Changing shapes in the nanoworld

What are the mechanisms leading to the shape relaxation of three dimensional crystallites ? Kinetic Monte Carlo simulations of fcc clusters show that the usual theories of equilibration, via atomic surface diffusion driven by curvature, are verified only at high temperatures. Below the roughening temperature, the relaxation is much slower, kinetics being governed by the nucleation of a critical germ on a facet. We show that the energy barrier for this step linearly increases with the size of the crystallite, leading to an exponential dependence of the relaxation time.Comment: 4 pages, 5 figures. Accepted by Phys Rev Let

Anisotropy of Growth of the Close-Packed Surfaces of Silver

The growth morphology of clean silver exhibits a profound anisotropy: The growing surface of Ag(111) is typically very rough while that of Ag(100) is smooth and flat. This serious and important difference is unexpected, not understood, and hitherto not observed for any other metal. Using density functional theory calculations of self-diffusion on flat and stepped Ag(100) we find, for example, that at flat regions a hopping mechanism is favored, while across step edges diffusion proceeds by an exchange process. The calculated microscopic parameters explain the experimentally reported growth properties.Comment: RevTeX, 4 pages, 3 figures in uufiles form, to appear in Phys. Rev. Let

Lattice Effects in Crystal Evaporation

We study the dynamics of a stepped crystal surface during evaporation, using the classical model of Burton, Cabrera and Frank, in which the dynamics of the surface is represented as a motion of parallel, monoatomic steps. The validity of the continuum approximation treated by Frank is checked against numerical calculations and simple, qualitative arguments. The continuum approximation is found to suffer from limitations related, in particular, to the existence of angular points. These limitations are often related to an adatom detachment rate of adatoms which is higher on the lower side of each step than on the upper side ("Schwoebel effect").Comment: DRFMC/SPSMS/MDN, Centre d'Etudes Nucleaires de Grenoble, 25 pages, LaTex, revtex style. 8 Figures, available upon request, report# UBFF30119

The effect of monomer evaporation on a simple model of submonolayer growth

We present a model for thin film growth by particle deposition that takes into account the possible evaporation of the particles deposited on the surface. Our model focuses on the formation of two-dimensional structures. We find that the presence of evaporation can dramatically affect the growth kinetics of the film, and can give rise to regimes characterized by different ``growth'' exponents and island size distributions. Our results are obtained by extensive computer simulations as well as through a simple scaling approach and the analysis of rate equations describing the system. We carefully discuss the relationship of our model with previous studies by Venables and Stoyanov of the same physical situation, and we show that our analysis is more general.Comment: 41 pages including figures, Revtex, to be published in Physical Review

Ratchet Effect in Surface Electromigration: Smoothing Surfaces by an ac Field

We demonstrate that for surfaces that have a nonzero Schwoebel barrier the application of an ac field parallel to the surface induces a net electro- migration current that points in the descending step direction. The magnitude of the current is calculated analytically and compared with Monte Carlo simulations. Since a downhill current smoothes the surface, our results imply that the application of ac fields can aid the smoothing process during annealing and can slow or eliminate the Schwoebel-barrier-induced mound formation during growth.Comment: 4 pages, LaTeX, 4 ps figure

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

Growth of Patterned Surfaces

During epitaxial crystal growth a pattern that has initially been imprinted on a surface approximately reproduces itself after the deposition of an integer number of monolayers. Computer simulations of the one-dimensional case show that the quality of reproduction decays exponentially with a characteristic time which is linear in the activation energy of surface diffusion. We argue that this life time of a pattern is optimized, if the characteristic feature size of the pattern is larger than $(D/F)^{1/(d+2)}$, where $D$ is the surface diffusion constant, $F$ the deposition rate and $d$ the surface dimension.Comment: 4 pages, 4 figures, uses psfig; to appear in Phys. Rev. Let

Diffusion processes and growth on stepped metal surfaces

We study the dynamics of adatoms in a model of vicinal (11m) fcc metal surfaces. We examine the role of different diffusion mechanisms and their implications to surface growth. In particular, we study the effect of steps and kinks on adatom dynamics. We show that the existence of kinks is crucially important for adatom motion along and across steps. Our results are in agreement with recent experiments on Cu(100) and Cu(1,1,19) surfaces. The results also suggest that for some metals exotic diffusion mechanisms may be important for mass transport across the steps.Comment: 3 pages, revtex, complete file available from ftp://rock.helsinki.fi/pub/preprints/tft/ or at http://www.physics.helsinki.fi/tft/tft_preprints.html (to appear in Phys. Rev. B Rapid Comm.

Kinetic roughening of surfaces: Derivation, solution and application of linear growth equations

We present a comprehensive analysis of a linear growth model, which combines the characteristic features of the Edwards--Wilkinson and noisy Mullins equations. This model can be derived from microscopics and it describes the relaxation and growth of surfaces under conditions where the nonlinearities can be neglected. We calculate in detail the surface width and various correlation functions characterizing the model. In particular, we study the crossover scaling of these functions between the two limits described by the combined equation. Also, we study the effect of colored and conserved noise on the growth exponents, and the effect of different initial conditions. The contribution of a rough substrate to the surface width is shown to decay universally as $w_i(0) (\xi_s/\xi(t))^{d/2}$, where $\xi(t) \sim t^{1/z}$ is the time--dependent correlation length associated with the growth process, $w_i(0)$ is the initial roughness and $\xi_s$ the correlation length of the substrate roughness, and $d$ is the surface dimensionality. As a second application, we compute the large distance asymptotics of the height correlation function and show that it differs qualitatively from the functional forms commonly used in the intepretation of scattering experiments.Comment: 28 pages with 4 PostScript figures, uses titlepage.sty; to appear in Phys. Rev.

Spiral surface growth without desorption

Spiral surface growth is well understood in the limit where the step motion is controlled by the local supersaturation of adatoms near the spiral ridge. In epitaxial thin-film growth, however, spirals can form in a step-flow regime where desorption of adatoms is negligible and the ridge dynamics is governed by the non-local diffusion field of adatoms on the whole surface. We investigate this limit numerically using a phase-field formulation of the Burton-Cabrera-Frank model, as well as analytically. Quantitative predictions, which differ strikingly from those of the local limit, are made for the selected step spacing as a function of the deposition flux, as well as for the dependence of the relaxation time to steady-state growth on the screw dislocation density.Comment: 9 pages, 3 figures, RevTe