Critical dimensions in coherently strained coaxial nanowire heterostructures

We present a methodology to determine critical dimensions for coherently strained coaxial nanowire heterostructures based on a well-known formalism used to determine the critical thickness in planar epitaxial growth. The unique geometry of the nanowire structure along with the volumetric similarity of the core and shell regions give rise to a number of possible stable core-shell configurations for a given choice of materials. We show that a unique critical core radius and critical shell thickness, dependent on core radius, can quantify these configurations. Illustrative calculations are presented for various nitride semiconductor-based core-shell structures. It is anticipated that this model will serve as a guide to determine the feasibility of specific coherently strained nanowire heterostructure designs.