Strained epitaxial islands

suppose that the artificial tractions, which were introduced in order to maintain the strain level everywhere in the film material, are relaxed. For any stable elastic material, the work done on the system by these tractions as they are relaxed is negative. Consequently, once the tractions have been completely removed, the total elastic energy has been decreased from its value at the start of the step. This decrease in elastic energy scales with the initial elastic energy density MfC.  

---

The calculation of free energy change in the transition of a uniformly strained film into an isolated epitaxial island which led to Figure 8.32 was based on the assumption that the elastic properties of the film material and substrate material are identical. If this is not the case, the modulus difference between the materials can have a significant influence on the change in elastic energy associated with island formation. To illustrate this point,... 

The conclusion follows directly from superposition of linear elastic fields, without the need for detailed calculation. The system under discussion is depicted in part (a) of Figure 8.34. The figure shows a relatively thick elastic substrate with a film of some uniform thickness bonded to its surface. The film supports a spatially uniform mismatch strain, presumably due to the constraint of epitaxy. The elastic properties of the film material may be different from those of the substrate material. Some of the film material has gathered into an isolated epitaxial island on the surface of the strained layer. The island material also supports the same mismatch strain. The lateral faces of the island are free of applied traction. As a result, the elastic strain field is spatially nonuniform and the elastic strain energy is... 

Johnson, H. T. and Freund, L. B. (1997), The mechanics of coherent and dislocated island morphologies in strained epitaxial material syste. Journal of Applied Physics 81, 6081-6090. 

---