Surfaces, vicinal

Although all real surfaces have steps, they are not usually labelled as vicinal unless they are purposely misoriented in order to create a regular array of steps. Vicinal surfaces have unique properties, which make them useful for many types of experiments. For example, steps are often more chemically reactive than terraces, so that vicinal surfaces provide a means for investigating reactions at step edges. Also, it is possible to grow nanowires by deposition of a metal onto a surface of another metal in such a way that the deposited metal diflfiises to and attaches at the step edges [3]. 

If one is interested in the configuration of a singular surface or a vicinal surface close to the singular orientation, the surface is better characterized by the local height hj. The description assumes that there should be no vacancy in the crystal, no floating-solid atoms in the ambient phase, nor... 

The secondary and ternary islands will keep growing in approximately concentric fashion, thereby producing a conical structure above the original nucleation centers. This process of kinetic roughening supported by the Schwoebel effect makes a rather bumpy surface structure. Looking finally at a vicinal surface, this will grow rather smoothly when the width of the terraces is smaller than the typical distance between nucleation centers 4i (see below), and becomes bumpy in the opposite case [12,93]. 

O. Pierre-Louis, C. Misbah, Y. Saito, J. Krug, P. Politi. New nonlinear evolution equation for steps during molecular beam epitaxy on vicinal surfaces. Phys Rev Lett 50 4221, 1998. 

O. Pierre-Louis, C. Misbah. Dynamics and fluctuations during MBE on vicinal surfaces. I. Formalism and results of linear theory. Phys Rev B 55 2259, 1998 II. Nonlinear analysis. Phys Rev B 55 2276, 1998. 

T. Ihle, C. Misbah, O. Pierre-Louis. Equilibrium step dynamics on vicinal surfaces revisited. Phvs Rev B 55 2289, 1998. 

B. Jobs, T. L. Einstein, N. C. Bartelt. Distribution of terrace width on a vicinal surface within the one-dimensional free-fermion model. Phys Rev B 45 8153, 1991. 

A. Pimpinelli, J. Villain, D. E. Wolf, J. J. Metois, J. C. Heyraud, I. Elkinani, G. Uimin. Equilibrium step dynamics on vicinal surfaces. Surf Sci 295 143, 1993. 

Z. Sh. Yanovitskaya, I. G. Neizvestny, N. L. Shwartz, M. I. Katkov, I. P. Ryzhenkov. Desynchronization mode of 2D-island creation on the vicinal surface during MBE growth. Appl Surf Sci 0 119, 1998. 

We can create surfaces from the fee, hep and bcc crystals by cutting them along a plane. There are many ways to do this Fig. A. 1 shows how one obtains the low-index surfaces. Depending on the orientation of the cutting plane we obtain atomically flat surfaces with a high density of atoms per unit area or more open surfaces with steps, terraces and kinks (often referred to as corrugated or vicinal surfaces). Thus, the surface of a metal does not exist one must specify its coordinates. 

The behaviour of the Pt(110) surface, as discussed above, is largely determined by a strong adsorption of anions in the steps of its 2(111)-(111) structure. The same is valid for vicinal surfaces such as Pt(320), which gives a sizable peak at the same potential as Pt(110). ... 

Ideal Surfaces, A model of an ideal atomically smooth (100) surface of a face-centered cubic (fee) lattice is shown in Figure 3.13. If the surface differs only slightly in orientation from one that is atomically smooth, it will consist of flat portions called terraces and atomic steps or ledges. Such a surface is called vicinal. The steps on a vicinal surface can be completely straight (Fig. 3.13a) or they may have kinks (Fig. 3.13b). 

Figure 3.13. Top Model of an ideal (100) surface of a face-centered crystal (fee) lattice. Center and bottom Model of a vicinal surface of an fee cut at 12° to the (100) plane a) with straight monatomic steps and (Z ) monatomic steps with kinks along the steps. (From Ref. 11, with permission from Pergamon Press.)...

Figure 1. Sets of constant height contours on 1- and 2-D sinusoidal surfaces. The contours correspond to the idealized shapes of the surface steps on modulated crystal surfaces, a) and c) correspond to modulations on singular planes b) and d) correspond to vicinal surfaces.

D Gratings on Si(OOl) There are some fundamental differences in the evolution of 1- and 2-D modulations on singular or vicinal surfaces. As illustrated in figure 1 and discussed by Rettori and Villain[4] the 2-D modulations will generally involve closed step contours so that decay is promoted by differences in curvature of neighbouring steps and also interactions among steps in... 

Periodic surface profiles on vicinal surfaces have received considerable attention in the past, both from a continuum as well as an atomistic point of view [8-18], Here we describe briefly some recent work for surfaces of miscut a (about 3-10°) based on continuum mechanics specifically designed to take the anisotropy of y(0) into account [18], The approach is based on eq. (1) and the excess chemical potential given by [2]... 

Figure 2. Polar plot of energy factor E, diffusion coefficient D and decay constant B for a vicinal surface ofmiscuta= 15°.

A simple model that illustrates the connection between faceting and step attraction is provided by the following hypothetical linear function F(n) giving the free energy of a bundle of n steps per unit length in local equilibrium on the vicinal surface... 

Eq. (22) gives a reduction of energy upon faceting of the vicinal surface with N separate steps into two surfaces, the singular one and the one composed of the single bundle of N steps, since... 

As a continuum approximation, this approach should break down by the atomistic level. For islands it is presumably inappropriate for the small clusters imaged with FIM. More importantly, in many cases the stiffness may not be nearly anisotropic, as we have assumed it to be in our analysis. Then, as perhaps for Ag( 100) islands, new mechanisms may play a role. For vacancy clusters, there can be trapping in corners in systems that might seem to be cases of PD from consideration of vicinal surfaces. 

In future work we plan to extend this approach to consider the effect of external fields due to applied potentials or adsorbed species, as well as the modifications when surface islands can change their mean size (ripening or decaying). Correspondingly, there is noteworthy current work on the effect of sublimation or deposition on the step fluctuations of a vicinal surface (E.g. Pierre-Louis and Misbah, 1996). It would also be interesting to consider the effects of weak pinning potentials. 

A series or bunch of m initially straight and parallel steps, between heights 0 and m, may be expected to relax with the same asymptotics as a pair of steps. Modifications may occur, already for a pair of steps, when step-step interactions are present in addition to the entropic step repulsion. Here, we merely refer to recent reviews on experiments and theoretical analyses " on the much studied phenomenon of step bunching for vicinal surfaces, which is accompanied by interesting phase transistions. 

For evaporation-condensation dynamics, there is a simple way to convert the equation of motion (16) for a single step to the equation of motion for a vicinal surface at a slope 5 1, assuming steps have a contact repulsion. The idea is that, if we scale... 

In this paper we review some of our recent work on the dynamics of step bunching and faceting on vicinal surfaces below the roughening temperature, concentrating on several cases where interesting two dimensional (2D) step patterns form as a result of kinetic processes. We show that they can be understood from a unified point of view based on an approximate but physically motivated extension to 2D of the kind of ID step models studied by a number of workers. For some early examples, see refs. [1-5]. We have tried to make the conceptual and physical foundations of our own approach clear, but have made no attempt to provide a comprehensive review of work in this active area. More general discussions from a similar perspective and a guide to the literature can be found in recent reviews by Williams and Williams and BartelF. 

Perhaps the most important conclusion arising from a study of such models is that the projected free energy density of a uniform vicinal surface with slope s is given by the familiar Gruber-Mullins " expression ... 

Surface reconstruction or adsorption can often cause a vicinal surface with a single macroscopic orientation to facet into surfaces with different orientations. Generally the reconstruction occurs on a particular low-index flat face, and lowers its free energy relative to that of an unreconstructed surface with the same orientation. However the same reconstruction that produces the lower free energy for the flat face generally increases the energy of surface distortions such as steps that disturb the reconstmction. Thus reconstmction is often observed only on terraces wider than some critical terrace width Wc. When steps are uniformly distributed initially and if Wc is much greater... 

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