Critical thickness theory was developed to account for the ability of thin epitaxial metal and semiconductor layers to support high misfit or coherency strain.The thermodynamic equilibrium theory is correct,and is well approximated by a theory based on geometrical arguments.The latter theory is readily extended to arbitrary misfit strain profiles including linearly graded layers,for which a surface layer free of misfit dislocations.This result applies as well to linear strain gradients introduced by deformation,in which case the misfit dislocations are known as geometrically necessary dislocation.We show that a consequence of this surface layer is that the apparent yield strength of the material increases in small structures such as thin wires in torison.Under large plastic deformation,even if the material is perfectly plastic,critical thickness theory also predicts an apparent work-hardening.The predictions of critical thickness theory are in excellent agreement with experimental data in the literature.
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