Ehrlich Schwoebel barrier

Fig. 1 shows surfaces obtained by this simulation. The surface is symmetric under the transformation h - h m case of high flux and high Ehrlich-Schwoebel barrier, while for other regions of the parameter space this symmetry is broken the... 

The surface current consists of a non-equilibrium part driven by the incident flux and the Ehrlich-Schwoebel barrier, and the equilibrium part driven by capillary forces ... 

Figure 5. The value of the coarsening exponent n of the Monte-Carlo surfaces and two experimental surfaces as a function of the growth parameters. The points (o) where n = 1/6 coincide with those simulations where the equilibrium part of the free energy did not match that of the continuum equation. The error bars show the parameter range/uncertanity of an Fe/Fe( 100) experiment of Ref. 10 (o measured n = 0.16 0.04) and Ref 12 ( measured n = 0.23 0.02). The estimate of the Ehrlich-Schwoebel barrier is taken from Ref 13 (thin line) and Ref. 14 (thick line).

Experimental results support this parameter-space dependence of the coarsening exponent as well. In case of Fe/Fe( 100) homoepitaxial growth (where there are estimates for the value of the Ehrlich-Schwoebel barrier), at room temperature n = 1/6 has been measured " ( = 0.16 0.02), while at elevated temperature the exponent is 1/4 ( = 0.234 0.02). These results are in excellent agreement with our predictions (Fig. 5). 

In case of relaxation to equilibrium, the process is diffusion-dominated and the presence of the A term is verified. For non-equilibrium conditions we have two cases For weakly out of equilibrium (low flux, low Ehrlich-Schwoebel barrier) the A term is still present and dominates the long-time coarsening, characterized by = 1/4. However, for strongly out of equilibrium cases (high flux, high Ehrlich-Schwoebel barrier) the Dt term seems to be dominated by the A term, causing coarsening with exponent n = 1/6. 

FIGURE 5.1.12 A monomolecular step as seen by an approaching admolecnle from above or below. Potential profiles both withont (middle) and with (bottom) and additional Ehrlich-Schwoebel barrier (as described in references 37 and 38). 

Concluding we should point out that Burton, Cabrera and Frank [4.35, 4.53] (see also Lorenz [4.54, 4.55]) have solved also the problem of stationary surface diffusion towards steps with circular symmetry. The theory of the more complex case of combined surface diffusion and bulk diffusion limitations can be found in the works of Fleischmann and Thirsk [4.48], Damjanovich and Bockris [4.50] and Gilmer et al. [4.56]. Note, however, that all these theoretical considerations do not accoimt for difficulties coimected with the so-called Ehrlich-Schwoebel barrier [4.57-4.62]. Elastic [4.63, 4.64] and entropic [4.65] interactions between growing steps are also neglected. 

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