The disordered flat phase of a crystal surface - critical and dynamic properties

We analyze a restricted SOS model on a square lattice with nearest and next-nearest neighbor interactions, using Monte Carlo techniques. In particular, the critical exponents at the preroughening transition between the flat and disordered flat (DOF) phases are confirmed to be non-universal. Moreover, in the DOF phase, the equilibration of various profiles imprinted on the crystal surface is simulated, applying evaporation kinetics and surface diffusion. Similarities to and deviations from related findings in the flat and rough phases are discussed.Comment: 4 pages, 4 figures, submitted to Phys. Rev.

Capture-zone scaling in island nucleation: phenomenological theory of an example of 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.Comment: 5 pages, 4 figures, originally submitted to Phys. Rev. Lett. on Dec. 15, 2006; revised version v2 tightens and focuses the presentation, emphasizes the importance of universal features of fluctuations, corrects an error for d=1, replaces 2 of the figure

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

Kinetic step bunching during surface growth

We study the step bunching kinetic instability in a growing crystal surface characterized by anisotropic diffusion. The instability is due to the interplay between the elastic interactions and the alternation of step parameters. This instability is predicted to occur on a vicinal semiconductor surface Si(001) or Ge(001) during epitaxial growth. The maximal growth rate of the step bunching increases like $F^{4}$, where $F$ is the deposition flux. Our results are complemented with numerical simulations which reveals a coarsening behavior on the long time for the nonlinear step dynamics.Comment: 4 pages, 6 figures, submitted to PR

Kinetic Monte Carlo simulations inspired by epitaxial graphene growth

Graphene, a flat monolayer of carbon atoms packed tightly into a two dimensional hexagonal lattice, has unusual electronic properties which have many promising nanoelectronic applications. Recent Low Energy Electron Microscopy (LEEM) experiments show that the step edge velocity of epitaxially grown 2D graphene islands on Ru(0001) varies with the fifth power of the supersaturation of carbon adatoms. This suggests that graphene islands grow by the addition of clusters of five atoms rather than by the usual mechanism of single adatom attachment. We have carried out Kinetic Monte Carlo (KMC) simulations in order to further investigate the general scenario of epitaxial growth by the attachment of mobile clusters of atoms. We did not seek to directly replicate the Gr/Ru(0001) system but instead considered a model involving mobile tetramers of atoms on a square lattice. Our results show that the energy barrier for tetramer break up and the number of tetramers that must collide in order to nucleate an immobile island are the important parameters for determining whether, as in the Gr/Ru(0001) system, the adatom density at the onset of island nucleation is an increasing function of temperature. A relatively large energy barrier for adatom attachment to islands is required in order for our model to produce an equilibrium adatom density that is a large fraction of the nucleation density. A large energy barrier for tetramer attachment to islands is also needed for the island density to dramatically decrease with increasing temperature. We show that islands grow with a velocity that varies with the fourth power of the supersaturation of adatoms when tetramer attachment is the dominant process for island growth

Effect of step stiffness and diffusion anisotropy on the meandering of a growing vicinal surface

We study the step meandering instability on a surface characterized by the alternation of terraces with different properties, as in the case of Si(001). The interplay between diffusion anisotropy and step stiffness induces a finite wavelength instability corresponding to a meandering mode. The instability sets in beyond a threshold value which depends on the relative magnitudes of the destabilizing flux and the stabilizing stiffness difference. The meander dynamics is governed by the conserved Kuramoto-Sivashinsky equation, which display spatiotemporal coarsening.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Lett. (February 2006

Pseudospectral versus finite-differences schemes in the numerical integration of stochastic models of surface growth

We present a comparison between finite differences schemes and a pseudospectral method applied to the numerical integration of stochastic partial differential equations that model surface growth. We have studied, in 1+1 dimensions, the Kardar, Parisi and Zhang model (KPZ) and the Lai, Das Sarma and Villain model (LDV). The pseudospectral method appears to be the most stable for a given time step for both models. This means that the time up to which we can follow the temporal evolution of a given system is larger for the pseudospectral method. Moreover, for the KPZ model, a pseudospectral scheme gives results closer to the predictions of the continuum model than those obtained through finite difference methods. On the other hand, some numerical instabilities appearing with finite difference methods for the LDV model are absent when a pseudospectral integration is performed. These numerical instabilities give rise to an approximate multiscaling observed in the numerical simulations. With the pseudospectral approach no multiscaling is seen in agreement with the continuum model.Comment: 13 single column pages, RevTeX, 6 eps fig

Finite-time Singularities in Surface-Diffusion Instabilities are Cured by Plasticity

A free material surface which supports surface diffusion becomes unstable when put under external non-hydrostatic stress. Since the chemical potential on a stressed surface is larger inside an indentation, small shape fluctuations develop because material preferentially diffuses out of indentations. When the bulk of the material is purely elastic one expects this instability to run into a finite-time cusp singularity. It is shown here that this singularity is cured by plastic effects in the material, turning the singular solution to a regular crack.Comment: 4 pages, 3 figure

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