Relaxation kinetics in two-dimensional structures

We have studied the approach to equilibrium of islands and pores in two dimensions. The two-regime scenario observed when islands evolve according to a set of particular rules, namely relaxation by steps at low temperature and smooth at high temperature, is generalized to a wide class of kinetic models and the two kinds of structures. Scaling laws for equilibration times are analytically derived and confirmed by kinetic Monte Carlo simulations.Comment: 6 pages, 7 figures, 1 tabl

Atomic step motion during the dewetting of ultra-thin films

We report on three key processes involving atomic step motion during the dewetting of thin solid films: (i) the growth of an isolated island nucleated far from a hole, (ii) the spreading of a monolayer rim, and (iii) the zipping of a monolayer island along a straight dewetting front. Kinetic Monte Carlo results are in good agreement with simple analytical models assuming diffusion-limited dynamics.Comment: 7 pages, 5 figure

Asymptotic step profiles from a nonlinear growth equation for vicinal surfaces

We study a recently proposed nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. (80), 4221 (1998)]. A careful numerical analysis shows that the dynamically selected step profile consists of sloped segments, given by an inverse error function and steepening as sqrt(t), which are matched to pieces of a stationary (time-independent) solution describing the maxima and minima. The effect of smoothening by step edge diffusion is included heuristically, and a one-parameter family of evolution equations is introduced which contains relaxation by step edge diffusion and by attachment-detachment as special cases. The question of the persistence of an initially imposed meander wavelength is investigated in relation to recent experiments.Comment: 4 pages, 5 included figures. Typo in Eq.(5) corrected, section headlines added and Ref.[12] update

Continuum description of profile scaling in nanostructure decay

The relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition is studied via a continuum approach that accounts for step energy g_1 and step-step interaction energy g_3>0. For diffusion-limited kinetics, free-boundary and boundary-layer theories are used for self-similar shapes close to the growing facet. For long times and g_3/g_1 < 1, (a) a universal equation is derived for the shape profile, (b) the layer thickness varies as (g_3/g_1)^{1/3}, (c) distinct solutions are found for different g_3/_1, and (d) for conical shapes, the profile peak scales as (g_3/g_1)^{-1/6}. These results compare favorably with kinetic simulations.Comment: 4 pages including 3 figure

Microstructure and velocity of field-driven Ising interfaces moving under a soft stochastic dynamic

We present theoretical and dynamic Monte Carlo simulation results for the mobility and microscopic structure of 1+1-dimensional Ising interfaces moving far from equilibrium in an applied field under a single-spin-flip ``soft'' stochastic dynamic. The soft dynamic is characterized by the property that the effects of changes in field energy and interaction energy factorize in the transition rate, in contrast to the nonfactorizing nature of the traditional Glauber and Metropolis rates (``hard'' dynamics). This work extends our previous studies of the Ising model with a hard dynamic and the unrestricted SOS model with soft and hard dynamics. [P.A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000); J. Phys. A 35, L117 (2002); Phys. Rev. E 66, 066116 (2002).] The Ising model with soft dynamics is found to have closely similar properties to the SOS model with the same dynamic. In particular, the local interface width does not diverge with increasing field, as it does for hard dynamics. The skewness of the interface at nonzero field is very weak and has the opposite sign of that obtained with hard dynamics.Comment: 19 pages LaTex with 7 imbedded figure

Fast coarsening in unstable epitaxy with desorption

Homoepitaxial growth is unstable towards the formation of pyramidal mounds when interlayer transport is reduced due to activation barriers to hopping at step edges. Simulations of a lattice model and a continuum equation show that a small amount of desorption dramatically speeds up the coarsening of the mound array, leading to coarsening exponents between 1/3 and 1/2. The underlying mechanism is the faster growth of larger mounds due to their lower evaporation rate.Comment: 4 pages, 4 PostScript figure

Dynamics of a faceted nematic-smectic B front in thin-sample directional solidification

We present an experimental study of the directional-solidification patterns of a nematic - smectic B front. The chosen system is C_4H_9-(C_6H_{10})_2CN (in short, CCH4) in 12 \mu m-thick samples, and in the planar configuration (director parallel to the plane of the sample). The nematic - smectic B interface presents a facet in one direction -- the direction parallel to the smectic layers -- and is otherwise rough, and devoid of forbidden directions. We measure the Mullins-Sekerka instability threshold and establish the morphology diagram of the system as a function of the solidification rate V and the angle theta_{0} between the facet and the isotherms. We focus on the phenomena occurring immediately above the instability threshold when theta_{0} is neither very small nor close to 90^{o}. Under these conditions we observe drifting shallow cells and a new type of solitary wave, called "faceton", which consists essentially of an isolated macroscopic facet traveling laterally at such a velocity that its growth rate with respect to the liquid is small. Facetons may propagate either in a stationary, or an oscillatory way. The detailed study of their dynamics casts light on the microscopic growth mechanisms of the facets in this system.Comment: 12 pages, 19 figures, submitted to Phys. Rev.

Analytical solution of generalized Burton--Cabrera--Frank equations for growth and post--growth equilibration on vicinal surfaces

We investigate growth on vicinal surfaces by molecular beam epitaxy making use of a generalized Burton--Cabrera--Frank model. Our primary aim is to propose and implement a novel analytical program based on a perturbative solution of the non--linear equations describing the coupled adatom and dimer kinetics. These equations are considered as originating from a fully microscopic description that allows the step boundary conditions to be directly formulated in terms of the sticking coefficients at each step. As an example, we study the importance of diffusion barriers for adatoms hopping down descending steps (Schwoebel effect) during growth and post-growth equilibration of the surface.Comment: 16 pages, REVTeX 3.0, IC-DDV-94-00

Microstructure and Velocity of Field-Driven SOS Interfaces: Analytic Approximations and Numerical Results

The local structure of a solid-on-solid (SOS) interface in a two-dimensional kinetic Ising ferromagnet with single-spin-flip Glauber dynamics, which is driven far from equilibrium by an applied field, is studied by an analytic mean-field, nonlinear-response theory [P.A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000)] and by dynamic Monte Carlo simulations. The probability density of the height of an individual step in the surface is obtained, both analytically and by simulation. The width of the probability density is found to increase dramatically with the magnitude of the applied field, with close agreement between the theoretical predictions and the simulation results. Excellent agreement between theory and simulations is also found for the field-dependence and anisotropy of the interface velocity. The joint distribution of nearest-neighbor step heights is obtained by simulation. It shows increasing correlations with increasing field, similar to the skewness observed in other examples of growing surfaces.Comment: 18 pages RevTex4 with imbedded figure

Surface Kinetics and Generation of Different Terms in a Conservative Growth Equation

A method based on the kinetics of adatoms on a growing surface under epitaxial growth at low temperature in (1+1) dimensions is proposed to obtain a closed form of local growth equation. It can be generalized to any growth problem as long as diffusion of adatoms govern the surface morphology. The method can be easily extended to higher dimensions. The kinetic processes contributing to various terms in the growth equation (GE) are identified from the analysis of in-plane and downward hops. In particular, processes corresponding to the (h -> -h) symmetry breaking term and curvature dependent term are discussed. Consequence of these terms on the stable and unstable transition in (1+1) dimensions is analyzed. In (2+1) dimensions it is shown that an additional (h -> -h) symmetry breaking term is generated due to the in-plane curvature associated with the mound like structures. This term is independent of any diffusion barrier differences between in-plane and out of-plane migration. It is argued that terms generated in the presence of downward hops are the relevant terms in a GE. Growth equation in the closed form is obtained for various growth models introduced to capture most of the processes in experimental Molecular Beam Epitaxial growth. Effect of dissociation is also considered and is seen to have stabilizing effect on the growth. It is shown that for uphill current the GE approach fails to describe the growth since a given GE is not valid over the entire substrate.Comment: 14 pages, 7 figure