Evaporation and Step Edge Diffusion in MBE

Using kinetic Monte-Carlo simulations of a Solid-on-Solid model we investigate the influence of step edge diffusion (SED) and evaporation on Molecular Beam Epitaxy (MBE). Based on these investigations we propose two strategies to optimize MBE-growth. The strategies are applicable in different growth regimes: during layer-by-layer growth one can reduce the desorption rate using a pulsed flux. In three-dimensional (3D) growth the SED can help to grow large, smooth structures. For this purpose the flux has to be reduced with time according to a power law.Comment: 5 pages, 2 figures, latex2e (packages: elsevier,psfig,latexsym

Crossover in the scaling of island size and capture zone distributions

Simulations of irreversible growth of extended (fractal and square) islands with critical island sizes i=1 and 2 are performed in broad ranges of coverage \theta and diffusion-to-deposition ratios R in order to investigate scaling of island size and capture zone area distributions (ISD, CZD). Large \theta and small R lead to a crossover from the CZD predicted by the theory of Pimpinelli and Einstein (PE), with Gaussian right tail, to CZD with simple exponential decays. The corresponding ISD also cross over from Gaussian or faster decays to simple exponential ones. For fractal islands, these features are explained by changes in the island growth kinetics, from a competition for capture of diffusing adatoms (PE scaling) to aggregation of adatoms with effectively irrelevant diffusion, which is characteristic of random sequential adsorption (RSA) without surface diffusion. This interpretation is confirmed by studying the crossover with similar CZ areas (of order 100 sites) in a model with freezing of diffusing adatoms that corresponds to i=0. For square islands, deviations from PE predictions appear for coverages near \theta=0.2 and are mainly related to island coalescence. Our results show that the range of applicability of the PE theory is narrow, thus observing the predicted Gaussian tail of CZD may be difficult in real systems.Comment: 9 pages, 7 figure

Scaling properties of step bunches induced by sublimation and related mechanisms: A unified perspective

This work provides a ground for a quantitative interpretation of experiments on step bunching during sublimation of crystals with a pronounced Ehrlich-Schwoebel (ES) barrier in the regime of weak desorption. A strong step bunching instability takes place when the kinetic length is larger than the average distance between the steps on the vicinal surface. In the opposite limit the instability is weak and step bunching can occur only when the magnitude of step-step repulsion is small. The central result are power law relations of the between the width, the height, and the minimum interstep distance of a bunch. These relations are obtained from a continuum evolution equation for the surface profile, which is derived from the discrete step dynamical equations for. The analysis of the continuum equation reveals the existence of two types of stationary bunch profiles with different scaling properties. Through a mathematical equivalence on the level of the discrete step equations as well as on the continuum level, our results carry over to the problems of step bunching induced by growth with a strong inverse ES effect, and by electromigration in the attachment/detachment limited regime. Thus our work provides support for the existence of universality classes of step bunching instabilities [A. Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002)], but some aspects of the universality scenario need to be revised.Comment: 21 pages, 8 figure

Correlations in nano-scale step fluctuations: comparison of simulation and experiments

We analyze correlations in step-edge fluctuations using the Bortz-Kalos-Lebowitz kinetic Monte Carlo algorithm, with a 2-parameter expression for energy barriers, and compare with our VT-STM line-scan experiments on spiral steps on Pb(111). The scaling of the correlation times gives a dynamic exponent confirming the expected step-edge-diffusion rate-limiting kinetics both in the MC and in the experiments. We both calculate and measure the temperature dependence of (mass) transport properties via the characteristic hopping times and deduce therefrom the notoriously-elusive effective energy barrier for the edge fluctuations. With a careful analysis we point out the necessity of a more complex model to mimic the kinetics of a Pb(111) surface for certain parameter ranges.Comment: 10 pages, 9 figures, submitted to Physical Review

Theoretical Characterization of the Interface in a Nonequilibrium Lattice System

The influence of nonequilibrium bulk conditions on the properties of the interfaces exhibited by a kinetic Ising--like model system with nonequilibrium steady states is studied. The system is maintained out of equilibrium by perturbing the familiar spin--flip dynamics at temperature T with completely--random flips; one may interpret these as ideally simulating some (dynamic) impurities. We find evidence that, in the present case, the nonequilibrium mechanism adds to the basic thermal one resulting on a renormalization of microscopic parameters such as the probability of interfacial broken bonds. On this assumption, we develop theory for the nonequilibrium "surface tension", which happens to show a non--monotonous behavior with a maximum at some finite T. It ensues, in full agreement with Monte Carlo simulations, that interface fluctuations differ qualitatively from the equilibrium case, e.g., the interface remains rough at zero--T. We discuss on some consequences of these facts for nucleation theory, and make some explicit predictions concerning the nonequilibrium droplet structure.Comment: 10 pages, 7 figures, submitted to Phys. Re

Scaling Theory for Migration-Driven Aggregate Growth

We give a comprehensive rate equation description for the irreversible growth of aggregates by migration from small to large aggregates. For a homogeneous rate K(i;j) at which monomers migrate from aggregates of size i to those of size j, that is, K(ai;aj) ~ a^{lambda} K(i,j), the mean aggregate size grows with time as t^{1/(2-lambda)} for lambda<2. The aggregate size distribution exhibits distinct regimes of behavior which are controlled by the scaling properties of the migration rate from the smallest to the largest aggregates. Our theory applies to diverse phenomena, such as the distribution of city populations, late stage coarsening of non-symmetric binary systems, and models for wealth exchange.Comment: 4 pages, 2-column revtex format. Revision to appear in PRL. Various changes in response to referee comments. Figure from version 1 deleted but is available at http://physics.bu.edu/~redne

Persistence and survival in equilibrium step fluctuations

Results of analytic and numerical investigations of first-passage properties of equilibrium fluctuations of monatomic steps on a vicinal surface are reviewed. Both temporal and spatial persistence and survival probabilities, as well as the probability of persistent large deviations are considered. Results of experiments in which dynamical scanning tunneling microscopy is used to evaluate these first-passage properties for steps with different microscopic mechanisms of mass transport are also presented and interpreted in terms of theoretical predictions for appropriate models. Effects of discrete sampling, finite system size and finite observation time, which are important in understanding the results of experiments and simulations, are discussed.Comment: 30 pages, 12 figures, review paper for a special issue of JSTA

Dynamics of surface steps

In the framework of SOS models, the dynamics of isolated and pairs of surface steps of monoatomic height is studied, for step--edge diffusion and for evaporation kinetics, using Monte Carlo techniques. In particular, various interesting crossover phenomena are identified. Simulational results are compared, especially, to those of continuum theories and random walk descriptions.Comment: 13 pages in elsart style, 4 eps figures, submitted to Physica

Spatio-temporal distribution of nucleation events during crystal growth

We consider irreversible second-layer nucleation that occurs when two adatoms on a terrace meet. We solve the problem analytically in one dimension for zero and infinite step-edge barriers, and numerically for any value of the barriers in one and two dimensions. For large barriers, the spatial distribution of nucleation events strongly differs from $\rho^2$, where $\rho$ is the stationary adatom density in the presence of a constant flux. The probability $Q(t)$ that nucleation occurs at time $t$ after the deposition of the second adatom, decays for short time as a power law [$Q(t)\sim t^{-1/2}$] in $d=1$ and logarithmically [$Q(t)\sim 1/\ln(t/t_0)$] in $d=2$; for long time it decays exponentially. Theories of the nucleation rate $\omega$ based on the assumption that it is proportional to $\rho^2$ are shown to overestimate $\omega$ by a factor proportional to the number of times an adatom diffusing on the terrace visits an already visited lattice site.Comment: 4 pages, 3 figures; accepted for publication on PR

Current-Induced Step Bending Instability on Vicinal Surfaces

We model an apparent instability seen in recent experiments on current induced step bunching on Si(111) surfaces using a generalized 2D BCF model, where adatoms have a diffusion bias parallel to the step edges and there is an attachment barrier at the step edge. We find a new linear instability with novel step patterns. Monte Carlo simulations on a solid-on-solid model are used to study the instability beyond the linear regime.Comment: 4 pages, 4 figure