An analytical expression for the critical thickness for the onset of misfit dislocations, as established by Matthews and Blakeslee, was presented here for the first time. It was found that the so-called Lambert W-function reflected the curvature of this critical thickness. Using the analytical solution, expressions of arbitrary complexity - that involved the critical thickness - could be handled much more easily. Its practical application was demonstrated by an implementation of Vegard’s rule.

Analytical Solution to Matthews and Blakeslee’s Critical Dislocation Formation Thickness of Epitaxially Grown Thin Films. A.Braun, K.M.Briggs, P.Böni: Journal of Crystal Growth, 2002, 241[1-2], 231-4