Example Stability of a strained epitaxial film

i9 alloy film is grown epitaxially on a (001) surface of the Si substrate. Estimate the critical wavelength Aor as defined in (8.61) for the nominally flat growth surface of the film. Base the calculation on the values of elastic constants given in Table 3.1 and the surface energy value of f/g = 1.2 J/m for the alloy. 

The mismatch strain between the film and substrate is approximated as described in (1.15) for a Ge concentration of x = 0.19, with the result that 

The elastic constants to use with the isotropic model are estimated in terms of the constants for single crystal Si and Ge given in Table 3.1 by assuming that the waviness is aligned with a (100) direction. In this case, the elastic modulus and Poisson ratio values of both Si and Ge are determined according to 

applying the linear rule of mixtures for the alloy, it follows that EsiGe 125 GPa and i siGe = 0.276. The mismatch stress is then 

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