PHY 598 (Venables) Sect E1

Notes for PHY 598 Sect E1 (Venables)

© Arizona Board of Regents for Arizona State University and John A. Venables

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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.

E. Surface Processes in Epitaxial Growth

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.

E1. Growth Modes and Nucleation Barriers

  • Growth Modes and Adsorption Isotherms
  • The classification of three growth modes (diagram E1) dates from 1958, when Ernst Bauer wrote a much quoted (review) paper in Zeitschrift fur Kristallographie. The Layer-by-Layer, or Frank- van der Merwe, growth mode arises because the atoms of the deposit material are more strongly attracted to the substrate than they are to themselves. In the opposite case, where the deposit atoms are more strongly bound to each other than they are to the substrate, the Island, or Volmer-Weber mode results. An intermediate case, the Layer-plus-Island, or Stranski-Krastanov growth mode is much more common than one might think. In this case, layers form first, but then for some reason or other the system gets tired of this, and switches to islands.

    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.

  • Nucleation Barriers in Classical and Atomistic Models
  • The same phenomena look a lot more complex when one considers what is going on at the atomic level (diagram E3), and in general only a few of these processes can be put into quantitative models at the same time. It may be useful to refresh your ideas about crystal growth in general now, by rereading section 1.3, and revisiting problems 2 and 3, since we will be looking into these atomic processes in more detail in the next section. In particular, the nucleation barrier concept can be explored in both classical (macroscopic surface energy) or in atomistic terms. The classical nucleation theory proceeds roughly as follows.

    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.

    Continue to section E2

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