Effect of a stress concentrator on nucleation

The circumstances of formation of a dislocation loop at the surface of a strained film considered in the preceding section presumed no conditions to make dislocation nucleation more likely at one location then at another. This is the essential characteristic of homogeneous nucleation. In reality, epitaxial films are never geometrically perfect. Irregularities can take the form of surface or interface features (Jesson et al. 1993), precipitate particles due to 

The work done against the background elastic deformation field, equivalent to Wja in (6.80) for homogeneous nucleation, is more involved in this case because the stress field varies nonuniformly over the glide plane prior to dislocation formation, as indicated in (6.85). This work of formation is readily determined to be 

A number of additional trends can be noted. For example, if the stress concentration factor is larger than 2 - it is approximately 3 for a circular groove in a tension field - then the site is more effective as a source of dislocations. If the configuration of the stress concentrator is a notch with a very high curvature of the notch surface at its root, then the stress concentration factor can be very large compared to 2, but the spatial extent of the localized stress field is significantly reduced from that of the circular stress concentrator. For the case of a planar crack, which is the ultimate sharp notch, the issue of dislocation nucleation has been modeled by Rice and Thomson (1973) and Rice and Beltz (1994). Similar techniques have been adapted for the study of dislocation nucleation at the edge of an epitaxial island (Johnson and Freund 1997). 

Spontaneous formation of a semicircular dislocation loop was considered in Section 6.8. Consider a thin film on a substrate for which the mismatch strain is Cm. 

A change in film deposition process is introduced as a consequence of which the film processing temperature is changed from 500 °C to 700 °G. Approximately what relative change in the film mismatch strain should occur, in response to this process change, in order that the dislocation nucleation rate remains fixed. 

---