Decay of Cu adatom islands on Cu(111)

Icking-Konert, G. Schulze; Giesen, Margret; Ibach, H.

doi:10.1016/s0039-6028(98)80009-5

Cited by 105 publications

(107 citation statements)

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“…This result is not unreasonable but still significantly larger than the corresponding theory result for the step formation energy of 0.156 eV͞a at 0 K as calculated by Stoltze using effective medium theory (EMT) [8]. The same experimental procedure applied to the Cu(111) surface by Schulze Icking-Konert et al [9] resulted in an even larger discrepancy: 0.45 eV͞a compared to an EMT result of 0.208 eV͞a [8], questioning whether or not this approach measures indeed the true step free energy [10].In this paper we describe a method to determine the step free energy on metal surfaces which appears to be more reliable. We measure the amplitude of island shape fluctuations around the equilibrium shape which can be directly related to the step free energy.…”

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confidence: 64%

Determination of Step Free Energies from Island Shape Fluctuations on Metal Surfaces

et al. 1999

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The absolute measurement of free energies associated with crystal steps on a metal surface has been a long-standing problem. We report a reliable estimate of the step free energy on a Cu(111) crystal surface, based on an analysis of island shape fluctuations directly imaged by scanning tunneling microscopy. The result of 0.22 eV per atomic distance for steps running into close-packed directions is in good agreement with theoretical predictions. [S0031-9007(99)09095-X] PACS numbers: 68.35. Md, 61.16.Ch, 68.35.Ja The step free energy is one of the fundamental quantities used to describe real crystal surfaces. It is defined as the free energy required to create a crystal step and it can be regarded as the low-dimensional analog of the surface free energy. Just as the angular variation of the surface free energy determines the equilibrium shape of threedimensional crystals via the famous Wulff construction [1], the variation of the step free energy with angle determines the equilibrium shape of monolayer islands on a crystal surface. Moreover, as stated by the well-known GibbsThomson relation [1], this quantity is proportional to the chemical potential of monolayer islands and curved steps, and hence its magnitude is directly linked to mass transport rates close to equilibrium.Given the fundamental importance of this material parameter, it is amazing how little experimental information is available on this quantity, at least for metal surfaces. While several estimates based on various computational schemes exist, experiments have mostly been limited to the determination of the relative magnitude of the free energies of differently oriented steps from equilibrium island shapes. A prominent example of studies of this type is the work of Michely et al. who determined a ratio of 0.87 6 0.02 for the step energies of so-called type B and type A steps on Pt(111), i.e., the (111)-and (100)-microfaceted close-packed steps [2]. This experimental result has been a challenge for advanced ab initio energy calculations [3], and could be reproduced only recently by calculations of Boisvert et al. [4]. Experiments suited to reliably determine the absolute value of the step free energy on metal surfaces, however, are hardly available [5]. Bonzel has estimated absolute step energies on metals by extrapolating old results on surface free energies at temperatures close to the melting point to low temperatures using the terrace-ledge-kink model and available estimates of step entropies [6]. For the Ag(111) surface, Morgenstern et al. have estimated the step free energy at about room temperature to 0.22 eV per atomic distance a by studying the decay of Ag adatom islands and fitting the shape of island decay curves with a theoretical model based on the Gibbs-Thomson equation [7]. This result is not unreasonable but still significantly larger than the corresponding theory result for the step formation energy of 0.156 eV͞a at 0 K as calculated by Stoltze using effective medium theory (EMT) [8]. The same experimental procedure applied to ...

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confidence: 64%

Determination of Step Free Energies from Island Shape Fluctuations on Metal Surfaces

et al. 1999

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“…However, according to a recent study [12] the large ES barrier in earlier work was caused by preferential adsorption of CO on A steps from the residual gas. On clean Cu(111) surfaces on the other hand, a significant ES barrier was found experimentally also for the A type step [13]. EAM calculations have further revealed significant differences in the ES barrier on a straight step and at kink sites [9,10].…”

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confidence: 84%

“…The STM setup and the crystal preparation was described in [13]. The observed surface density of pinning sites was 10 27 per surface atom and the surface remained clean after 10 h of observation.…”

Section: Institut F üR Grenzflächenforschung Und Vakuumphysik Forschmentioning

confidence: 99%

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Interlayer Mass Transport and Quantum Confinement of Electronic States

1999

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A numerical analysis of the ripening of multilayer islands on Cu(111) shows that the EhrlichSchwoebel barrier for interlayer mass transport is independent of the terrace width w as long as w . w c 14 6 2 Å, but vanishes for w , w c . The critical width w c corresponds exactly to the terrace width below which the surface state is pushed above the Fermi level due to quantum confinement. The Ehrlich-Schwoebel barrier is therefore correlated with the occupation of surface states.[ S0031-9007(99)08912-7] PACS numbers: 68.35.Fx, 73.20.Dx The growth of atomically flat epitaxial films requires a facile mass transport across the step edges which separate terraces of different height. Diffusion across a step edge is frequently hindered by an activation barrier for interlayer mass transport (Ehrlich-Schwoebel barrier [1,2]). The existence of a significant EhrlichSchwoebel barrier (ES barrier) is well documented for the (111) surfaces of Pt, Rh, Ag,. In these and other experiments, merely an average ES barrier is typically determined. Total energy calculations based on the embedded atom model (EAM) [8][9][10] as well as recent ab initio calculations in the local density approximation [11] have shown that activation energies for mass transport across a step depend on the type of steps and involve an exchange of the adatom with a step atom. For the experimentally rather extensively studied Pt(111) surface Feibelman [11] has shown that the activation energy is practically zero (0.02 eV) for crossing the A step [displaying a (100) facet], but large (0.35 eV) for the B step [(111) facet]. This result is at variance with the large effective ES barrier observed in earlier experiments [3]. However, according to a recent study [12] the large ES barrier in earlier work was caused by preferential adsorption of CO on A steps from the residual gas. On clean Cu(111) surfaces on the other hand, a significant ES barrier was found experimentally also for the A type step [13]. EAM calculations have further revealed significant differences in the ES barrier on a straight step and at kink sites [9,10]. Whether the calculated differences are always significant for the interlayer mass transport depends on the preexponential factors which are presently not known and may (partly) compensate different activation barriers (see, e.g., [14]).Faced with the unpleasantly complex situation, both on the experimental and theoretical side, a better understanding as to why and when larger ES barriers exist, would be rather welcome. An attempt in that direction was made several years ago by Memmel and Bertel [15] who conjectures that the existence of an ES barrier on (111) oriented fcc surfaces is correlated with the nearly free electron surface state [16]. It was argued that the boundary condition for the surface state wave function at the steps leads to a reduction of the binding energy at steps and hence to an ES barrier. While the concept is appealing, convincing evidence for a correlation between the existence of surface states and the ES barrier ...

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“…One of the widely used model systems for such investigations is the decay of two-dimensional ͑2D͒ metal islands on metal substrates. [2][3][4][5][6][7][8][9][10][11] The thermal decay of such islands was found to reduce the island area with time t proportional to (t 0 Ϫt) 2␤ , where t 0 is the time at which the island is fully dissolved. 12 The value of the exponent ␤ is a signature of the dominant microscopic mechanism governing the rate of decay.…”

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Decay characteristics of two-dimensional islands on strongly anisotropic surfaces

Yao

Ebert

et al. 2002

Phys. Rev. B

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We investigate analytically the decay characteristics of two-dimensional islands on strongly anisotropic surfaces. We show that a generic scaling law can always be established in describing the dynamical evolution of such islands, given by Lϰ(t 0 Ϫt) ␤ , where L is the island width, and t 0 is the lifetime of the islands. The value of the scaling exponent ␤ in the fast-decay direction is always 1/2 in the low-temperature regime where the decay is quasi-one-directional, irrespective of the specific dominant decaying mechanism involved. At higher temperatures where the decay proceeds effectively in both directions, ␤ is again a good measure of the dominant microscopic decaying mechanism involved, just like the isotropic case. We discuss these results in connection with recent experiments. There has been an overwhelming wealth of research activity on fabricating various nanostructures that may possess unique physical properties. Nevertheless, the stability of nanostructures, once formed, often poses a limiting factor for their practical applications. 1,2 Therefore, understanding the physical mechanisms involved in the stability and the dynamical evolution of nanostructures after their formation is both scientifically intriguing and technologically significant, and has been receiving increasing attention in recent years. One of the widely used model systems for such investigations is the decay of two-dimensional ͑2D͒ metal islands on metal substrates. [2][3][4][5][6][7][8][9][10][11] The thermal decay of such islands was found to reduce the island area with time t proportional to (t 0 Ϫt) 2␤ , where t 0 is the time at which the island is fully dissolved. 12 The value of the exponent ␤ is a signature of the dominant microscopic mechanism governing the rate of decay. In the case where attachment and detachment of atoms from the island edges dominate the rate of decay, ␤ equals 1/2 whereas for the diffusion-limited case, i.e., where diffusion of adatoms on the terrace limits the decay rate, ␤ is 1/3. These results very well describe the decay of islands on isotropic surfaces, which in fact has attracted most of the attention so far. However, the decay of islands on anisotropic substrates, i.e., surfaces with different energy barriers along the nonequivalent crystallographic directions, is expected to be more complex and may provide additional insight into the physical nature of island dissolution. Indeed the larger complexity was substantiated by the observation of a transition from a 2D decay mode at high temperatures to a quasi-onedimensional ͑1D͒ decay mode at low temperatures for the anisotropic system of Ag islands on Ag͑110͒. 11 Several more recent studies have also studied the evolution of islands and voids on other metal ͑110͒ surfaces, 13-15 but to date, the theoretical basis for description of island decay on anisotropic substrates is still lacking.In this paper we develop a comprehensive analytical description of the decay of two dimensional islands on highly anisotropic surfaces. We find that even for highl...

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Decay of Cu adatom islands on Cu(111)

Cited by 105 publications

References 22 publications

Determination of Step Free Energies from Island Shape Fluctuations on Metal Surfaces

Determination of Step Free Energies from Island Shape Fluctuations on Metal Surfaces

Interlayer Mass Transport and Quantum Confinement of Electronic States

Decay characteristics of two-dimensional islands on strongly anisotropic surfaces

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