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5
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84927850724
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A. A. Chernov, Modern Crystallography III (Springer-Verlag, Berlin, 1984).
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14
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84927850723
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Our assumption of a steady-state adatom density at each R implies that even atoms landing on the island eventually diffuse across the edge and are incorporated into the island. Thus the flux over the entire area π Ln2 contributes to island growth. The steady-state assumption may break down for very large barriers, but then Rc2<< Ln, so Eq. (6) is still rather accurate at the point where second-layer growth begins. However, once a second layer nucleates, it traps many or most atoms landing on the island. Then growth of the first layer slows and Eq. (6) no longer holds.
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19
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84927850722
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Essentially, Ln is the nearness of adatom ``sinks'' needed to keep the density eta below the threshold for significant further nucleation [7,8]. Similarly, if island edges act as sinks for adatoms on top of the island (case 1), then Rc1 is the nearness required for the sink to prevent further nucleation. Thus Ln and Rc1 are determined by roughly the same condition, and so Rc1approx Ln. (We assume throughout that the initial island nucleation takes place at the same temperature and flux as subsequent growth.)
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20
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84927850721
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Just as a surfactant coats the surface and lowers the surface energy, in small quantities we expect the surfactant to segregate at steps, lowering the step energy and so reducing the barrier to nucleation. The net result is a much higher nucleation density, with smaller islands at a given coverage. The surfactant could also increase the nucleation density by reducing the adatom mobility;
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23
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84927850720
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This is a sufficient condition for step-flow growth. Since step flow is not a central concern here, we do not further pursue the necessary conditions.
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24
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84927850719
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Roughly speaking, Lnapp Ln0e-En/kT [7], where En is related to the island energy and diffusion barrier. The step-flow condition Ln> Ls= h / tan theta then translates (for theta << 1) to lnθ > En/ kT + ln ( h/Ln0).
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