### Browsing by Author "Gebremariam, Hailu"

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Item Analysis of terrace-width distributions using the generalized Wigner surmise: Calibration using Monte Carlo and transfer-matrix calculations(American Physical Society, 2004) Gebremariam, Hailu; Cohen, Saul D.; Richards, Howard L.; Einstein, Theodore L.Measurement of terrace-width distributions (TWD’s) of vicinal surfaces is used routinely to find the dimensionless strength Ã of the elastic repulsion between steps. For sufficiently strong repulsions, the TWD can be described by a Gaussian about the mean step spacing, but controversy has arisen on the correct prefactor in the relation of the TWD variance to Ã. Instead of the various Gaussian approximations, we have advocated for several years that the TWD be fit with the generalized Wigner distribution, essentially a gamma distribution in the normalized squared TWs. The basis for this idea stems from a mapping of the step model to the Sutherland model of fermions in one dimension. While several applications to experiment have been successful, definitive comparison of the various approximations requires high-quality numerical data. We report transfer matrix and extensive Monte Carlo simulations of terrace-step-kink models to support our contentions. Our work includes investigation of finite-size effects and of the breakdown of the continuum picture for values of Ã larger than in typical experiments.Item Evolution of Terrace-Width Distributions on Vicinal Surfaces: Fokker-Planck Derivation of the Generalized Wigner Surmise(American Physical Society, 2005) Pimpinelli, Alberto; Gebremariam, Hailu; Einstein, Theodore L.We use a Fokker-Planck equation to justify the generalization of the Wigner surmise for the energy-level spacing in quantum systems to the simple expression for the equilibrium terrace-width distribution of steps—with arbitrary-strength repulsions—on a vicinal surface, taking advantage of analogies to one-dimensional models of interacting, spinless fermions. This approach leads to an analytic description of the evolution toward equilibrium of steps from several experimentally relevant initial distributions: step bunches, perfect cleaved crystals, and prequench equilibrated distributions at different temperatures.Item Fluctuations, line tensions, and correlation times of nanoscale islands on surfaces(American Physical Society, 2005) Szalma, F.; Gebremariam, Hailu; Einstein, Theodore L.We analyze in detail the fluctuations and correlations of the (spatial) Fourier modes of nanoscale single-layer islands on (111) fcc crystal surfaces. We analytically show that the Fourier modes of the fluctuations couple due to the anisotropy of the crystal, changing the power spectrum of the fluctuations, and that the actual eigenmodes of the fluctuations are the appropriate linear combinations of the Fourier modes. Using kinetic Monte Carlo simulations with bond-counting parameters that best match realistic energy barriers for hopping rates, we deduce absolute line tensions as a function of azimuthal orientation from the analyses of the fluctuation of each individual mode. The autocorrelation functions of these modes give the scaling of the correlation times with wavelength, providing us with the rate-limiting kinetics driving the fluctuations, here step-edge diffusion. The results for the energetic parameters are in reasonable agreement with available experimental data for Pb(111) surfaces, and we compare the correlation times of island-edge fluctuations to relaxation times of quenched Pb crystallites.Item Low-temperature orientation dependence of step stiffness on (111) surfaces(American Physical Society, 2005) Stasevich, T. J.; Gebremariam, Hailu; Einstein, Theodore L.; Giesen, Margret; Steimer, C.; Ibach, HaraldFor hexagonal nets, descriptive of (111) fcc surfaces, we derive from combinatoric arguments a simple, low-temperature formula for the orientation dependence of the surface step line tension and stiffness, as well as the leading correction, based on the Ising model with nearest-neighbor (NN) interactions. Our formula agrees well with experimental data for both Ag and Cu(111) surfaces, indicating that NN interactions alone can account for the data in these cases (in contrast to results for Cu(001)). Experimentally significant corollaries of the low-temperature derivation show that the step line tension cannot be extracted from the stiffness and that with plausible assumptions the low-temperature stiffness should have six-fold symmetry, in contrast to the three fold symmetry of the crystal shape. We examine Zia’s exact implicit solution in detail, using numerical methods for general orientations and deriving many analytic results including explicit solutions in the two high-symmetry directions. From these exact results we rederive our simple result and explore subtle behavior near close-packed directions. To account for the three-fold symmetry in a lattice gas model, we invoke an orientation-dependent trio interaction and examine its consequences.Item Refined evaluation of the level-spacing distribution of symplectic ensembles: Moments and implications(American Physical Society, 2006) Gebremariam, Hailu; Einstein, Theodore L.To obtain a more precise value for the variance ?2 of the joint probability distribution of a symplectic ensemble, we extend previous numerical evaluations of a power series. Our result ?2?0.1041 shows that the excellent approximation using the analytically simple Wigner surmise fractionally overestimates this value. This behavior is important in establishing the trend of a generalization of the surmise to describe the terrace-width distribution on vicinal surfaces. We also obtain precise estimates of the skewness and the kurtosis of the exact distribution, as well as the related moments.Item Si(111) step fluctuations at high temperature: Anomalous step-step repulsion(American Physical Society, 2002) Cohen, Saul D.; Schroll, Robert D.; Einstein, Theodore L.; Metois, J.-J.; Gebremariam, Hailu; Richards, Howard L.; Williams, Ellen D.Using reflection electron microscopy we examine the step fluctuations of Si(111) at 1100°C. Evaporation is compensated by a replenishing flux. The step fluctuation behavior is qualitatively similar to that at 900°C (where sublimation is negligible), with unexplained quantitative differences. We focus on the three parameters of the step continuum model of vicinals. The step stiffness scales with an increase in T from 900°C as predicted by an appropriate lattice model. The kinetic coefficient is larger than scaling of the parameters from 900°C would predict. The step-step correlations are assessed in traditional and novel ways; step repulsions are at least 6 times as strong as predicted from lower temperatures, suggesting nonequilibrium effects probably due to electromigration.