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.


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

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.