Absolute step and kink formation energies of Pb derived from step roughening of two-dimensional islands and facets

Nowicki, Marek; Bombis, C.; Emundts, A.; Bonzel, H.P.

doi:10.1103/physrevb.67.075405

Cited by 31 publications

(19 citation statements)

References 46 publications

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“…The inverted Wulff construction [29] in good agreement with DFT predictions [102]. A similar analysis has been performed for Pb(111)-terminated crystallites grown on Cu(111) [235,236]. For further examples of Ag, Cu, Pt, and Ir(111) see Ref.…”

Section: Compact Adatom and Vacancy Islandssupporting

confidence: 60%

Epitaxial Growth of Thin Films

Brune

2014

Surface and Interface Science

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This chapter gives an introduction to the epitaxial growth of thin films on solid substrates. The term epitaxy refers to the growth of a crystalline layer on (epi) the surface of a crystalline substrate, where the crystallographic orientation of the substrate surface imposes a crystalline order (taxis) onto the thin film. This implies that film elements can be grown, up to a certain thickness, in crystal structures differing from their bulk. If film and substrate have the same crystal lattices, but different lattice constants, the film will be under strain, that is, it will have a slightly different lattice constant than in its own bulk. Both effects, together with the electronic hybridization at the interface, lead to novel properties.One distinguishes homo-and heteroexpitaxy, where the former refers to the growth on one element on a crystal surface of its own and the latter refers to the more general case, where film and substrate materials are different. Note that the first distinguishes itself from crystal growth, as we will see in more detail later.We start this chapter by giving examples from technology, illustrating where thin epitaxial films are used and outlining potential applications that become reality once we are able to grow the respective thin film sequences. We then contrast thin film and crystal growth, respectively, with kinetics and thermodynamics of growth. We introduce the deposition techniques used in epitaxial thin film growth and then discuss the classical thermodynamic approach, which led to the definition of the growth modes. These modes refer to the morphology taken on by a system grown close to thermodynamic equilibrium. Often films are grown far away from equilibrium and their morphology is determined by kinetics, that is, it is the result of the microscopic path taken by the system during growth. This path is determined by the hierarchy of rates of the single atom, cluster or molecular precursor displacements as compared to the deposition rate. Owing to the importance of kinetics, we focus in the rest of the chapter on the kinetic description of growth. In order to simplify the topic, we start with coverages below one atomic layer that is referred to as a monolayer. The first submonolayer part will be on nucleation, followed by a discussion of island shapes that, very much like snowflakes, tell us about the elementary processes that took place during their formation. We then discuss island coarsening, either by evaporation of atoms from their edges, referred to as the Ostwald ripening, or by the diffusion and subsequent coalescence of entire islands, referred to as the

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Section: Compact Adatom and Vacancy Islandssupporting

confidence: 60%

Epitaxial Growth of Thin Films

Brune

2014

Surface and Interface Science

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“…For the low-index surfaces of lead, the surface energies, step energies, and kink formation energies were obtained as best fit parameters and then extrapolated to zero Kelvin. [1][2][3][4] This experimental work forms the basic motivation for our density-functional theory study with the intention to provide an independent check of the employed methodology. Furthermore, this experimental study enables us to analyze the accuracy of state-of-the-art exchange-correlation functionals for the description of surface energies, also providing deeper, microscopic insight into what is behind these important parameters.…”

Section: Introductionmentioning

confidence: 99%

First-principles study of low-index surfaces of lead

Scheffler

2004

Phys. Rev. B

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We report a density-functional theory study for Pb͑111͒, Pb͑100͒, and Pb͑110͒ surfaces using ab initio pseudopotentials and a plane-wave basis set. Creating the pseudopotential with the 6s, 6p, and 6d states in the valence shell is found to yield good results for the bulk lattice constant, bulk modulus, and cohesive energy. Convergence of the surface energies with plane-wave cutoff, k-mesh, vacuum and slab thickness was carefully checked, as was the effect of the nonlinearity of the core-valence exchange-correlation interaction. Employing the local-density approximation of the exchange-correlation functional we obtain excellent agreement of the calculated surface energies and surface-energy anisotropies with recent experimental results. However, with the generalized gradient approximation the calculated surface energies are about 30% too low. For all three studied surfaces, the calculations give interlayer relaxations that are in reasonable agreement with low-energy electron diffraction analysis. The relaxations exhibit a damped oscillatory behavior away from the surface, which is typical for a metal surface.

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“…Because of numerous publications dealing with various aspects of Pb equilibrium crystal shapes (ECS) [19,43,44,64,[68][69][70][71][72][73][74][75][76][77] we will provide here just a brief summary of the results from this work.…”

Section: Experimental Results Of the Equilibrium Crystal Shape Of Pb mentioning

confidence: 99%

“…-Absolute step free energies and kink formation energies of A and B steps were obtained from analyzing the temperature dependence of (111) oriented facets on 3D crystallites and of 2D islands on flat Pb(111) substrates [74,76]. The values for the step energies (at T = 0 K) are 128 meV and 116 meV for A and B steps, respectively.…”

Section: Experimental Results Of the Equilibrium Crystal Shape Of Pb mentioning

confidence: 99%

“…Feibelman employing the GGA reported 95 and 78 meV for A and B steps [14] while Yu et al found 158 and 139 meV based on the LDA [18]. The corresponding experimental values are 128 meV and 116 meV, respectively [76]. It was concluded that LDA should be preferred because of the same arguments put forward for the theoretical surface energies [16,20,57,85].…”

Section: Comparison Of Theory and Experimentsmentioning

confidence: 96%

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The three-dimensional equilibrium crystal shape of Pb: Recent results of theory and experiment

Bonzel

Scheffler

2007

Appl. Phys. A

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The three-dimensional equilibrium crystal shape (ECS) is constructed from a set of 35 orientation-dependent surface energies of fcc Pb which are calculated by density functional theory in the local-density approximation and distributed over the [110] and [001] zones of the stereographic triangle. Surface relaxation has a pronounced influence on the equilibrium shape. The (111), (100), (110), (211), (221), (411), (665), (15,1,1), (410) and (320) facets are present after relaxation of all considered surfaces, while only the low-index facets (111), (100) and (110) exist for the unrelaxed ECS. The result for the relaxed Pb crystal state is in support of the experimental ECS of Pb at 320-350 K. On the other hand, approximating the surface energies of vicinal surfaces by assuming a linear relationship between the Pb(111) first-principles surface energy and the number of broken bonds of surface atoms leads to a trivial ECS that shows only (111) and (100) facets, with a sixfold symmetric (111) facet instead of the correct threefold symmetry. It is concluded that the broken bond rule in this simple linear form is not a suitable approximation for obtaining the proper three-dimensional ECS and correct step formation energies.PACS 05.70.Np; 61.50.Jr; 68.35.Md; 71.15.Mb IntroductionThe surface free energy is a fundamental property of solids and liquids. For crystalline solids it is generally anisotropic, i.e., it depends on the orientation of the surface. In this case the surface free energy is particularly difficult to measure, especially for structurally and chemically well-defined surfaces [1][2][3][4]. Hence it is not surprising that many theoretical attempts have been undertaken to generate hopefully trustworthy values of this quantity. Some were empirical, starting from surface free energies of liquids (e.g., metals) and transposing them to the solid state [5,6]. Other semi-empirical studies have been summarized by Galanakis et al. [7]. More recently, full potential first principles calculations have produced surface energies of many crystalline materials [7][8][9][10][11][12][13][14][15][16][17][18] mostly for low-index orientations. Although there can be considerable scatter in theoretical values for a single material and orientation [16,19], it has been suggested by u Fax: +49 2461 61 2950, E-mail: h.bonzel@fz-juelich.de some authors that the lack of experimental surface energy data for well-defined orientations may be replaced by ab initio calculations [15,17,20].Theoretical attempts of describing the more or less complete anisotropy of the surface free energy of crystals by invoking attractive pairwise atomic interaction potentials have been numerous, beginning in 1931 with the work by Stranski et al. [21][22][23][24][25][26] followed by others [27][28][29][30]. A different phenomenological description of the anisotropy and to some extent of the temperature dependence of the surface free energy was based on the terrace-step-kink model of a crystalline surface [31] assuming the existence of steps of monoat...

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Absolute step and kink formation energies of Pb derived from step roughening of two-dimensional islands and facets

Cited by 31 publications

References 46 publications

Epitaxial Growth of Thin Films

Epitaxial Growth of Thin Films

First-principles study of low-index surfaces of lead

The three-dimensional equilibrium crystal shape of Pb: Recent results of theory and experiment

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