Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session A12: Focus Session: Steps, Growth, and Smoothing |
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Sponsoring Units: DMP DCMP Chair: Mina Yoon, Oak Ridge National Laboratory Room: Baltimore Convention Center 304 |
Monday, March 13, 2006 8:00AM - 8:36AM |
A12.00001: Crystal Surface Morphological Evolution: From Step Motion to A Continuum Theory Invited Speaker: Modern technological advances rely on the synthesis of nanoscale surface features on crystalline materials. Despite 50 years of progress, the related evolution laws have evaded a complete theoretical description. In this talk I describe analytically the recent derivation and applications of a continuum theory in 2+1 dimensions for crystal surfaces evolving below the roughening temperature. First, microscopic laws are formulated for the motion of atomic steps, which compose crystal surfaces, by incorporating: (i) diffusion of point defects (adatoms) on each terrace between steps; (ii) atom attachment-detachment at step edges; (iii) step curvature and elastic step interactions; and (iv) material deposition from above. Second, macroscopic laws are derived from step models: The surface height satisfies a fourth-order, nonlinear PDE for the anisotropic effect of fluxes of adatoms via an appropriate tensor mobility. The continuum solutions become questionable near macroscopic, flat surface regions (``facets'') and step bunches. Third, particular solutions are invoked to plausibly unify experimental observations of decaying bi-directional profiles via an interplay of step kinetics and surface topography. Fourth, free-boundary problems are solved for the facet evolution of axisymmetric crystal shapes: The appropriate boundary conditions are nonlocal with time. The continuum predictions compare favorably with numerical simulations for individual steps. The formation of step bunches is studied via suitable continuum coordinates of step motion. [Preview Abstract] |
Monday, March 13, 2006 8:36AM - 8:48AM |
A12.00002: Mass Transport in Nano-scale Step Fluctuations Ferenc Szalma, T.L. Einstein, M. Degawa, E.D. Williams, D.B. Dougherty Extending earlier work,\footnote{F. Szalma et al., Phys. Rev. B 71, 035422 (2005)} we investigate the linear response of a 2D nano-scale system to small perturbations and determine its transport properties. We use a 2-parameter-based energy landscape to simulate a supersaturated lattice gas by a BKL kinetic MC algorithm. The 2D gas atoms condense into a small island surrounded by a dilute gas. Island-edge fluctuations are due to both the diffusion of island atoms along its edge and atom exchange with the surrounding rare gas. Their relative importance depends on the ratio of the two energy parameters. We focus on adatom diffusion on Pb(111) surfaces below the roughening temperature, with energy parameters taken from EAM calculations. We find that edge fluctuations are mainly due to diffusion along the island edge, and determine the temperature dependence of the associated hopping rate. The Arrhenius behavior of the rates yields an effective energy barrier which fits well in the series of similar barriers for Pt, Au, and Ag. After comparing with experiments involving spirals as well as islands on Pb, we assess our simple model. [Preview Abstract] |
Monday, March 13, 2006 8:48AM - 9:00AM |
A12.00003: Persistence Properties of Interacting Steps: Qualitative Failure of Mean Field Hailu Gebremariam, T. L. Einstein, Chandan Dasgupta In studying the persistence properties of fluctuating steps on a vicinal surface, we examine the effect of interactions between steps on the correlation function $C(t)$ of step excursions from their mean position. For times much longer than the correlation time $\tau_c$, $C(t) \propto exp(-t/\tau_c)$. The standard way to include step repulsions ($\propto A/l^2$) simply is the mean field, Gruber-Mullins (GM) approximation, in which each step experiences a harmonic potential that narrows with increasing repulsion.\footnote{C. Dasgupta et al., Phys. Rev. B 69, 022101 (2004)} Monte Carlo simulations of a terrace-step-kink model show that $\tau_c$ then decreases with increasing $A$. Including the full repulsion between neighboring steps, we find the opposite trend: $\tau_c$ increases with $A$, due to in-phase meandering absent in GM.\footnote{Hailu Gebremariam, Ph.D thesis, and HG, CD, \& TLE, to be published.} However, the time constant $\tau_s$ associated with the exponential decay of the survival probability decreases with $A$. The ratio $\tau_s/\tau_c$ decreases slowly with $A$, from 0.38 at $A=0$, thereby satisfying the theorem that this ratio be $<1.^2$. We also discuss the scaling properties of autocorrelation and survival, in particular the dependence on sampling time and on lateral system size. [Preview Abstract] |
Monday, March 13, 2006 9:00AM - 9:12AM |
A12.00004: Debye Model of Steps on Vicinal Crystal Surfaces Howard~L. Richards, Clint~A. Greene The steps on a vicinal crystal surface can be mapped onto the world lines of spinless fermions, with the average direction of the steps (the $y$-direction) being mapped to time. If the interaction energy per unit length between neighboring steps is given by $V(L) \! = \! A/L^2$ (as is common), this resulting quantum system is integrable for only three values of $\tilde {A} \! \equiv \! \tilde{\beta}A/(k_{\rm B}T)^2$. For other values of $\tilde{A}$, the Pairwise Einstein Model gives an excellent approximation for the Terrace Width Distribution (TWD, the histogram of $x_{i+1}(y)-x_{i}(y)$) but is severely limited in describing $g_x(\Delta y) \! \equiv \! \langle [x_i (y+\Delta y) - x_i(y)]^2\rangle$, particularly for $\Delta y \! > \! \xi$, the correlation length. Here we show how the one- dimensional Debye model correctly gives $g_x(\Delta y)$ even for large $\Delta y$. The Pairwise Einstein Model also suggests a relationship between the compressibility of the steps and the tails of the TWD, a relationship we clarify using the Debye model. [Preview Abstract] |
Monday, March 13, 2006 9:12AM - 9:24AM |
A12.00005: Step Evolution Toward Equilibrium: Fokker-Planck Approach Ajmi Ben Hamouda, Alberto Pimpinelli, Hailu Gebremariam, T. L. Einstein We have derived a Fokker-Planck equation (FPE) that describes the relaxation of steps on vicinal surfaces toward the generalized Wigner surmise $P_\varrho(s)=as^\varrho\exp(-bs^2)$, arguably the best (both conceptually and quantitatively) description of the equilibrium terrace-width distribution (TWD) of steps on a vicinal surface.\footnote{A. Pimpinelli, Hailu Gebremariam, \& T.L. Einstein, Phys. Rev. Lett. 95, xxx (2005)} Focusing on the variance of the terrace-width distribution, we consider several physically-relevant initial states: perfect cleavage (straight, uniformly spaced), step bunch, and equilibrated distributions at different temperatures (prior to quenching), as well as other models. We compare analytic results with Monte Carlo studies, Metropolis and kinetic. We discuss the crucial question of how to make connections between the FPE time scale in analytic results and the actual time scale in simulations of models and in measurements of physical systems. [Preview Abstract] |
Monday, March 13, 2006 9:24AM - 9:36AM |
A12.00006: Ab-initio Evaluation of Extended Lattice Gas Interactions of Cu on Cu(111) and Cu(001) T. J. Stasevich, T. L. Einstein, S. Stolbov Lattice gas models connect macroscopic evolution to microscopic energies. The traditional empirical parameterization of these models can lead to incomplete descriptions that yield effective rather than actual energies. More recently, self-consistent computations from first principles of the relevant interaction energies can be used to diminish the risk of incompleteness. We have used such an approach to calculate a variety of lattice-gas interaction energies between Cu adatoms on Cu(001) and Cu(111). We find that pair interactions beyond first neighbors are negligible on Cu(111), whereas second neighbor interactions are significant on Cu(001). Besides pair-interactions, we find that trio-interactions can also be quite large. On Cu(111) these include two orientation dependent trios that account for the difference in the formation energies of A- and B-steps. When taken together, the calculated interaction energies are self-consistent and compare well with previous theory and experiment \footnote{T. J. Stasevich et al., Phys. Rev. B 70, 245404 (2004); 71, 245414 (2005)}. [Preview Abstract] |
Monday, March 13, 2006 9:36AM - 9:48AM |
A12.00007: Surface Smoothening Mechanism of Plasma-Deposited Amorphous Silicon Thin Films Mayur Valipa, Tamas Bakos, Eray Aydil, Dimitrios Maroudas An important concern in the plasma deposition of thin hydrogenated amorphous silicon (a-Si:H) films is to obtain smooth surfaces. Under conditions that lead to device-quality a-Si:H films, the dominant deposition precursor is the SiH$_{3}$ radical. In this presentation, we report results of molecular-dynamics simulations combined with first-principles density functional theory calculations to elucidate the smoothening mechanism of plasma deposited a-Si:H thin films. We show that SiH$_{3}$ may diffuse rapidly on the a-Si:H film surface via overcoordinated surface Si atoms and incorporate into the film preferentially in surface valleys, after H atom transfer and formation of two Si-Si backbonds, with activation barriers for incorporation dependent on the local surface morphology. Experimental data on smoothening and SiH$_{3}$ diffusion are accounted for. [Preview Abstract] |
Monday, March 13, 2006 9:48AM - 10:00AM |
A12.00008: On the Phase Shift of RHEED Intensity Oscillation during Homoepitaxy by MBE B. Shin, J.P. Leonard, J.W. McCamy, M.J. Aziz Despite the widespread usage of RHEED over many years, there still remain fundamental questions unanswered with regard to the interpretation of RHEED measurements. One of these issues is the phase shift of the RHEED intensity oscillations upon changing the incidence angle of electron beams. Therefore, we have conducted a systematic investigation of the phase shift of the RHEED intensity oscillations during homoepitaxy of Ge(001) by MBE for a wide range of diffraction conditions. Our results show that for small incidence angles with a beam azimuth several degrees away from crystallographic symmetry directions, the phase stays the same; it starts to shift once the (004) Kikuchi line appears in the RHEED pattern. Moreover, under some conditions we observe the oscillations from only the Kikuchi feature and not from the specular spot, and the oscillatory behavior of the Kikuchi feature is almost out of phase with that of the specular spot. All these results convincingly demonstrate that the phase shift is caused by the interference of the specular spot by the Kikuchi features. The lesson that can be learned from our study is that in order to use the RHEED specular intensity oscillation to learn about surface morphology, one must be extremely careful that the RHEED measurements be conducted under conditions where the influence of the Kikuchi features is minimal. [Preview Abstract] |
Monday, March 13, 2006 10:00AM - 10:12AM |
A12.00009: Properties of steps at faceted crystal-melt interfaces from molecular dynamics simulations Dorel Buta, Mark Asta, Jeffrey Hoyt The properties of steps at faceted solid-liquid interfaces are key elements to understanding the anisotropy of interfacial free energies and mobilities, which in turn control the morphology of crystals grown from the melt. We investigate the equilibrium and non-equilibrium dynamics of arrays of steps at vicinal interfaces of Si(111) with molecular dynamics simulations of the Stillinger-Weber model. Step mobilities determined from isothermal crystallization simulations are found to decrease as the density of steps increases. We relate the decrease in step mobility to an increase in the effective stiffness of the interacting steps, manifested by a reduction in the width of equilibrium step fluctuations as the average distance between steps decreases. The analysis of step fluctuations is also instrumental in determining the nature of step-step interactions. [Preview Abstract] |
Monday, March 13, 2006 10:12AM - 10:24AM |
A12.00010: Ensemble Approach to Vicinal Crystal Surfaces Ryan P. Jacob, Howard L. Richards, T.L. Einstein Recent studies of the Step Position Distribution (SPD) have made it clear that there exists a characteristic length $L_W$ (along the $y$-axis, parallel to the average step direction) at which the variance of the SPD is correctly predicted by the Pairwise Einstein Model. We extend this to the case when neighboring steps have different stiffnesses. A similar characteristic length along $y$ must be introduced to calculate average properties from an ensemble of Gruber-Mullins models, subject to the constraint that the variance of the Terrace Width Distribution (TWD) is as given by the Pairwise Einstein Model. We discuss the relationship between these length scales for a range of step interactions. [Preview Abstract] |
Monday, March 13, 2006 10:24AM - 10:36AM |
A12.00011: Growth and Atomic Structure of Periodically Striped Ag Films on a One-dimensional Surface Reconstruction Takashi Uchihashi, Chigusa Ohbuchi, Shigeru Tsukamoto, Tomonobu Nakayama We report the growth behavior of Ag thin films formed on the Si (111)4x1-In reconstruction, which is composed of periodic indium atomic chain arrays on a silicon surface. We use a two- step growth method, i.e., low temperature (~100K) deposition of a Ag film followed by annealing up to room temperature. Scanning tunneling microscope (STM) and low energy electron diffraction (LEED) measurements clarify that Ag films have stripe structures with a periodicity equal to that of the Si (111)4x1-In reconstruction (= 1.33 nm), thus demonstrating its viability of an atomic-scale geometrical template. The stripe structure persists up to the film thickness as large as 30 monolayers (ML), contrary to the expectation that strained films should relax rapidly. We attribute this stability to a coincidental matching of the transverse periodicity and the corrugation amplitude between the stripe structure and the substrate, which is realized by periodic insertion of stacking faults into the Ag fcc lattice. [Preview Abstract] |
Monday, March 13, 2006 10:36AM - 10:48AM |
A12.00012: Mound slope and shape selection during unstable multilayer growth: Exact continuum formulation from a step dynamics model Jim Evans, Maozhi Li Multilayer growth is unstable in the presence of a step-edge barrier which leads to the formation of mounds. Mound sides steepen at first, but then often attain a selected slope controlled by such processes as downward funneling. Atomistic modeling is very successful in describing such behavior [1], but continuum PDE formulations are often more efficient and instructive [2]. However, by analysis of a step-dynamics model for mound formation, we show that existing phenomenological PDEs fail to correctly predict mound slopes and shapes [3]. We coarse-grain the step-dynamics models to obtain a correct theory. [1] K.J. Caspersen et al. PRB 65 (2002) 194407; [2] M. Siegert, PRL 81 (1998) 5481; [3] M. Li and J.W. Evans, PRL in press. [Preview Abstract] |
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