Thermodynamic Aspects
There are, in general, four basic conceptual tools required for a formal description of epitaxy. These are: (i) thermodynamics of phase transitions and interface formation [11.1–3] (ii) fluid dynamics (hydro-, and gasodynamics) of mass transport [11.4–6]
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There are, in general, four basic conceptual tools required for a formal description of epitaxy. These are: (i)
thermodynamics of phase transitions and interface formation [11.1-3],
(ii)
fluid dynamics (hydro-, and gasodynamics) of mass transport [11.4-6],
(iii)
statistical mechanics of crystal growth processes [11.7], including the kinetics of surface migration/diffusion and ordering processes [11.8], and
(iv)
quantum mechanics of chemical bond formation (chemisorption and lattice incorporation) [11.9]
(the problem of heat transport in the solid or liquid phases, important for understanding bulk crystal growth, is omitted, because of the fairly low growth rates characteristic of epitaxial growth). The extent of applicability of these formal tools for analyzing the definite epitaxial growth process depends on the physical approach which is chosen for describing this process. In general, three approaches are most frequently used when studying epitaxy [11.10]. The first is the phenomenological or macroscopic approach, which provides a boundary between what is possible and what is not (this results from phase diagram analysis). This approach is suitable for analyzing phase transitions, phenomenological aspects of interface formation, as well as mass transport phenomena. The second approach is based on the atomistic description of epitaxy, involving statistical thermodynamics (the one-dimensional two-body interaction potentials are usually sufficient for a description of adsorption processes essential for epilayer formation). In the framework of this approach tangible previsions may be advanced which concern the topology of epitaxial growth, discrete island formation (2D and 3D nucleation), growth in continuous layers (SF-, FM-, and SK-modes) and influence of external parameters (photo- or plasma-assisted growth) modifying the growth process. However, the most fundamental processes of the growth, i.e., incorporation into the crystal lattice, and the anisotropic effects, resulting from crystallographic orientation and reconstruction of the surface on which the epitaxial growth proceeds, require quantum mechanical treatment (the wave functions of the valence electrons of the relevant atoms here play a dominant role). M. A. Herman et al., Epitaxy © Springer-Verlag Berlin Heidelberg 2004
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11. Thermodynamic Aspects
Thus, the quantum mechanical wave function approach to epitaxy is the third, most fundamental, and simultaneously most sophisticated approach. In this chapter, these approaches will be discussed, taking as the most general model of the epitaxial growth system the one illustrated schematically in Fig. 1.1 (Sect. 1.1).
11.1 The Driving Force for Epitaxy Epitaxial crystal growth is an example of a dynamical phase transition. A stable phase, the epilayer, grows out from a metastable phase, that is from an amorphous solid, melt (or liquid solution) or vapor (including the special case of growth from the rarified gas phase of intersecting atomic or molecular beams). The driving force for the growth is t
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