Lecture notes by John A. Venables. Lecture given 21 March 96 and updated 12 Dec 96. I then gave a series of lectures at EPFL in the Fall of '97, and EPFL Lecture #4 is on closely related topics.
Refs: Luth, Chap 3.5 and 3.6, pages 94-114; Zangwill, Chap 16, pages 421-432; R. Kern, G. LeLay and J.J Metois, Current Topics in Materials Sci 3 (1979) 139; J.A. Venables, G.D.T. Spiller and M. Hanbuchen, Reports in Progress on Physics 47 (1984) 399; J.A. Venables, Phys. Rev. B36 (1987) 4153; Surface Science 299/300 (1994) 798.
For each of these growth modes, there is a corresponding adsorption isotherm (diagram E2), as discussed in section C. In the island growth mode, the adatom concentration on the surface is small at the equilibrium vapor pressure of the deposit; no deposit would occur at all unless one has a large supersaturation. In layer growth, the equilibrium vapor pressure is approached from below, so that all the processes occur at undersaturation. In the S-K mode, there are a finite number of layers on the surface in equilibrium. The new element here is the idea of a nucleation barrier, dashed on diagram E2. The existence of such a barrier means that a finite supersaturation is required to nucleate the deposit.
This way of looking at the problem is less than 100% realistic, perhaps not surprisingly. It is rather artificial to think about surface energies of monolayers and very small clusters in terms of macroscopic concepts like surface energy. Numerically, the critical nucleus size, i, can be quite small, sometimes even one atom; this is the justification for developing an atomistic model, as discussed in the next section. However, an atomistic model should be consistent with the macroscopic thermodynamic viewpoint in the large-i limit. To ensure this is not trivial; most models donít even try; if I harp on about this, it is because I am attempting to do this in my research papers. In other words, there are (at least) two traditions in the literature; it would be nice to unify them.
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