Step-edge diffusion

Figure 1. Three limiting mechanisms for atomic processes which mediate step fluctuations, a) Step-edge diffusion b) Evaporation-recondensation c) Terrace diffusion with diffusion kernel P(). By appropriate choice of P(J), this case can reduce to cases a) and b) (see text).

Ignoring direct interactions, neighbouring steps do not influence each other if the dynamics is dominated by evaporation-recondensation or by step-edge diffusion. In either of these cases, the single step results derived in Section 2 (i.e. Eq. (22) and (26)) then hold. However, if the dynamics is mediated by terrace diffusion, neighbouring steps influence each other through the diffusion field on the terraces, and a coupled set of Langevin equations must be solved, as shown below (see also [13-17]). 

Thus, in a step-edge site transfer mechanism there are two possible paths direct transfer to a kink site and the step-edge diffusion path. 

One of the most important attributes of STM is the ability to quantitative evaluate the rate parameters associated with various surface processes. The dynamics of individual surface atoms, that is, terrace and step edge diffusion, have been monitored with STM, although for many... 

If the kinetics is fast enough and the diffusion of adatoms along the step edge or perimeter is rate limiting, then the width increases slowly as [66]... 

In this case, however, if the step separation i is small, the consecutive steps are coupled via the terrace diffusion held, and the width cannot increase as fast as but increases slowly, like the edge-diffusion-limited growth, as [68]... 

Iodine and bromine adsorb onto Au(l 11) from sodium iodide or sodium bromide solutions under an applied surface potential with the surface structure formed being dependent on the applied potential [166]. The iodine adsorbate can also affect gold step edge mobility and diffusion of the Au surface. Upon deposition of a layer of disordered surface iodine atoms, the movement of gold atoms (assisted by the 2-dimensional iodine gas on the terrace) from step edges out onto terraces occurs. However, this diffusion occurs only at the step edge when an ordered adlayer is formed [167]. 

In the discussion of atomistic aspects of electrodepKJsition of metals in Section 6.8 it was shown that in electrodeposition the transfer of a metal ion M"+ from the solution into the ionic metal lattice in the electrodeposition process may proceed via one of two mechanisms (1) a direct mechanism in which ion transfer takes place on a kink site of a step edge or on any site on the step edge (any growth site) or (2) the terrace-site ion mechanism. In the terrace-site transfer mechanism a metal ion is transferred from the solution (OHP) to the flat face of the terrace region. At this position the metal ion is in an adion state and is weakly bound to the crystal lattice. From this position it diffuses onto the surface, seeking a position with lower potential energy. The final position is a kink site. 

Usually, experimentalists quantify step fluctuations by averaging the data to find the correlation function G(t) = 0.5 < (h(x,i) - h(x,0)Y >, where h x,t) specifies the step position at time t and the average is over many sample points, x. G(f) measures how far a position on a step wanders with time. If that position were completely free to wander, it would obey a diffusive law G(t) t. However, its motion is restricted by the fact that it is connected to the other parts of the step. For that reason G(t) is sub-diffusive. The detailed law which G(f) obeys is dependent on the atomic processes which mediate step motion. For example, if the step edge is able to freely exchange... 

Over broad temperature regimes, terrace diffusion is the dominant kinetic mechanism. In this process, an atom detaches onto the lower terrace with probability pi, and onto the upper terrace with probability pu. It then diffuses on the terrace and reattaches to the step edge(see Fig. Ic). We define the sticking coefficient on approach to the step edge from the lower terrace to be a, while the sticking coefficient on approach to the step edge from the upper terrace is ajj (here we use continuum sticking coefficients, and relate them to lattice parameters in Appendix B). In Appendix C we calculate P(J) for terrace diffusion (see Eq. (106) for Pi(/) with d <=<>), from which we find. 

The anisotropy in the diffusion barriers sets up natural diffusion barriers for step flow. Thus, in the absence of any additional barriers at the step edges, and under the constraint of a constant external flux, one can expect the rate with which adatoms reach the SA step edge from the lower terrace to be higher than the rate with which they come in from the upper terrace. The opposite will hold for the Sb case. 

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