Critical Thickness and Radius for Axial Heterostructure Nanowires Using Finite-Element Method

Finite-element methods are used to simulate a heterostructured nanowire grown on a compliant mesa substrate. The critical thickness is calculated based on the overall energy balance approach. The strain field created by the first pair of misfit dislocations, which offsets the initial coherent strain field, is simulated. The local residual strain is used to calculate the total residual strain energy. The three-dimensional model shows that there exists a radius-dependent critical thickness below which no misfit dislocations could be generated. Moreover, this critical thickness becomes infinity for a radius less than some critical values. The simulated results are in good agreement with the experimental data. The critical radius from this work is smaller than that obtained from previous models that omit the interaction between the initial coherent strain field and the dislocation-induced strain field.