Energy barriers for diffusion on heterogeneous stepped metal surfaces: Ag/Cu(110) (original) (raw)
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Diffusion processes and growth on stepped metal surfaces
Physical review. B, Condensed matter, 1995
) We study the dynamics of adatoms in a model of vicinal (11m) fcc metal surfaces. We examine the role of different diffusion mechanisms and their implications to surface growth. In particular, we study the effect of steps and kinks on adatom dynamics. We show that the existence of kinks is crucially important for adatom motion along and across steps. Our results are in agreement with recent experiments on Cu and Cu(1,1, surfaces. The results also suggest that for some metals exotic diffusion mechanisms may be important for mass transport across the steps. PACS numbers: 61.50. Cj, 68.35.Fx, 68.55.Bd Diffusion of adatoms on solid surfaces is an extensively studied subject [1]. In particular, adatom dynamics on vicinal metal and semiconductor surfaces has important implications to surface growth under non-equilibrium conditions [2,3]. However, barring a few special cases, the atomistic details of diffusion processes near steps and kinks are not known. Current experimental techniques are now able to yield atomistic information about adatom dynamics near steps and kinks [4], and growth of surfaces [3,. Clearly, careful microscopic calculations are needed to understand these phenomena. Our aim in this Letter is to study models of surfaces of fcc metals vicinal to the plane. The open structure of the (100) facets can be expected to give rise to some unconventional diffusion processes that are not seen for instance on stepped surfaces with fcc(111) terraces. First, we want to identify the various microscopic mechanisms relevant to self-diffusion near steps and kinks. Second, we shall discuss the implications of our results to the morphological stability of these surfaces under growth [6], and suggest a phenomenological model for step growth. Our results are consistent with experiments on Cu [3] and Cu (1,1, [4] surfaces. The geometric structure of an fcc(119) surface is shown in . An ideal fcc(11m) facet, with odd m > 1, consists of (100) terraces of width (m − 1)r nn /2 separated by (111) steps of height r nn / √ 2, where r nn is the distance between nearest neighbor atoms. Due to the geometry, only one kind of steps (of monolayer height) with close-packed edges exist on these surfaces. The metallic interactions between atoms in our model are derived from the semi-empirical Effective Medium Theory (EMT). The formalism of EMT is presented in Ref. , and a description of the implementation for molecular dynamics (MD) simulations of the present work can be found in Ref. . In the case of copper, EMT has been shown to give a reasonably accurate quantitative description of many different surface phenomena [7-11], which motivates its use for the present case. We shall divide the discussion of the microscopic mechanisms near step edges into three parts: standard hopping events (denoted by H), exchange and other exotic mechanisms (X), and the effect of kinks on diffusion near and across step edges (K). For each mechanism M the activation barrier is denoted by E M , and that of the reversed process by E rev M . In we show a contour plot of the adiabatic energy surface E(x, y) experienced by a single adatom on the Cu(119) surface at zero temperature. The potential across the terrace is shown in , indicating the activation energy for diffusion on the terrace E A , and the height of the Schwoebel step barrier E rev H1 . It is evident that the barrier in the x direction is appreciably modulated only at the immediate vicinity of the steps . We have verified this for the Cu ) surface also. Activation energies for simple hopping mechanisms on surfaces of several fcc metals with different orientations, as given by EMT, have been extensively tabulated in Ref. [10]. Our results for copper are fully consistent. The barrier height for a single jump on a flat terrace far from step edges is found to be E A = 0.399 eV, and that for diffusion of a vacancy in the first layer of the terrace is E V = 0.473 eV. The lowest barrier is that of an adatom diffusing along a straight step edge, and has a value E H2 = 0.258 eV. As expected, on Cu(11m) surfaces we find E H2 < E A < E rev H1 < E H1 . The inequality E H2 < E A is consistent with experimental results . In addition to ground-state calculations we have performed extensive MD simulations [15] to identify possible exotic diffusion mechanisms and to study entropic contributions to the rates . A well-known mechanism for step crossing, the replacement of an edge atom by an adatom from the terrace (mechanism X1) is observed in our simulations. In our model the activation energies for hopping and the simple exchange across the step edge are approximately equal: E H1 ≈ E X1 . We have also found more complicated mechanisms for step crossing. In we show two examples: a "coherent" chain transfer and an atom-by-atom replacement mechanism (vacancy 1
Numerical study of atomic diffusion processes of copper on silver (110) surface: Cu/Ag (110)
The aim of this paper is to study the diffusion of Cu adatom on Ag (110) by using the molecular dynamics simulation in the framework of the embedded atom method (EAM) as model of atomic interaction. Our simulation results predict that several diffusion processes such as simple jump, long jump and exchange mechanism may occur in the same system. The static barrier is calculated for each process by the drag method. The dynamic activation energy calculated from the Arrhenius law is in a good agreement with the static barrier. The presence of double jump is studied using velocity correlation function showing small contributions in diffusion process. Implications of these findings are discussed in more details.
Diffusion of Ag dimer on Cu (110) by dissociation-reassociation and concerted jump processes
2012 14th International Conference on Transparent Optical Networks (ICTON), 2012
In this work we investigate the diffusion of Ag dimer on Cu(110) surface by molecular dynamics simulation based on semi-empirical many-body potentials derived from the embedded atom method. The dissociationreassociation process is predicted to be dominant in static regime and this is confirmed by the dynamic investigation. A good agreement is found between static activation barrier and dynamic potential barrier.
Atomic jumps during surface diffusion
Physical Review B, 2009
The characteristics of atomic displacements during surface diffusion of Cu on Cu͑111͒ are studied by means of molecular dynamics simulations. It is found that even at very low substrate temperatures, the majority of the jumps are correlated, i.e., the displacement directions are not randomly chosen but rather keep some sort of memory from the previous moves and are influenced by them. Long jumps, spanning several surface unit cells, are observed at all temperatures. From an analysis of their length probability distribution information can be obtained about the mechanisms of friction and energy transfer between the diffusing adatom and the substrate. Both long jumps and recrossings ͑displacements in which the adatom moves back and forth between two adjacent adsorption sites͒ appear with a higher activation energy than normal diffusion. Finally, the influence of the instantaneous atomic configuration of the substrate on the adatom's trajectory is also highlighted.
Copper 10-Atom Island Diffusion on an Ag(1 1 1) Surface
Chinese Journal of Physics- Taipei-
This work presents the results of the diffusion of a copper 10-atom island on an Ag(111) surface using the molecular dynamics technique based on the embedded-atom method (EAM) potentials. Diffusion is carried out at three different temperatures: namely 300, 500, and 700 K. An obvious observation is that the rate of diffusion increases with an increase in temperature. An Arrhenius plot of the diffusion coefficient provides the effective energy barrier value of 143.55 ± 5 meV and diffusion prefactor value of 5.24 × 10 11Å2 /s. A plot of the Arrhenius law shows that the diffusion is independent of temperature in the range 300-700 K. The values of the diffusion coefficient and the effective energy barrier are in the same range as for the other islands regarding the theoretical and experimental work done so far. Near the islands dislocations and fissures have also been observed at 300 K.
Influence of short-range adatom-adatom interactions on the surface diffusion of Cu on Cu(111)
Physical Review B, 2004
The EAM potential set up by Mishin et al. [Phys. Rev. B 63 224106 (2001)] is used to study some elementary processes in the homoepitaxy of Cu on Cu͑111͒. After having checked its ability to reproduce surface physical quantities, this potential is applied to an investigation of the energetics, the vibrations and the surface diffusion of Cu N close-packed adislands ͑1 ഛ N ഛ 7͒. In each case we determine the most stable configurations, the corresponding activation barriers, the local vibrational spectra, and the Vineyard prefactors. In particular it is found that, at room temperature, dimers and trimers are still very mobile and move by concerted jumps much faster than tetramers while heptamers can be considered as immobile. The very good agreement of our results with scanning tunneling microscopy observations justifies the use of Mishin et al. potential for treating surface diffusion. This allowed us to study in details the influence of the lateral atomic environment of the adatoms along its diffusion path. An effective lateral pair interaction model is set up which is able to predict the existence of a saddle point along the path and to give a very good estimation of the activation barrier height. This model will be very useful in kinetic Monte Carlo simulations of homoepitaxial growth of Cu͑111͒.
Physical Review B, 2005
The surface diffusion of Cu adatoms in the presence of an adisland at FCC or HCP sites on Cu(111) is studied using the EAM potential derived by Mishin et al. [Phys. Rev. B 63 224106 (2001)]. The diffusion rates along straight (with close-packed edges) steps with (100) and (111)-type microfacets (resp. step A and step B) are first investigated using the transition state theory in the harmonic approximation. It is found that the classical limit beyond which the diffusion rates follow an Arrhenius law is reached above the Debye temperature. The Vineyard attempt frequencies and the (static) energy barriers are reported. Then a comparison is made with the results of more realistic classical molecular dynamic simulations which also exhibit an Arrhenius-like behavior. It is concluded that the corresponding energy barriers are completely consistent with the static ones within the statistical errors and that the diffusion barrier along step B is significantly larger than along step A. In contrast the prefactors are very different from the Vineyard frequencies. They increase with the static energy barrier in agreement with the Meyer-Neldel compensation rule and this increase is well approximated by the law proposed by Boisvert et al. [Phys. Rev. Lett. 75 469 (1995)]. As a consequence, the remaining part of this work is devoted to the determination of static energy barriers for a large number of diffusion events that can occur in the presence of an adisland. In particular, it is found that the corner crossing diffusion process for triangular adislands is markedly different for the two types of borders (A or B). From this set of results the diffusion rates of the most important atomic displacements can be predicted and used as input in Kinetic Monte-Carlo simulations.
Origin of quasi-constant pre-exponential factors for adatom diffusion on Cu and Ag surfaces
Physical Review B, 2007
Many-body interaction potentials from the embedded atom method with two functionals and electronic structure calculations based on density functional theory and the plane-wave pseudopotential method are used to calculate the pre-exponential factors for self-diffusion of adatoms via hopping on Cu͑100͒ and Ag͑100͒ surfaces with and without steps. The pre-exponential factors are found to be in the range of 10 −3 cm 2 / s for all investigated processes regardless of whether substrate vibrational dynamics are included or omitted. When substrate dynamics are ignored, compensation effects between stiffening and softening of the vibrational frequencies of the diffusing atom are responsible for this quasi-constant pre-exponential. When these dynamics are included, subtle cancellations in the vibrational free energy make the local contribution of the diffusing atom the dominant one.
Diffusion processes relevant to the epitaxial growth of Ag on Ag (110)
1996
By means of quenched molecular dynamics, we have studied the elementary diffusion processes (intralayer and interlayer diffusion) relevant for the epitaxial growth of Ag on Ag(ll0). Silver has been modeled by many-body potentials derived in the framework of the second-moment approximation to the tight-binding model. Energy barriers for diffusion on the fiat surface are found strongly anisotropic. The proximity to steps alters these barriers considerably. The adatom descent from islands takes place by different mechanisms depending on the orientation and some of those mechanisms depend strongly on the island size and shape. In particular, the adatom descent at kinks is much easier on small islands than on large ones. This fact may have a strong influence on the growth character at low temperatures. Finally, the energetics of small adatom clusters is presented.
Diffusion mechanism of Cu adatoms on a Cu(001) surface
Surface Science, 1994
Ab initio calculations on surface diffusion of Cu adatoms on Cu (00 1) are presented. The hopping mechanism with a calculated energy barrier of 0.69 eV is found to be favorable over the exchange mechanism with 0.97 eV. We find from the geometry relaxations that adatoms are significantly attracted to the surface and push away nearest-neighbor atoms in the surface. Lateral relaxations of atoms in the surface are larger than vertical ones.