Analytical solution to Matthews' and Blakeslee's critical dislocation formation thickness of epitaxially grown thin films

For the first time, an analytical expression for the critical thickness for the onset of misfit dislocations as established by Matthews and Blakeslee is presented. It is the so-called Lambert W function which reflects the curvature of this critical thickness. With the arrive of the analytical solution, expressions of arbitrary complexity that involve the critical thickness can be handled much more easily. Its practical application is demonstrated by implementation of Vegard's rule.