Anisotropic profile decay on perturbed Au(111) vicinal surfaces

The anisotropy of the surface free energy has a large influence on the decay rate of periodic surface profiles at temperatures below the roughening temperature. This has been demonstrated by a study of the periodic surface profiles that were etched into vicinal Au(111) crystals in two orientations: with their wavevector parallel (ψ = 0) and perpendicular (ψ = π/2) to the intrinsic step direction of the vicinal surface. Due to this modulation, steps become either oscillatory in shape or remain straight, with their average separation modulated. Accordingly, profile decay is driven primarily by step self-energy (ψ = 0) or step interaction energy (ψ = π/2). The rate of decay was measured under ultra-high vacuum conditions at 750°C using a scanning tunneling microscope for imaging. A large anisotropy of decay was observed on two vicinal crystals of 1.5 and 5° miscut, with the ψ = 0 decay being much faster than with ψ = π/2). The results are evaluated and discussed in the framework of recent theory.     

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.     

Step patterns on vicinal reconstructed surfaces

Step patterns on vicinal (2 × 1) reconstructed surfaces of noble metals Au(110) and Pt(110), miscut towards the (100) orientation, are investigated. The free energy of the reconstructed surface with a network of crossing opposite steps is calculated in the strong chirality regime when the steps cannot make overhangs. It is explained why the steps are not perpendicular to the direction of the miscut but form in equilibrium a network of crossing steps which make the surface to look like a fish skin. The network formation is the consequence of competition between the — predominantly elastic — energy loss and entropy gain. It is in agreement with recent scanning tunnelling microscopy observations on vicinal Au(110) and Pt(110) surfaces.     

Instability of vicinal crystal surfaces with transparent steps: Transient kinetics and non-local electromigration

The steps at the crystal surfaces could be partially transparent in the sense that the migrating adatoms can cross the steps without visiting a kink position. In the case of significant transparency the velocity of a given step in a given moment is affected by atomic processes which took place at rather distant terraces in rather earlier moments. The reason is that an adatom needs time to cross many terraces before attaching to a kink position. That is why the theory of crystallization with non-local kinetics should account for the time dependence of the adatom concentrations on the terraces. Such a transient growth model (going beyond the quasi-static approximation of the BCF theory of crystal growth) is developed here for the limit of slow kinetics at the steps and fast surface diffusion. This model predicts instability of the vicinal surface (in agreement with the earlier studies) but rather different expression for the wavelength of the most unstable mode, which depends only on the ratio between the step transparency and the step kinetic coefficients.     

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.     

Step bunching to step-meandering transition induced by electromigration on Si(1 1 1) vicinal surface

The step configuration of a vicinal Si surface is studied under electromigration and a gradient of temperature. An abrupt transition (ΔT = 4 °C) from step-meandering to step bunching is found at 1225 °C for a step-down direct-current direction. This transition starts by random fluctuations which then extend on the whole surface. The transition is studied in the framework of a linear stability analysis of the usual Burton-Cabrera-Frank model by comparing the amplification factors of step-meandering and step bunching instabilities. Both compete at a given temperature, but since the amplification factors behave differently with temperature, bunching abruptly supersedes meandering above a critical temperature.     

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.     

Stable surface termination on vicinal 6H-SiC(0 0 0 1) surfaces

Ordered nanofacet structures on vicinal 6H-SiC(0 0 0 1) surfaces, consisting of pairs of a (0 0 0 1) basal plane and a facet, are investigated in terms of stable surface stacking of the (0 0 0 1) basal planes. The surface termination of S3 (or S3*), i.e., ABC (or A*C*B*), was suggested by a structural model based on quantized step-bunching, which typically gives a one-unit-cell bunched step configuration at the facet. Here, we evaluate the surface termination at basal planes covered with a layer of silicon oxynitride by means of quantitative low-energy electron diffraction (LEED) analysis combined with scanning tunneling microscopy (STM), and show the validity of the structural model proposed.     

Adatom diffusion on vicinal surfaces with permeable steps

We study the behavior of single atoms on an infinite vicinal surface assuming certain degree of step permeability. Assuming complete lack of re-evaporation and ruling out nucleation the atoms will inevitably join kink sites at the steps but will do many attempts before that. Increasing the probability for step permeability or the kink spacing lead to increase of the number of steps crossed before incorporation of the atoms into kink sites. The asymmetry of the attachment-detachment kinetics (Ehrlich-Schwoebel effect) suppresses the step permeability and completely eliminates it in the extreme case of the infinite Ehrlich-Schwoebel barrier. A negligibly small drift of the adatoms in a direction perpendicular to the steps leads to a significant asymmetry of the distribution of the permeability events, the atoms thus visiting more distant steps in the direction of the drift. The curves are fitted with an exponential function containing a constant which can be considered as a length scale of the effect of the drift. Some conclusions concerning the stability of the vicinals are drawn.      

一种增强结构信息的图像平滑算法

基于非线性扩散滤波提出了可以同时对同质区域进行平滑和对结构信息进行增强的算法．该算法在同质区域采用各项同性滤波而在边缘附近采用各项异性扩散滤波，避免了图像平滑和增强结构信息之间的矛盾．在实现时，根据一致性程度选择扩散矩阵的扩散系数，可确保偏微分方程在离散化时的简洁性和一致性．数字实验结果表明，可以有效的平滑一致性低的区域并增强一致性高的结构．     

The roughening transition of vicinal surfaces

Facetting of a vicinal surface is due to an arrangement of parallel primary steps which is commensurate with the substrate in plane periodicity (for instance one step every pth atomic row). It was shown by [#!Grempel!#] that such a locking requires an interaction between steps together with a finite step stiffness. But this early approach only reveals part of the story, as it is limited to sharp solid-vacuum interfaces in which thermal excitation of energetically expensive kinks controls all fluctuations. In this paper the problem is taken afresh in a language which applies equally well to “soft” interfaces, with important changes in the conclusions. Received 26 June 2001     

The instability of vicinal electrode surfaces against step bunching II: Theory

It is shown that vicinal surfaces with a regular step array in contact with an electrolyte are intrinsically unstable against a phase separation into areas of flat terraces and areas of step bunches. The effect is caused by the step dipole moment which lowers the potential of zero charge (pzc) of stepped surfaces. Specific calculations performed for vicinal surfaces of silver are qualitatively in keeping with experimental observations. Step bunching is likewise expected for vicinal surfaces of gold and platinum.     

The instability of vicinal electrode surfaces against step bunching I: Experiment

Using electrochemical STM we have studied the stability of arrays of parallel, single atom height steps on vicinal Ag(1 1 1) electrodes in electrolyte. We find that the steps for Ag(1 1 1) electrodes are unstable and form first double-steps and later multiple steps, separated by wide, flat terraces. In this paper denoted as “I: Experiment” we deal with the experimental aspects whereas theoretical aspects are discussed in the following paper “II: Theory”.     

Smoothing of an atomically rough vicinal surface – STM observation and MC simulation

Smoothing of an atomically rough vicinal surface of SrTiO₃ is studied by scanning tunneling microscope (STM) observation and by Monte Carlo (MC) simulation. A complex step pattern that resembles a two-dimensional phase separation pattern is observed on the surface. Analysis of the step pattern during annealing obtained by the STM in comparison with the MC simulation reveals an asymmetry of the relaxation pattern between islands and holes. The asymmetry is attributed to the difference of the mobility of an adatom and an atomic hole, and the asymmetry is enhanced by the step edge diffusion barrier. Values of an effective bond energy and an effective diffusion barrier as well as the surface diffusion coefficient are deduced from the relaxation pattern.     

Thermodynamics of solid surfaces

In contrast to the thermodynamics of fluid surfaces, the thermodynamics of solid surfaces was not elaborated in detail by Gibbs and other founders of surface thermodynamics. During recent decades, significant progress in this field has been achieved in both the understanding of old notions, like chemical potentials, and in formulating new areas. Applying to solid surfaces, basic relationships of classical theory of capillarity, such as the Laplace equation, the Young equation, the Gibbs adsorption equation, the Gibbs-Curie principle, the Wulff theorem and the Dupré rule, were reformulated and generalized. The thermodynamics of self-dispersion of solids and the thermodynamics of contact line phenomena were developed as well. This review provides a fresh insight into the modern state of the thermodynamics of solid surfaces. Not only a solid surface itself, both in a macroscopic body and in the system of fine particles, but also the interaction of solid surfaces with fluid phases, such as wetting phenomenon, will be analyzed. As the development of surface thermodynamics has given a powerful impetus to the creation of new experimental methods, some of these will be described as examples.     

On the microscopic origin of the kinetic step bunching instability on vicinal Si(0 0 1)

A scanning tunneling microscopy/atomic force microscopy study is presented of a kinetically driven growth instability, which leads to the formation of ripples during Si homoepitaxy on slightly vicinal Si(0 0 1) surfaces miscut in [1 1 0] direction. The instability is identified as step bunching, that occurs under step-flow growth conditions and vanishes both during low-temperature island growth and at high temperatures. We demonstrate, that the growth instability with the same characteristics is observed in two dimensional kinetic Monte Carlo simulation with included Si(0 0 1)-like diffusion anisotropy. The instability is mainly caused by the interplay between diffusion anisotropy and the attachment/detachment kinetics at the different step types on Si(0 0 1) surface. This new instability mechanism does not require any additional step edge barriers to diffusion of adatoms. In addition, the evolution of ripple height and periodicity was analyzed experimentally as a function of layer thickness. A lateral “ripple-zipper” mechanism is proposed for the coarsening of the ripples.     

Orientation and structure of triple step staircase on vicinal Si(1 1 1) surfaces

The vicinal Si(1 1 1) surface, inclined towards the direction, was investigated by scanning tunnelling microscopy and spot profile analysing low energy electron diffraction. It has been established that the surface, consisting of regularly spaced triple steps and (1 1 1) terraces with a width equal to that of a single unit cell of the Si(1 1 1)-7 × 7 surface structure, has the (7 7 10) orientation. An atomic model of the triple step is proposed.     

Ge diffusion on Si surfaces

Ge diffusion on Si(100), (111), and (110) surfaces has been studied by Auger electron spectroscopy and low energy electron diffraction in the temperature range from 600 to 800 °C. Surface diffusion coefficients versus temperature have been measured.     

Diffusivity of adatoms on plasma-exposed surfaces determined from the ionization energy approximation and ionic polarizability

Microscopic surface diffusivity theory based on atomic ionization energy concept is developed to explain the variations of the atomic and displacement polarizations with respect to the surface diffusion activation energy of adatoms in the process of self-assembly of quantum dots on plasma-exposed surfaces. These polarizations are derived classically, while the atomic polarization is quantized to obtain the microscopic atomic polarizability. The surface diffusivity equation is derived as a function of the ionization energy. The results of this work can be used to fine-tune the delivery rates of different adatoms onto nanostructure growth surfaces and optimize the low-temperature plasma based nanoscale synthesis processes.