Critical dimensions for the plastic relaxation of strained axial heterostructures in free-standing nanowires

We consider strained layers at the top of free-standing nanowires. We show that there exists a radius-dependent critical layer thickness below which no interfacial dislocation should be introduced. This critical thickness becomes infinite for radii less than some critical value, below which arbitrarily thick coherent layers should be obtainable. Implicit equations allowing the calculation of these critical dimensions from material parameters are given. These are derived from an evaluation of the elastic energy stored in the system with a coherent interface, the areal density of which is shown to be much less than in a laterally infinite system.