The limit of crystal lattice coherency of a cross-sectional hetero-epitaxial junction in a nanowire was calculated in terms of the critical nanowire radius, Rc, based upon a general calculation of the elastic stresses in a long cylindrical rod. The value of Rc was deduced from the kinetics of a possible misfit dislocation which could slip in the hetero-interface and rest in an energetic minimum (if such existed), regardless of whether it was of zero total energy; as assumed in the literature. A comparison was made with known models for the critical radius of a dislocation half-loop and the critical thickness, hc, of a hetero-epitaxial film; where all of the models were refined by including the energy of the slip-step formed or accidentally annihilated. For a symmetrical abrupt heterojunction, Rc was obtained as a lower limit; about 5 times higher than hc for a comparable thin film. An even larger Rc value was found for junctions of finite transition width, instead of abrupt transitions. It was estimated that nucleating the dislocations in a perfect nanowire was difficult; in agreement with experimental reports of dislocation-free nanowires having R well above the theoretical Rc value.

Stress and Dislocations at Cross-Sectional Heterojunctions in a Cylindrical Nanowire. G.Kästner, U.Gösele: Philosophical Magazine, 2004, 84[35], 3803-24