Ordered step arrays on evaporated As (0001) vicinal surfaces

A computational procedure dealing with a one-dimensional epitaxial monolayer model was developed in part I. In this part it is extended and applied to the two-dimensional case, allowing for misfit along two perpendicular interfacial directions. The model employed differs slightly from that used by van der Merwe in that the overgrowth film is simulated by a plane of atoms linked to each other by elastic springs. This allows for an exact determination of the equilibrium boundary conditions. The results show (i) that the rectangular boundary edge is slightly deformed, lateral contractions occurring where the misfit dislocations intersect the boundary edge, (ii) that the dependence of stable structures on misfit is in good agreement with the analytical results of van der Merwe, (iii) that misfit dislocations are introduced alternately at the mutually perpendicular edges of a system having quadratic symmetry, (iv) that a segmented dependence of lowest energy on crystal size is obtained, one segment for each additional dislocation, (v) that a saw-toothed dependence of average strain on crystal size, in qualitative agreement with the experimental work of Vincent, results and (vi) that a fine structure in the energy curves results from discrete adatom peripheral growth.     

Non-conserved dynamics of steps on vicinal surfaces during electromigration-induced step bunching

We report new results on the non-conserved dynamics of parallel steps on vicinal surfaces in the case of sublimation with electromigration and step-step interactions. The derived equations are valid in the quasistatic approximation and in the limit f ^-1 ≫ l _D  ≫ l _± ≫ l _i , where f is the inverse electromigration length, l _D the diffusion length, l _± the kinetic lengths and l _i the terrace widths. The coupling between crystal sublimation and step-step interactions induces non-linear, non-conservative terms in the equations of motion. Depending on the initial conditions, this leads to interrupted coarsening, anticoarsening of step bunches or periodic switching between step trains of different numbers of bunches.     

In-phase step wandering on vicinal Si(1 1 1) surfaces

The step structure transition between a regular step and a bunched step on vicinal Si(1 1 1) surfaces induced by DC is studied by the kinetic Monte Carlo simulation in a terrace-adatom-step-kink (TASK) model. In the TASK model, effective force due to DC is taken into account explicitly on the mass transport of Si adatoms. In the diffusion-limited regime corresponding to the experimental temperature range II, step bunching is induced by step-up force and in-phase wandering of a regular step is formed by step-down force. The in-phase wandering of a regular step is formed by nucleation growth mode and the amplitude of wandering grows with time in proportion to . The period of in-phase wandering decreases as the effective force increases, consistent with the recent experimental results.     

Adatom ascending at step edges and faceting on fcc metal (110) surfaces

Using first-principles total-energy calculations, we show that an adatom can easily climb up at monatomic-layer-high steps on several representative fcc metal (110) surfaces via a place exchange mechanism. Inclusion of such novel adatom ascending processes in kinetic Monte Carlo simulations of Al(110) homoepitaxy as a prototypical model system can lead to the existence of an intriguing faceting instability, whose dynamical evolution and kinetic nature are explored in comparison with experimental observations.     

Current-induced step bunching at vicinal surfaces during crystal sublimation

The limits of the applicability of the generalized BCF model of electromigration-affected sublimation are discussed in detail. Only in surface-diffusion limited sublimation are the steps boundaries, effectively separating the transport processes at neighbouring terraces. In the opposite case of high surface mobility and slow exchange between the 2D gas of mobile adatoms and the crystal, many atoms simply cross the steps, spending some time in an intermediate state of adsorption at the step edge, but never becoming “crystal atoms”. In this regime of sublimation the steps are no longer boundaries. Therefore, one cannot analyze diffusion and desorption on one separate terrace (as in the generalized BCF model) since the coupling between the adatom concentration fields on neighbouring terraces cannot be neglected. A relevant model for this regime of electromigration-affected sublimation is proposed in this paper. This model manifests step buching at the step-up direction of the adatom electromigration. The central result of the mathematical treatment is the formula (x₂−x₁)^{n + 2}=(4kT/F) l^{n + 1}₀, relating the interstep distance x₂−x₁ in a stable pair of steps with the electromigration inducing force F. Here n and l₀ determine the form and the magnitude of the step-step interaction. The formula obtained for x₂−x₁ provides a gound to evaluate n and l₀ from a set of experimental data on sublimation by combined DC and radiative heating.     

Mixing length scales: step meandering and island nucleation on vicinal surfaces

Simultaneous island nucleation and step flow growth on vicinal surfaces are studied by Monte Carlo simulations. Step edges experience meandering instability under growth conditions if there is a kink barrier suppressing adatom jumps around kink sites. This instability has a characteristic length scale, with different scaling properties from the island separation scale. We show that there is a coupling between island nucleation and step edge instability. The length scale associated with nucleation begins to couple with the wavelength of the step edge patterns when islands and steps coalesce. Only in the submonolayer regime step meandering is independent of island formation. In this regime the island separation has a cross-over scaling behaviour as terrace width is varied.Received: 9 April 2003, Published online: 19 November 2003PACS: 81.15.Aa Theory and models of film growth - 68.55.Ac Nucleation and growth: microscopic aspects - 81.16.Rf Nanoscale pattern formationM. Rusanen: Present address: Institut Français du Pétrole, Groupe de Modélisation Moléculaire, BP 311, 92852 Rueil-Malmaison, FranceJ. Kallunki: Present address: Laboratory of Physics, PO Box 1100, FIN-02015 HUT, Espoo, Finland     

Oxygen adsorption on (110) silver

The adsorption of oxygen on a (110)Ag surface is investigated by means of Auger electron spectroscopy, LEED and low energy helium ion scattering (IS). With LEED two ordered structures, i.e. (3×1) and (2×1) were observed at oxygen exposures of 1700 L and 7000 L respectively. The oxygen signal observed by AES and IS increases monotonically with oxygen exposure. The signals can be related to absolute coverage by comparison with Δφ measurements and by the use of the LEED data. With this calibration and with theoretical scattering cross-sections the IS measurements allow the position of the adsorbed oxygen to be estimated. The observation of a strong azimuthal anisotropy of the IS signal, e.g. a large oxygen signal if the plane of scattering is parallel to the [110] direction and a relatively small oxygen signal in the [100] direction, leads to the conclusion that the oxygen is adsorbed in a bridge position between two Ag atoms of the [110] surface channels, its centre being slightly below the centres of the Ag atoms.     

Instability and wavelength selection during step flow growth of metal surfaces vicinal to fcc(001)

We study the onset and development of ledge instabilities during growth of vicinal metal surfaces using kinetic Monte Carlo simulations. We observe the formation of periodic patterns at [110] close packed step edges on surfaces vicinal to fcc(001) under realistic molecular beam epitaxy conditions. The corresponding wavelength and its temperature dependence are studied in detail. Simulations suggest that the ledge instability on fcc(1,1,m) vicinal surfaces is controlled by the strong kink Ehrlich-Schwoebel barrier, with the wavelength determined by dimer nucleation at the step edge. Our results are in agreement with recent continuum theoretical predictions, and experiments on Cu(1,1,17) vicinal surfaces.     

Peculiar effects of anisotropic diffusion on dynamics of vicinal surfaces

We report on peculiar behaviors due to anisotropic terrace diffusion on step meandering on a vicinal surface. We find that anisotropy triggers tilted ripples. In addition, if the fast diffusion direction is perpendicular to the steps, the instability is moderate and coarsening is absent, while in the opposite case the instability is promoted, and interrupted coarsening may be observed. Strong enough anisotropy restabilizes the step for almost all step orientations. These findings point to the nontrivial effect of anisotropy and open promising lines of inquiries in the design of surface architectures.     

A two-region diffusion model for current-induced instabilities of step patterns on vicinal Si(1 1 1) surfaces

We study current-induced step bunching and wandering instabilities with subsequent pattern formations on vicinal surfaces. A novel two-region diffusion model is developed, where we assume that there are different diffusion rates on terraces and in a small region around a step, generally arising from local differences in surface reconstruction. We determine the steady state solutions for a uniform train of straight steps, from which step bunching and in-phase wandering instabilities are deduced. The physically suggestive parameters of the two-region model are then mapped to the effective parameters in the usual sharp step models. Interestingly, a negative kinetic coefficient results when the diffusion in the step region is faster than on terraces. A consistent physical picture of current-induced instabilities on Si(1 1 1) is suggested based on the results of linear stability analysis. In this picture the step wandering instability is driven by step edge diffusion and is not of the Mullins–Sekerka type. Step bunching and wandering patterns at longer times are determined numerically by solving a set of coupled equations relating the velocity of a step to local properties of the step and its neighbors. We use a geometric representation of the step to derive a nonlinear evolution equation describing step wandering, which can explain experimental results where the peaks of the wandering steps align with the direction of the driving field.