weak barriers, the attachment is limited by diffusion while for strong barriers it is limited by reaction.

Fragmentation approach to the point-island model with hindered aggregation: Accessing the barrier energy.

We study the effect of hindered aggregation on the island formation process in a one- (1D) and two-dimensional (2D) point-island model for epitaxial growth with arbitrary critical nucleus size i. In our model, the attachment of monomers to preexisting islands is hindered by an additional attachment barrier, characterized by length l_{a}. For l_{a}=0 the islands behave as perfect sinks while for l_{a}→∞ they behave as reflecting boundaries.

Coverage dependent molecular assembly of anthraquinone on Au(111).

A scanning tunneling microscopy study of anthraquinone (AQ) on the Au(111) surface shows that the molecules self-assemble into several structures depending on the local surface coverage. At high coverages, a close-packed saturated monolayer is observed, while at low coverages, mobile surface molecules coexist with stable chiral hexamer clusters. At intermediate coverages, a disordered 2D porous network interlinking close-packed islands is observed in contrast to the giant honeycomb networks observed for the same molecule on Cu(111).

Chemical insight from density functional modeling of molecular adsorption: Tracking the bonding and diffusion of anthracene derivatives on Cu(111) with molecular orbitals.

We present a method of analyzing the results of density functional modeling of molecular adsorption in terms of an analogue of molecular orbitals. This approach permits intuitive chemical insight into the adsorption process. Applied to a set of anthracene derivates (anthracene, 9,10-anthraquinone, 9,10-dithioanthracene, and 9,10-diselenonanthracene), we follow the electronic states of the molecules that are involved in the bonding process and correlate them to both the molecular adsorption geometry and the species' diffusive behavior.

How "hot precursors" modify island nucleation: a rate-equation model.

We propose a novel island nucleation and growth model explicitly including transient (ballistic) mobility of the monomers deposited at rate F, assumed to be in a hot precursor state before thermalizing. In limiting regimes, corresponding to fast (diffusive) and slow (ballistic) thermalization, the island density N obeys scaling N∝F(α). In between is found a rich, complex behavior, with various distinctive scaling regimes, characterized by effective exponents α(eff) and activation energies that we compute exactly.

Interacting steps with finite-range interactions: analytical approximation and numerical results.

We calculate an analytical expression for the terrace-width distribution P(s) for an interacting step system with nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent one-dimensional system of classical particles. The validity of the model is tested with several numerical simulations and experimental results.

Charge inhomogeneity determines oxidative reactivity of graphene on substrates.

Single-layer graphene (SLG) supported on SiO(2) shows anomalously large chemical reactivity compared to thicker graphene, with charge inhomogeneity-induced potential fluctuations or topographic corrugations proposed as the cause. Here we systematically probe the oxidative reactivity of graphene supported on substrates with different surface roughnesses and charged impurity densities: hexagonal boron nitride (hBN), mica, thermally grown SiO(2) on Si, and SiO(2) nanoparticle thin films. SLG on low charge trap density hBN is not etched and shows little doping after oxygen treatment at temperatures up to 550 °C, in sharp contrast with oxidative etching under similar conditions of graphene on high charge trap density SiO(2) and mica.

Mean-field approximation for spacing distribution functions in classical systems.

We propose a mean-field method to calculate approximately the spacing distribution functions p((n))(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p((n))(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation.

Voronoi cell patterns: theoretical model and applications.

We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a homogeneous and isotropic set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell.

Coalescence of 3-phenyl-propynenitrile on Cu(111) into interlocking pinwheel chains.

3-phenyl-propynenitrile (PPN) adsorbs on Cu(111) in a hexagonal network of molecular trimers formed through intermolecular interaction of the cyano group of one molecule with the aromatic ring of its neighbor. Heptamers of trimers coalesce into interlocking pinwheel-shaped structures that, by percolating across islands of the original trimer coverage, create the appearance of gear chains. Density functional theory aids in identifying substrate stress associated with the chemisorption of PPN's acetylene group as the cause of this transition.

Do two-dimensional "noble gas atoms" produce molecular honeycombs at a metal surface?

Anthraquinone self-assembles on Cu(111) into a giant honeycomb network with exactly three molecules on each side. Here we propose that the exceptional degree of order achieved in this system can be explained as a consequence of the confinement of substrate electrons in the pores, with the pore size tailored so that the confined electrons can adopt a noble-gas-like two-dimensional quasi-atom configuration with two filled shells. Formation of identical pores in a related adsorption system (at different overall periodicity due to the different molecule size) corroborates this concept.

One-dimensional model of interacting-step fluctuations on vicinal surfaces: analytical formulas and kinetic Monte Carlo simulations.

We study analytically and numerically a one-dimensional model of interacting line defects (steps) fluctuating on a vicinal crystal. Our goal is to formulate and validate analytical techniques for approximately solving systems of coupled nonlinear stochastic differential equations (SDEs) governing fluctuations in surface motion. In our analytical approach, the starting point is the Burton-Cabrera-Frank (BCF) model by which step motion is driven by diffusion of adsorbed atoms on terraces and atom attachment-detachment at steps.

Adsorbates in a box: titration of substrate electronic states.

Nanoscale confinement of adsorbed CO molecules in an anthraquinone network on Cu(111) with a pore size of ≈4  nm arranges the CO molecules in a shell structure that coincides with the distribution of substrate confined electronic states. Molecules occupy the states approximately in the sequence of rising electron energy. Despite the sixfold symmetry of the pore boundary itself, the adsorbate distribution adopts the threefold symmetry of the network-substrate system, highlighting the importance of the substrate even for such quasi-free-electron systems.

Strong quantum size effects in Pb(111) thin films mediated by anomalous Friedel oscillations.

Using first-principles calculations within density functional theory, we study Friedel oscillations (FOs) in the electron density at different metal surfaces and their influence on the lattice relaxation and stability of ultrathin metal films. We show that the FOs at the Pb(111) surface decay as 1/x with the distance x from the surface, different from the conventional 1/x(2) power law at other metal surfaces. The underlying physical reason for this striking difference is tied to the strong nesting of the two different Fermi sheets along the Pb(111) direction.

Power of confinement: adsorbate dynamics on nanometer-scale exposed facets.

The diffusion and arrangements of CO adsorbates within nanometer-scale pores on a copper surface are investigated by low-temperature scanning tunneling microscopy. In contrast to extended terraces, confinement stabilizes dislocation lines that expose more than one-fourth of the adsorbate population to potentially more reactive adsorption configurations. Confinement allows correlation between adsorbate diffusivity and the number of adsorbates in the pore.

Impurity decoration for crystal shape control: C60 on Ag(111).

The decoration of hexagonal Ag/Ag(111) monolayer islands by chains of C60, observed via STM at 300 K, dramatically changes the nanocrystalline shape and fluctuations of the islands. We tune coverage so that a single chain of C60 fully decorates each Ag island boundary, forming a closed circular "necklace." We model the C60-induced rounding in terms of competing energetic and entropic effects.

Effects of impurities on surface morphology: some examples.

Small amounts of impurities are known to have remarkably great influence on surface morphology. We discuss three examples that arise in our research. First, we consider impurities codeposited during epitaxial growth, paying particular attention to Cu(100).

Capture-zone scaling in island nucleation: universal fluctuation behavior.

In island nucleation and growth, the distribution of capture zones (in essence proximity cells) can be described by a simple expression generalizing the Wigner surmise (power-law rise, Gaussian decay) from random matrix theory that accounts for spacing distributions in a host of fluctuation phenomena. Its single adjustable parameter, the power-law exponent, can be simply related to the critical nucleus of growth models and the substrate dimensionality. We compare with extensive published kinetic Monte Carlo data and limited experimental data.

Metal-molecule interface fluctuations.

We have created self-assembled circular chains of C60 laterally bound to a layer of Ag atoms as a model system for characterizing fluctuations at a metal-molecule interface. STM measurements show that the Ag and C60 sides of the interface fluctuate independently, with frequency-dependent amplitudes of magnitude 0.1 nm at approximately 1 Hz for the Ag edge and approximately 0.

Distinctive fluctuations in a confined geometry.

Spurred by recent theoretical predictions [Phys. Rev. E 69, 035102(R) (2004)10.

Refined evaluation of the level-spacing distribution of symplectic ensembles: moments and implications.

To obtain a more precise value for the variance sigma2 of the joint probability distribution of a symplectic ensemble, we extend previous numerical evaluations of a power series. Our result sigma2 approximately 0.1041 shows that the excellent approximation using the analytically simple Wigner surmise fractionally overestimates this value.

Beyond the Wigner distribution: Schrödinger equations and terrace width distributions.

The so-called generalized Wigner distribution has earlier been shown to be an excellent approximation for the terrace width distribution (TWD) of vicinal surfaces characterized by step-step interactions that are perpendicular to the average step direction and fall off as the inverse square of the step spacing. In this paper, we show that the generalized Wigner distribution can be derived from a plausible, phenomenological model in which two steps interact with each other directly and with other steps through a position-dependent pressure. We also discuss generalizations to more general step-step interactions and show that the predictions are in good agreement with TWDs derived from numerical transfer-matrix calculations and Monte Carlo simulations.