Freund-Chason Model

6.3.3 Freund-Chason Model

Freund and Chason took a completely different approach for the islands’ encounter [107]. They treated the problem using the Hertzian contact theory with cohesive attraction [108], in an attempt to overcome the deficiencies in the description of the zipping process by Nix and Clemens. The geometry of the problem was also changed; in fact, they claim that the conditions in the Nix-Clemens model are suitable in the case of a fully covered substrate while the depositing material is only filling gaps. Therefore, Freund and Chason proposed a change in the perspective of the problem. Instead of using a transversal cross section, they decided to analyze the process using a top view of the structure, as shown in Fig. 6.7.

pict

Figure 6.7.:

Freund-chason model.

In fact, the Freund-Chason model expands the dimensionality of the problem and a 3D description of the geometry is also possible. The stress estimation using the Freund-Chason model is given by

( )cN -σ = A 2γsv −-γgb , N = 1,2,3 , E N Ea

(6.7)

where $N$ is the problem dimensionality. $AN$ and $cN$ are parameters which depend on the stated problem dimension with values $A1 = 0.82$ , $A2 = 0.44$ , $A3 = 4$ , and $c1 = 1∕2$ , $c2 = 2∕3$ , $c3 = 1$ . The Freund-Chason model is more in line with experimental measurements, especially for materials with high adatom mobility.

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