Growth modes based on surface energies

As before, it will be assumed that the shape of the cluster is a spherical cap. Following the development in Section 1.3.3, the free energy change 

Qualitative implications for the behavior of the system are evident from the form of (1.10). If the quantity enclosed within brackets is positive, then there is an activation barrier to formation of the cluster. The height of the energy activation barrier is. F =. F(u, 0 ) where = 87t(2 —3c..y + c )/3 and 0 = cos (c. ) the roots of dfFjdv = 0, dfFjdd = 0. The point u = 0 = 0, is a saddle point of the function fF v,6), with paths of 

Consequently, an activation barrier exists for Cy 1 or 7s 7f + 7fs- This implies that clusters nucleate with a nonzero contact angle 0. Consequently, the film nuclei form on the substrate as islands and the ensuing film growth mode is the Volmer-Weber island growth mode, as was noted in Section 1.3. This mode is preferred when the atoms or molecules deposited onto the substrate are more strongly bound to one another than to the underlying substrate, as in the case of many metals on insulator substrates. 

---