### Browsing by Author "Pimpinelli, Alberto"

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Item A facet is not an island: step-step interactions and the fluctuations of the boundary of a crystal facet(Elsevier, 2005) Pimpinelli, Alberto; Degawa, M.; Einstein, Theodore L.; Williams, Ellen D.Item Analyzing Capture Zone Distributions (CZD) in Growth: Theory and Applications(Elsevier, 2014) Einstein, Theodore L.; Pimpinelli, Alberto; Gonzalez, Diego LuisItem Capture-Zone Scaling in Island Nucleation: Universal Fluctuation Behavior(American Physical Society, 2007) Pimpinelli, Alberto; Einstein, Theodore L.In island nucleation and growth, the distribution of capture zones (in essence proximity cells) can be described by a simple expression generalizing the Wigner surmise (power-law rise, Gaussian decay) from random matrix theory that accounts for spacing distributions in a host of fluctuation phenomena. Its single adjustable parameter, the power-law exponent, can be simply related to the critical nucleus of growth models and the substrate dimensionality. We compare with extensive published kinetic Monte Carlo data and limited experimental data. A phenomenological theory elucidates the result.Item Distinctive Fluctuations in a Confined Geometry(American Physical Society, 2006) Degawa, M.; Stasevich, T. J.; Cullen, W. G.; Pimpinelli, Alberto; Einstein, Theodore L.; Williams, Ellen D.Spurred by recent theoretical predictions (Phys. Rev. E 69, 035102(R) (2004); Surf. Sci. Lett. 598, L355 (2005)), we find experimentally using STM line scans that the fluctuations of the step bounding a facet exhibit scaling properties distinct from those of isolated steps or steps on vicinal surfaces.Item Dynamical Scaling Implications of Ferrari, Prähofer, and Spohn’s Remarkable Spatial Scaling Results for Facet-Edge Fluctuations(Springer, 2014) Einstein, Theodore L.; Pimpinelli, AlbertoSpurred by theoretical predictions from Spohn and coworkers (Phys. Rev. E 69, 035102(R) (2004)), we rederived and extended their result heuristically as well as investigated the scaling properties of the associated Langevin equation in curved geometry with an asymmetric potential. With experimental colleagues we used STM line scans to corroborate their prediction that the fluctuations of the step bounding a facet exhibit scaling properties distinct from those of isolated steps or steps on vicinal surfaces. The correlation functions was shown to go as t 0.15(3) decidedly different from the t 0.26(2) behavior for fluctuations of isolated steps. From the exponents, we were able to categorize the universality, confirming the prediction that the non-linear term of the KPZ equation, long known to play a central role in non-equilibrium phenomena, can also arise from the curvature or potential-asymmetry contribution to the step free energy. We also considered, with modest Monte Carlo simulations, a toy model to show that confinement of a step by another nearby step can modify as predicted the scaling exponents of the step’s fluctuations. This paper is an expansion of a celebratory talk at the 95th Rutgers Statistical Mechanics Conference, May 2006.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 Fragmentation approach to the point-island model with hindered aggregation: Accessing the barrier energy(American Physical Society, 2017) Gonzalez, Diego Luis; Pimpinelli, Alberto; Einstein, Theodore L.We study the effect of hindered aggregation on the island formation process in a one- (1D) and two-dimensional (2D) point-island model for epitaxial growth with arbitrary critical nucleus size i. In our model, the attachment of monomers to preexisting islands is hindered by an additional attachment barrier, characterized by length la. For la=0 the islands behave as perfect sinks while for la?? they behave as reflecting boundaries. For intermediate values of la, the system exhibits a crossover between two different kinds of processes, diffusion-limited aggregation and attachment-limited aggregation. We calculate the growth exponents of the density of islands and monomers for the low coverage and aggregation regimes. The capture-zone (CZ) distributions are also calculated for different values of i and la. In order to obtain a good spatial description of the nucleation process, we propose a fragmentation model, which is based on an approximate description of nucleation inside of the gaps for 1D and the CZs for 2D. In both cases, the nucleation is described by using two different physically rooted probabilities, which are related with the microscopic parameters of the model (i and la). We test our analytical model with extensive numerical simulations and previously established results. The proposed model describes excellently the statistical behavior of the system for arbitrary values of la and i=1, 2, and 3.Item How "Hot Precursors" Modify Island Nucleation: A Rate-Equation Model(American Physical Society, 2014) Morales-Cifuentes, Josue R.; Einstein, Theodore L.; Pimpinelli, AlbertoWe propose a novel island nucleation and growth model explicitly including transient (ballistic) mobility of the monomers deposited at rate F, assumed to be in a hot precursor state before thermalizing.Item Kinetic-thermodynamic model for carbon incorporation during step-flow growth of GaN by metalorganic vapor phase epitaxy(American Physical Society, 2019) Inatomi, Y.; Kangawa, Y.; Pimpinelli, Alberto; Einstein, Theodore L.Relationships between concentration of unintentionally doped carbon in GaN and its metalorganic vapor phase epitaxy conditions were investigated theoretically. A kinetic-thermodynamic model which considers kinetic behavior of adsorbed atoms on vicinal surface was proposed.Item Mean-field approximation for spacing distribution functions in classical systems(American Physical Society, 2012) Gonzalez, Diego Luis; Pimpinelli, Alberto; Einstein, Theodore L.We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.Item Pimpinelli and Einstein Reply(American Physical Society, 2010) Pimpinelli, Alberto; Einstein, Theodore L.A Reply to the Comment by Maozhi Li, Yong Han, and J.W. Evans.Item Role of codeposited impurities during growth. I. Explaining distinctive experimental morphology on Cu(0 0 1)(American Physical Society, 2011) Hamouda, Ajmi BH.; Sathiyanarayanan, Rajesh; Pimpinelli, Alberto; Einstein, Theodore L.A unified explanation of the physics underlying all the distinctive features of the growth instabilities observed on Cu vicinals has long eluded theorists. Recently, kinetic Monte Carlo studies showed that codeposition of impurities during growth could account for the key distinctive experimental observations (Hamouda et al., Phys. Rev. B 77, 245430 (2008)). To identify the responsible impurity atom, we compute the nearest-neighbor binding energies (ENN) and terrace diffusion barriers (Ed) for several candidate impurity atoms on Cu(0 0 1) using DFT-based VASP. Our calculations show that codeposition (with Cu) of midtransition elements, such as Fe, Mn, and W, could—in conjunction with substantial Ehrlich-Schwoebel barriers—cause the observed instabilities; when the experimental setup is considered, W emerges to be the most likely candidate. We discuss the role of impurities in nanostructuring of surfaces.Item Spacing distribution functions for the one-dimensional point-island model with irreversible attachment(American Physical Society, 2011) Gonzalez, Diego Luis; Pimpinelli, Alberto; Einstein, Theodore L.We study the configurational structure of the point-island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps.