Kinetics of step bunching during growth: A minimal model

We study a minimal stochastic model of step bunching during growth on a one-dimensional vicinal surface. The formation of bunches is controlled by the preferential attachment of atoms to descending steps (inverse Ehrlich-Schwoebel effect) and the ratio $d$ of the attachment rate to the terrace diffusion coefficient. For generic parameters ($d > 0$) the model exhibits a very slow crossover to a nontrivial asymptotic coarsening exponent $\beta \simeq 0.38$. In the limit of infinitely fast terrace diffusion ($d=0$) linear coarsening ($\beta$ = 1) is observed instead. The different coarsening behaviors are related to the fact that bunches attain a finite speed in the limit of large size when $d=0$, whereas the speed vanishes with increasing size when $d > 0$. For $d=0$ an analytic description of the speed and profile of stationary bunches is developed.Comment: 8 pages, 10 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

Breakdown of step-flow growth in unstable homoepitaxy

Two mechanisms for the breakdown of step flow growth, in the sense of the appearance of steps of opposite sign to the original vicinality, are studied by kinetic Monte Carlo simulations and scaling arguments. The first mechanism is the nucleation of islands on the terraces, which leads to mound formation if interlayer transport is sufficiently inhibited. The second mechanism is the formation of vacancy islands due to the self-crossing of strongly meandering steps. The competing roles of the growth of the meander amplitude and the synchronization of the meander phase are emphasized. The distance between vacancy islands along the step direction appears to be proportional to the square of the meander wavelengthComment: 7 pages, 9 figure

Drift causes anomalous exponents in growth processes

The effect of a drift term in the presence of fixed boundaries is studied for the one-dimensional Edwards-Wilkinson equation, to reveal a general mechanism that causes a change of exponents for a very broad class of growth processes. This mechanism represents a relevant perturbation and therefore is important for the interpretation of experimental and numerical results. In effect, the mechanism leads to the roughness exponent assuming the same value as the growth exponent. In the case of the Edwards-Wilkinson equation this implies exponents deviating from those expected by dimensional analysis.Comment: 4 pages, 1 figure, REVTeX; accepted for publication in PRL; added note and reference

New mechanism for impurity-induced step bunching

Codeposition of impurities during the growth of a vicinal surface leads to an impurity concentration gradient on the terraces, which induces corresponding gradients in the mobility and the chemical potential of the adatoms. Here it is shown that the two types of gradients have opposing effects on the stability of the surface: Step bunching can be caused by impurities which either lower the adatom mobility, or increase the adatom chemical potential. In particular, impurities acting as random barriers (without affecting the adatom binding) cause step bunching, while for impurities acting as random traps the combination of the two effects reduces to a modification of the attachment boundary conditions at the steps. In this case attachment to descending steps, and thus step bunching, is favored if the impurities bind adatoms more weakly than the substrate.Comment: 7 pages, 3 figures. Substantial revisions and correction

Records and sequences of records from random variables with a linear trend

We consider records and sequences of records drawn from discrete time series of the form $X_{n}=Y_{n}+cn$, where the $Y_{n}$ are independent and identically distributed random variables and $c$ is a constant drift. For very small and very large drift velocities, we investigate the asymptotic behavior of the probability $p_n(c)$ of a record occurring in the $n$th step and the probability $P_N(c)$ that all $N$ entries are records, i.e. that $X_1 < X_2 < ... < X_N$. Our work is motivated by the analysis of temperature time series in climatology, and by the study of mutational pathways in evolutionary biology.Comment: 21 pages, 7 figure

Spiral Growth and Step Edge Barriers

The growth of spiral mounds containing a screw dislocation is compared to the growth of wedding cakes by two-dimensional nucleation. Using phase field simulations and homoepitaxial growth experiments on the Pt(111) surface we show that both structures attain the same characteristic large scale shape when a significant step edge barrier suppresses interlayer transport. The higher vertical growth rate observed for the spiral mounds on Pt(111) reflects the different incorporation mechanisms for atoms in the top region and can be formally represented by an enhanced apparent step edge barrier.Comment: 11 pages, 4 figures, partly in colo

Driven Lattice Gases with Quenched Disorder: Exact Results and Different Macroscopic Regimes

We study the effect of quenched spatial disorder on the steady states of driven systems of interacting particles. Two sorts of models are studied: disordered drop-push processes and their generalizations, and the disordered asymmetric simple exclusion process. We write down the exact steady-state measure, and consequently a number of physical quantities explicitly, for the drop-push dynamics in any dimensions for arbitrary disorder. We find that three qualitatively different regimes of behaviour are possible in 1-$d$ disordered driven systems. In the Vanishing-Current regime, the steady-state current approaches zero in the thermodynamic limit. A system with a non-zero current can either be in the Homogeneous regime, chracterized by a single macroscopic density, or the Segregated-Density regime, with macroscopic regions of different densities. We comment on certain important constraints to be taken care of in any field theory of disordered systems.Comment: RevTex, 17pages, 18 figures included using psfig.st

Bottleneck-induced transitions in a minimal model for intracellular transport

We consider the influence of disorder on the non-equilibrium steady state of a minimal model for intracellular transport. In this model particles move unidirectionally according to the \emph{totally asymmetric exclusion process} (TASEP) and are coupled to a bulk reservoir by \emph{Langmuir kinetics}. Our discussion focuses on localized point defects acting as a bottleneck for the particle transport. Combining analytic methods and numerical simulations, we identify a rich phase behavior as a function of the defect strength. Our analytical approach relies on an effective mean-field theory obtained by splitting the lattice into two subsystems, which are effectively connected exploiting the local current conservation. Introducing the key concept of a carrying capacity, the maximal current which can flow through the bulk of the system (including the defect), we discriminate between the cases where the defect is irrelevant and those where it acts as a bottleneck and induces various novel phases (called {\it bottleneck phases}). Contrary to the simple TASEP in the presence of inhomogeneities, many scenarios emerge and translate into rich underlying phase-diagrams, the topological properties of which are discussed.Comment: 14 pages, 15 figures, 1 tabl

An Exactly Solved Model of Three Dimensional Surface Growth in the Anisotropic KPZ Regime

We generalize the surface growth model of Gates and Westcott to arbitrary inclination. The exact steady growth velocity is of saddle type with principal curvatures of opposite sign. According to Wolf this implies logarithmic height correlations, which we prove by mapping the steady state of the surface to world lines of free fermions with chiral boundary conditions.Comment: 9 pages, REVTEX, epsf, 3 postscript figures, submitted to J. Stat. Phys, a wrong character is corrected in eqs. (31) and (32