Comparison of Theoretical Approaches Predicting the Coherent-Semicoherent Transition in Nanoscale Axial Heterostructures

The formation of misfit dislocations is an important issue for the performance of heteroepitaxial micro- and optoelectronic devices. We analyze three approaches that quantify the stability of misfit dislocations in axial-heteroepitaxial nanowires with respect to applicability and predictions of critical nanowire dimensions. The “nanoheteroepitaxy” approach of Zubia and Hersee proves suitable for determination of strain partitioning in the presence of an elastic mismatch. Concerning the critical thickness and diameter however the descriptions of Ertekin et al. and Glas respectively yield more reliable results, owing to the consideration of the total coherent and dislocation related energies plus the residual strain energy. In contrast to the model of Ertekin et al., which refers to infinitely long nanowires, the other two mentioned approaches allow predictions of the critical thickness of mismatched deposits on the nanowire axial face.