Alberto Pimpinelli

Equilibrium step dynamics on vicinal surfaces

The time τ necessary for the formation of bumps due to thermal fluctuations on steps of vicinal surfaces is evaluated in various relevant cases. Formulae already derived by Mullins and Bales and Zangwill and other expressions recently published by Bartelt et al., are found as special cases. For Si(111) at 900°C we predict that τ is proportional to the step-step separation l and to the square of the fluctuation wavelength L. This prediction is found to be in reasonable agreement with direct experimental observations of equilibrium step fluctuations.

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

In studies of island nucleation and growth, the distribution of capture zones, essentially proximity cells, can give more insight than island-size distributions. In contrast to the complicated expressions, ad hoc or derived from rate equations, usually used, we find the capture-zone distribution can be described by a simple expression generalizing the Wigner surmise from random matrix theory that accounts for the distribution of spacings in a host of fluctuation phenomena. Furthermore, its single adjustable parameter 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. A phenomenological theory sheds light on the result.

What does an evaporating surface look like

The Burton, Cabrera and Frank model for step flow is discussed in the case of evaporation, taking into account vacancy formation. In this framework, the criterion for nucleation of polyvacancies (“Lochkeime”) on an evaporating vicinal surface with step—step separation l is found to be roughly κl >βγ, where γ is the step stiffness, 1/κ = √Dτv, D is the adatom diffusion constant, τv is the average residence time of adatoms on the surface before desorption and 1/β = kBT. Application to silicon is discussed.

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. Application to N(F,T) of recent organic-molecule deposition experiments yields an excellent fit.

Scaling and crossovers in molecular transport in nano-fluidic systems

A simple, analytically soluble model for transport in nanoconfined systems is presented here. The effect of confinement is introduced as a dependence of the solute diffusivity on the concentration, channel size, and intermolecular interactions. We apply the model to the description of molecule and nanoparticle release from devices consisting of slit-nanochannel membranes. We show that, in general, the cumulative amount of analyte released obeys a scaling form as a function of time. Additionally, the model is extended to more complicate situations in which the physico-chemical characteristics of membrane and solvent vary with time, and crossovers between different regimes appear.

Analyzing capture zone distributions (CZD) in growth: Theory and applications

A1. Crystal morphology A1. Growth models A1. Low dimensional structures A1. Surface structure A2. Single crystal growth abstract We have argued that the capture-zone distribution (CZD) in submonolayer growth can be well described by the generalized Wigner distribution (GWD) Pðs Þ¼ as β exp ð� bs 2 Þ ,w heres is the CZ area divided by its average value. This approach offers arguably the most robust (least sensitive to mass transport) method to find the critical nucleus size i ,s inceβ � i þ2. Various analytical and numerical investigations, which we discuss, show that the simple GWD expression is inadequate in the tails of the distribution, it does account well for the central regime 0:5oso2, where the data is sufficiently large to be reliably accessible experimentally. We summarize and catalog the many experiments in which this method has been applied.

Narrowing of terrace-width distributions during growth on vicinal surfaces

We present analytic and numerical results for the steady-state, non-equilibrium terrace-width distribution (TWD) of steps during growth on vicinal surfaces. Kinetic Monte Carlo shows that the TWD narrows progressively with increasing flux until the model breaks down. The narrowing corresponds to kinetic repulsion between moving steps, due to the intrinsic asymmetry of the adatom diffusion current on a growing surface. With a 1-dimensional (1D) model, from a Burton-Cabrera-Frank approach, we make contact with previous work, in which the attachment asymmetry can also be due to electromigration or to asymmetry in attachment rates; we deduce an expression for the narrowing via a Fokker-Planck analysis. We illustrate how Ehrlich-Schwoebel barriers (although inducing an instability in 2D) also lead to such asymmetry and narrowing.

Spacing distribution functions for the one-dimensional point-island model with irreversible attachment.

We study the configurational structure of the point-island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density p(n)(XY)(x,y), which represents the probability density to have nucleation at position x within a gap of size y. Our proposed functional form for p(n)(XY)(x,y) describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system.

Unexpected behaviors in molecular transport through size-controlled nanochannels down to the ultra-nanoscale

Ionic transport through nanofluidic systems is a problem of fundamental interest in transport physics and has broad relevance in desalination, fuel cells, batteries, filtration, and drug delivery. When the dimension of the fluidic system approaches the size of molecules in solution, fluid properties are not homogeneous and a departure in behavior is observed with respect to continuum-based theories. Here we present a systematic study of the transport of charged and neutral small molecules in an ideal nanofluidic platform with precise channels from the sub-microscale to the ultra-nanoscale (<5 nm). Surprisingly, we find that diffusive transport of nano-confined neutral molecules matches that of charged molecules, as though the former carry an effective charge. Further, approaching the ultra-nanoscale molecular diffusivities suddenly drop by up to an order of magnitude for all molecules, irrespective of their electric charge. New theoretical investigations will be required to shed light onto these intriguing results.Transport through nanochannels is usually dominated by electrostatic interactions and depends on the charge of diffusing molecules. Here the authors show that for channel heights between 2 and 4 nanometers, transport is insensitive to molecule charge.

Ferrimagnetic-helimagnetic transition in an XY magnet with infinitely many phases

The authors present an anisotropic frustrated classical spin model, in which the coexistence of continuous and discrete degrees of freedom can be explicitly considered. They investigate an array of planar (XY) spins with usual bilinear exchange, on decorated lattices both in two and three dimensions, whose zero-temperature state is infinitely degenerate. The set of ground states includes a uniform ferrimagnetic arrangement, a uniform helimagnet, and any arbitrary admixture of these in the form of coexisting striped domains. Each ground state in the degeneracy manifold can be exactly mapped to a specified configuration of an anisotropic Ising model on the dual lattice. Ising spins represent the discrete chirality degrees of freedom. Low-temperature continuous excitations (spin waves) couple these Ising spins, selecting the configuration corresponding to the ferrimagnetic state (order by thermal disorder). Adding a competing next-nearest-neighbour interaction allows one to tune a transition to the helimagnet; at low temperature the transition occurs through an infinite sequence of steps, consisting of first-order phase transitions to successive ferrimagnetic phases, each made of helimagnetically ordered stripes of constant width. The width increases from phase to phase, and chirality alternates from stripe to stripe. A discussion of the relationship between decorated continuous spin models and multi-spin interaction is given.