Dependence of critical thickness on mismatch strain

The Burgers vector in either of the two slip directions depends on the sign of Cm. If em 0, the Burgers vector of length b is 

If Cm 0, the direction of the Burgers vector must be reversed, but the calculation is otherwise identical. 

The discussion here is restricted, for the most part, to cases of isotropic elastic response of both the film and substrate materials. However, the influences of two of the most important consequences of anisotropy can be taken into account in a relatively straightforward way. One principal influence of anisotropy concerns the level of resolved shear stress due to the mismatch stress on the potential glide planes for dislocation motion. This influence 

A single crystal alloy thin film with composition Sio.ssGeo.is is grown on an initially flat Si(OOl) substrate which is 0.5 mm thick. The lattice parameter of Si at room temperature is asi = 0.5431 nm, while that of Ge is ace = 0.5656 nm. Any dislocations formed as a consequence of epitaxial mismatch between the film and the substrate are known to be 60° dislocations with Burgers vectors in the family represented by (6.18). Assume that the biaxial moduli of Si(OOl) and Ge(OOl) crystals are Mgi(ooi) = 180.5 GPa and MGe(ooi) = 142 GPa, respectively, that the Poisson ratio of the film is i/f R 0.25, that Vq = 6/2, and that 6 w 0.4 nm. Curvature measurements are made continuously using the multibeam optical stress sensor method (see Section 2.3.2) so as to monitor the evolution of internal stress during film deposition. Estimate the substrate curvature at which misfit dislocations are first able to form at the interface between the film and the substrate. 

Using (1-14), the mean lattice parameter of the Sio.85Geo.15 alloy at room temperature is approximated as 

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