Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session H40: Focus Session: Morphology and Evolution at Surfaces: Persistence and Islands |
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Sponsoring Units: DMP DCMP Chair: Ted Einstein, University of Maryland Room: LACC 408A |
Tuesday, March 22, 2005 8:00AM - 8:12AM |
H40.00001: Mapping spatial persistent large deviations of nonequilibrium surface growth processes onto the temporal persistent large deviations of stochastic random walk processes Magdalena Constantin, Sankar Das Sarma Spatial persistent large deviations probability of surface growth processes governed by the Edwards-Wilkinson dynamics, $P_x(x,s)$, with $-1 \leq s \leq 1$ is mapped isomorphically onto the temporal persistent large deviations probability $P_t(t,s)$ associated with the stochastic Markovian random walk problem. We show using numerical simulations that the infinite family of spatial persistent large deviations exponents $\theta_x(s)$ characterizing the power law decay of $P_x(x,s)$ agrees, as predicted on theoretical grounds by Majumdar and Bray [Phys. Rev. Lett. {\bf 86}, 3700 (2001)] with the numerical measurements of $\theta_t(s)$, the continuous family of exponents characterizing the long time power law behavior of $P_t(t,s)$. We also discuss the simulations of the spatial persistence probability corresponding to a discrete model in the Mullins-Herring universality class, where our discrete simulations do not agree well with the theoretical predictions perhaps because of the severe finite-size corrections which are known to strongly inhibit the manifestation of the asymptotic continuum behavior in discrete models involving large values of the dynamical exponent and the associated extremely slow convergence to the asymptotic regime. [Preview Abstract] |
Tuesday, March 22, 2005 8:12AM - 8:24AM |
H40.00002: Survival Probability in the Fluctuations of Interacting Steps Hailu Gebremariam, C. Dasgupta, T.L. Einstein We have performed Monte Carlo studies of survival probabilities $S(t)$ and autocorrelation functions $C(t)$ [1] of interacting steps on vicinal surfaces within the terrace-step-kink (TSK) model. Using Langevin formalism, the analytical and numerical investigations in [1] assumed a step fluctuates in a harmonic confining potential, reminiscent of the Gruber-Mullins model. However, the interaction between steps separated by $\ell$ has the form $A/\ell^2$. Adapting the program written to study distribution of $\ell$ [2], we investigate how $A/\ell ^2$ repulsions alter the relation between long-time behaviors of $S(t)$ and $C(t)$ established in [1]. The ratio of their respective characteristic times decreases as $A$ increases. We also investigate the scaling behavior of $S(t)$ vs.\ system size and sampling time.\\ \noindent [1] C.\ Dasgupta, M.\ Constantin, S.\ Das Sarma, and Satya N.\ Majumdar, Phys.\ Rev.\ E {\bf 69}, 022101 (2004).\\ \noindent [2] Hailu Gebremariam, S.\ D.\ Cohen, H.\ L.\ Richards, and T.\ L.\ Einstein, Phys.\ Rev.\ B {\bf 69}, 125404 (2004). [Preview Abstract] |
Tuesday, March 22, 2005 8:24AM - 8:36AM |
H40.00003: Island-Size Distribution and Capture Numbers in 3D Nucleation and Growth Feng Shi, Y. Shim, J.G. Amar The scaling of the island-size distribution (ISD) in irreversible 3D growth is studied using a simple point-island model on a cubic lattice. Our model is a 3D analog of submonolayer nucleation and may also be viewed as a simple model of the early stages of vacancy cluster nucleation and growth under irradiation. The scaling of the monomer and island densities and ISD, capture number distribution (CND), and capture zone distribution (CZD) is studied as a function of the fraction of occupied sites (coverage) and ratio D/F of the monomer hopping rate D to the monomer creation rate F. While mean-field behavior is not observed, the scaled ISD still diverges with increasing D/F, while the scaled CND depends only weakly on the island-size. The weak dependence of the CND on island-size is due to the decreased influence of correlations and fluctuations in 3D as compared to 2D. A comparison of our simulation results with self-consistent rate-equation calculations is also presented. [Preview Abstract] |
Tuesday, March 22, 2005 8:36AM - 8:48AM |
H40.00004: Nucleation and Kinetic Study of Pb Quantum Size Effect Islands Grown on Si(111) R. Feng, E.H. Conrad, M.C. Tringides, C. Kim, C. Jeffrey, P.F. Miceli The early stage nucleation and growth process of Pb quantum size effect islands grown on Si(111) 7X7 between 193K and 227K has been studied using in situ X-ray scattering experiments . The number density of Pb islands were measured from transverse scans across Pb(111) Bragg peak. The experiments were performed as functions of temperature, deposition rate and coverage to obtain the critical cluster size and energy barriers. Even more interesting is the rapid island coarsening observed at very low coverage (0.2ML above the wetting layer). We find a characteristic coarsening time of 10's of minutes at 208K. The implication of these results will be discussed in terms of island height and shape stability. [Preview Abstract] |
Tuesday, March 22, 2005 8:48AM - 9:00AM |
H40.00005: Multiscale modeling of Ge islands on Si(001): growth mode and morphological transition Francesco Montalenti, Silvia Cereda, Leo Miglio Deposition of Ge on Si(001) induces the formation of nanometric Ge pyramids bounded by {105} facets. Pyramids grow self-similarly until, at a critical size, they transform into dome-shaped islands. A very detailed, microscopic explanation of the evolution is given, based on high-resolution STM images and extensive theoretical modeling [1]. It is shown by ab initio calculations that Ge atoms are able to easily climb the {105} facets, reaching the island top, where nucleation is favored. The new pyramid layer is then completed by a fast step-flow process. When pyramids reach a critical size, however, steps start to group at the top, bunching together and eventually evolving into steep new facets, typical of the dome geometry. The appearance of multistepped pyramids, clearly imaged by STM, is explained by a simple, local-thermodynamic model based on the above described results and on further Tersoff-potential simulations of realistically-sized islands. [1] F. Montalenti et al., Phys. Rev. Lett. 93, 216102 (2004) [Preview Abstract] |
Tuesday, March 22, 2005 9:00AM - 9:12AM |
H40.00006: One-dimensional Ostward ripening on island growth F.K. Men, A.L. Chin, C.R. Lee We have studied the growth of nano-scaled islands by post-annealing a Co-deposited Au/Si(111)-(5$\times $2) surface of 0.3\r{ } miscut with scanning tunneling microscopy. At the early time of the growth, islands emerge randomly both on terraces and on top of step edges. Islands on steps then grow at the expense of those on terraces, most of which dissolve completely at later time. The island density and size dependences on the annealing time have been obtained and compared with a one-dimensional model based on the classical theory of diffusive decomposition. The agreement between the experiment and the theory leads to the conclusion that Ostwald ripening with steps acting as one-dimensional diffusive pathways for mass transfer governs the observed phenomenon. [Preview Abstract] |
Tuesday, March 22, 2005 9:12AM - 9:24AM |
H40.00007: Atomistic and Continuum Simulations of Island Coalescence Edmund Webb III, Steven Seel, Jonathan Zimmerman Volmer-Weber thin film growth involves nucleation of discrete islands that grow, impinge upon one another, and coalesce into a film. Coalescence has been proposed to generate stress in thin films so it is useful to study stress evolution upon coalescence. Results are presented from atomistic simulations of nanometer island coalescence. Molecular dynamics simulations are used to examine coalescence for islands with D = 2 - 200 nm in a parallel hemi-cylindrical capping geometry (D is the cylinder diameter). Atomic interactions are governed by embedded atom method potentials; the zero mismatch case of Au islands on Au(100) is modeled. Coalescence height is calculated and demonstrated to behave in accord with continuum predictions for large D but, for the smallest sizes studied, deviations are observed between atomistic and continuum results due to atomic relaxation resolved in the former but not the latter. To calculate local stress in the atomistic simulations, a spatial homogenization technique is used that permits more robust estimates of stress in small volume elements near surfaces. Stress distributions in pre and post-coalescence structures are presented to further explain observed relaxations. [Preview Abstract] |
Tuesday, March 22, 2005 9:24AM - 9:36AM |
H40.00008: Simulation of Growth Shape of Stressed/Strained 2D Monolayer Island Naiyang Ma, Feng Liu Growth shape of a 2D monolayer island is determined by the competition between thermodynamics (governing the equilibrium shape) and kinetics. The island boundary propagates via two fundamental mechanisms: one from deposition flux driving island growth and the other from edge diffusion along island periphery equilibrating island shape. We develop a model to directly simulate the growth a stressed/strained 2D island, including the elastic contribution to the island boundary chemical potential calculated from continuum theory. A front tracking algorithm is used to define the positions of island boundary and a cubic spline fitting is used to remove the shape discontinuity. A series of simulations are conducted to reveal the physical conditions governing the equilibrium vs. the non- equilibrium growth shape in terms of competition between the rate of deposition vs. the rate of edge diffusion. \textbf{* This work is supported by DOE and NSF.} [Preview Abstract] |
Tuesday, March 22, 2005 9:36AM - 9:48AM |
H40.00009: Prediction of Macroscopic Surface Shapes from Adatom Rate Equations in Epitaxial Growth A. Ballestad, Bayo Lau, J. H. Schmid, T. Tiedje, M. Whitwick Epitaxial growth involves adatom diffusion on terraces interrupted by step edge attachment/detachment, and island nucleation. On the other hand macroscale surface morphology is commonly described by continuum growth equations such as the KPZ or MBE equations with coefficients that are expressed in terms of derivatives of thermodynamic quantities. The connection with the microscopic phenomena that occur during growth is typically obscure. For example in experiments the coefficients depend strongly on growth rate, which is not readily apparent in the thermodynamic analysis. Therefore we have developed a perturbation method for low surface slopes, by which the rate equations that describe the adatom dynamics can be converted into continuum growth equations. This method also generates expressions for the coefficients in the growth equations in terms of microscopic parameters. For conditions appropriate for GaAs MBE growth we find a KPZ-like growth equation with a conservative non-linear term $\nabla ^2\left( {\nabla h} \right)^2$. From experimental measurements of the smoothing rate and shape of patterned substrates during GaAs MBE growth, and the theoretical expressions for the growth coefficients, we can determine various interesting microscopic parameters as a function of growth rate and temperature. [Preview Abstract] |
Tuesday, March 22, 2005 9:48AM - 10:00AM |
H40.00010: Lattice-Gas Modeling of Stiffness on fcc(111) Surfaces: General Results T. L. Einstein, T. J. Stasevich In a nearest-neighbor (NN) lattice-gas model of the island atoms on a (111) fcc surface,\footnote{T. J. Stasevich, Hailu Gebremariam, T. L. Einstein, M. Giesen, C. Steimer, and H. Ibach, submitted to PRB [cond-mat/0412002].} the entropy of the leading term in the low-temperature expansion of the orientation-dependent free energy—relevant for understanding experiments on noble metals--comes exclusively from geometric considerations.\footnote{ C. Rottman and M. Wortis, PRB {\bf 24}, 6274 (1981).} There are several remarkable consequences:$^2$ 1) The lowest-order stiffness (LOS) has no contribution from the energy. 2) Therefore, the step line tension cannot be extracted from the LOS. 3) The LOS has 6-fold symmetry, even though the line tension has only 3-fold symmetry. 4) The reduced LOS has the strikingly simple form $2\surd 3/\sin(3\theta)$. Near close-packed orientations, the LOS is not adequate at these temperatures; by explicating the exact implicit solution for the hexagonal lattice gas,\footnote{R.K.P. Zia, J. Stat. Phys. {\bf 45}, 801 (1986).} we provide quantitative markers for where this breakdown occurs. Lastly, we show how to account for the energy difference between A and B steps by invoking a novel orientation-dependent trio interaction between atoms forming an equilateral triangle with NN legs. [Preview Abstract] |
Tuesday, March 22, 2005 10:00AM - 10:12AM |
H40.00011: Surface Step Stiffness: Next-Nearest Neighbor Interactions and Beyond T. J. Stasevich, T. L. Einstein Most theoretical treatments of the orientation-dependence of step stiffness consider only attractive nearest-neighbor (NN) interactions. Recent experiments\footnote{S.Dieluweit, H.Ibach, M.Giesen \& T.L.Einstein, PRB {\bf 67}, 1614 (2003).} on Cu(100) suggest that this approximation leads to an underestimation of the measured stiffness for orientations far from close-packed directions. Including attractive next-nearest-neighbor (NNN)\footnote{H.J.W.Zandvliet,R.VanMoere \& B. Poelsema., PRB {\bf 68}, 073404 (2003).} and/or right-triangle trio interactions (consisting of two NN legs and one NNN hypotenuse) can ameliorate the discrepancy.\footnote{T. J. Stasevich et al., Phys.\ Rev.\ B (in press) [cond-mat/0408496].} Reaching good agreement, however, may require other, more novel interactions. To determine which of these are most relevant, we have performed ab-initio calculations using VASP, seeking the relative strengths of NN, NNN, and various trio interactions on Cu(100) and Cu(111) surfaces. On Cu(100) we find that NNN interactions are indeed attractive and relatively large (consistent with experimental results). We also find a significant attractive right-triangle trio interaction, as well as a repulsive linear trio interaction. On Cu(111), in contrast, we find that NNN interactions are negligibly small, again consistent with experiment \footnote{ T. J. Stasevich et al., submitted to PRB [cond-mat/0412002].} [Preview Abstract] |
Tuesday, March 22, 2005 10:12AM - 10:24AM |
H40.00012: Diffusion of Small 2D-Cu Clusters on Cu (111) Altaf Karim, Ahlam N. Al-Rawi, Abdelkader Kara, Talat S. Rahman Diffusion of small Cu clusters containing 2 to 10 atoms on Cu (111) has been studied in detail using Kinetic Monte Carlo (KMC) and molecular dynamics simulations (MD). Our KMC simulations are based on a comprehensive database including more than 500 mechanisms for cluster diffusion and their related energetics calculated using embedded atom potential method. The MD simulations, at 500K and 700K, have been instrumental in revealing several mechanisms for cluster diffusion especially those involving concerted motion of several atoms. From the calculated diffusion coefficients at 300K, 500K, and 700K, we find that the effective diffusion barriers increase almost monotonically with increasing cluster size. The inclusion of the newly revealed mechanisms from MD in our KMC simulations thus negates an earlier finding of magic cluster sizes. Contrary to the case of larger clusters (20 to 1000 atoms), we do not find a simple scaling of the diffusion coefficient with cluster size. [Preview Abstract] |
Tuesday, March 22, 2005 10:24AM - 10:36AM |
H40.00013: Evolution of Sub-Monolayer Films of Thiolphenol Molecules on Cu(111) Studied by STM Kin Wong, Ki-Young Kwon, Robert A. Perry, Bommisetty V. Rao, Erick Ulin-Avila, Greg Pawin, Anwei Liu, Ludwig Bartels We performed an STM study of the diffusion and aggregation of thiophenol (TP) molecules on Cu(111) at sub-monolayer coverages. Two types of movements were observed in the temperature interval 50K-80K. One is the in-plane rotation of the molecule with the sulfur bond fixed at an adsorption site. The other is the lateral place exchange of the whole molecule to a different adsorption site. The barriers for rotations and hops are 100meV and 120meV respectively. At sufficient substrate temperatures, the TP molecules are found to aggregate into clusters of up to 7 molecules. Increasing the coverage further, no stable islands of more than 7 molecules can be found; instead the density of evenly distributed 7-molecule clusters increases. Further increase of the coverage leads to formation of a disordered film. This is in stark contrast to the behavior of halogen substituted X-TP molecules where X is Br, Cl or F. X-TP molecules readily form ordered islands at low coverage, which grow into continuous films with increasing coverage in agreement with Oswald ripening. [Preview Abstract] |
Tuesday, March 22, 2005 10:36AM - 10:48AM |
H40.00014: Theoretical Analysis of Electromigration-Induced Void Migration and Surface Waves in Metallic Thin Films Jaeseol Cho, M. Rauf Gungor, Dimitrios Maroudas Electromigration-induced void dynamics in metallic thin films is of major interest for fundamental understanding of driven surface morphological evolution and for addressing important materials reliability problems. In this presentation, we report results of self-consistent numerical simulations of current-induced void morphological response in metallic thin films accounting rigorously for current crowding, surface curvature, and surface diffusional anisotropy effects. We demonstrate that as the morphological stability limit is approached the migration speed of a stable void deviates substantially from being inversely proportional to the void size and derive a universally valid relationship for a properly rescaled void migration speed as a function of void size. Furthermore, in grains characterized by high symmetry of surface diffusional anisotropy, we predict the onset of stable surface waves that propagate on voids migrating along the metallic film at constant speeds as either the applied electric field strength, or the void size, or the diffusional anisotropy strength is increased over a critical value. This onset of stable time-periodic solutions corresponds to a Hopf bifurcation in the void surface morphological response. [Preview Abstract] |
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