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 ΑΓΝ. The critical thickness is determined to be 29 ± 4 Å.
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We thank Dr. Mauro Sardela for useful discussions. This work was supported by the United States Department of Energy under grant DEFG02-91ER45439 and by Samsung Electronics Co. Ltd.. NSLS (National Synchrotron Light Source) is supported by the U. S. DOE under grant DE-AC012-76CH00016.
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Kim, C., Robinson, I.K., Myoung, J. et al. Extrapolation of critical thickness of GaN thin films from lattice constant data using synchrotron X-ray. MRS Online Proceedings Library 423, 557–561 (1996). https://doi.org/10.1557/PROC-423-557