Growth patterning due to misfit dislocations

In this subsection, it is assumed that a thin film has been deposited epitaxially onto the surface of a relatively thick substrate with lattice mismatch. 

The film thickness is assumed to be beyond its critical thickness, and consequently misfit dislocations have been formed at the film-substrate interface. Thereafter, additional material with a lattice mismatch with respect to the unrelaxed film material is to be deposited on the surface of the film. Subsequent deposit would be expected to nucleate most readily at places on the growth surface at which the mismatch is smallest. For example, suppose that a SiGe film with a mismatch strain Cm is deposited onto Si(OOl) to a thickness beyond her as defined in Chapter 5 and that the strain is then partially relaxed through formation of misfit dislocations. As a result, the elastic strain at the surface becomes nonuniform. Then, Ge is deposited on the surface of the dislocated film. Because the lattice parameter of Ge is larger than the effective lattice parameter of SiGe, the conditions are most favorable for attachment of the Ge deposit at points on the surface at which the remaining surface strain is the least compressive or the most relaxed. 

The surface stress field is readily determined by application of (6.2) and (6.3), and the surface strain field follows readily by means of Hooke s law. The sum of the elastic extensional strain components in the surface due to the dislocations is 

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