Extrapolation of critical thickness of GaN thin films from lattice constant data using synchrotron X-ray

In some materials, Van der Merwe's equilibrium theory of strain relief is believed to explain the sudden transition from pseudomorphic growth of a thin film to a progressively relaxed state. We show, for the first time for GaN, how an accurate estimate of the critical thickness of a thin film can be extrapolated from suitable measurements of lattice constants as a function of film thickness using synchrotron X-ray. We do this both for an elementary elastic energy function, in which the interactions between the dislocations are ignored, and for a more realistic energy estimate due to Kasper. The method is found to work quantitatively for thin films of GaN on AlN. The critical thickness is determined to be 29±4 angstroms.