### Browsing by Author "Richards, Howard L."

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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 Beyond the Wigner distribution: Schrodinger equations and terrace width distributions(American Physical Society, 2005) Richards, Howard L.; Einstein, Theodore L.The so-called generalized Wigner distribution has earlier been shown to be an excellent approximation for the terrace width distribution (TWD) of vicinal surfaces characterized by step-step interactions that are perpendicular to the average step direction and fall off as the inverse square of the step spacing. In this paper, we show that the generalized Wigner distribution can be derived from a plausible, phenomenological model in which two steps interact with each other directly and with other steps through a position-dependent pressure. We also discuss generalizations to more general step-step interactions and show that the predictions are in good agreement with TWDs derived from numerical transfer-matrix calculations and Monte Carlo simulations. This phenomenological approach allows the step-step interaction to be extracted from experimental TWDs.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.Item Step-position distributions and the pairwise Einstein model for steps on crystal surfaces(American Physical Society, 2006) Benson, Amber N.; Richards, Howard L.; Einstein, Theodore L.The pairwise Einstein model of steps not only justifies the use of the generalized Wigner distribution (GWD) for terrace width distributions (TWDs), it also predicts a specific form for the step position distribution (SPD), i.e., the probability density function for the fluctuations of a step about its average position. The predicted form of the SPD is well approximated by a Gaussian with a finite variance.