Mechanism Frank-van der Merwe

All interface tensions are defined as positive and we consider yijw > yiinv in order to intentionally account for anisotropy. This favours 2D growth but does not prioritize the Frank-van der Merwe mechanism over the others. In fact growth is always 2D, as indicated by the BCF model, but depends on the lateral size of the terraces. Small terraces necessarily imply 3D growth. 

Stranski—Krastanov Often, growth of thin films occurs in the regime between the Volmer—Weber and Frank—van der Merwe mechanisms, in which an initial layer is formed on the substrate, but then 3D island structures form. 

Figure 1.18. Modes of epitaxial growth according to E.Bauer [1.77]. (a) Volmer-Weber mechanism, (b) Frank-Van der Merwe mechanism, (c) Stranski-Krastanow mechanism.

Cu deposited onto Ru(0001) at 100K grows in 2-d islands via a Frank-van der Merwe (layer by layer growth) mechanism up to 2 ML. The island sizes but not the basic growth mode are altered by a post-deposition anneal at 900 K. 

Figure 5.1. Scheme of the different mechanisms of growth (a) Frank-van der Merwe, (b) Voimer-Weber and (c) Stranski-Krastanov. The substrate and overlayers are represented by dark grey and light grey shading, respectively. 

In the case of a strong Me-S interaction, the structure and orientation of a Me deposit on top of Me UPD modified S according to the Frank-van der Merwe (cf. Fig. 1.1b) or Stranski-Krastanov mechanisms (cf. Fig. 1.1c) strongly depend on the substrate structure. Independently of crystallographic Me-S lattice misfit, distinct correlations between the epitaxy of a condensed 2D Meads phase and/or 2D Me-S surface alloy phase and the epitaxy of a 3D Me bulk phase can be expected. 

In the case of strong Meads-S interaction, expanded commensurate Meads overlayers as well as one or two close-packed commensurate or incommensurate Meads monolayers can be formed in the UPD range depending on AE (Fig. 6.13). Then, metal deposition in the OPD range follows either the Frank-van der Merwe (Fig. 6.13a) or the Stranski-Krastanov (Fig. 6.13b) growth mechanisms in the absence or presence of significant crystallographic Me-S misfit, respectively. In the first case, a... 

Figure 2.23. Growth of metal overlayers can occur in three different modes. Shown here is the behavior of the ratio of substrate and adsorbate Auger signals as a function of the deposition time for films that grow by the Volmer-Weber, Frank-van der Merwe, and Stranski-Krastanov types of mechanisms.

When considered in this framework, the resulting critical thickness condition is independent of any physical mechanism by which the interface misfit dislocation is actually formed in the system. This approach to critical thickness is an outgrowth of the pioneering work of Frank and Van der Merwe (1949) and the criterion was formulated in the way described here by Van der Merwe and van der Berg (1972). The most commonly observed mechanism for formation of misfit dislocations is through glide of a threading dislocation. In this section, the notion of critical thickness is re-examined on the basis of this mechanism. 

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