Analytical elastoplastic analysis of heteroepitaxial core-shell nanowires

Abstract

Semiconductor nanowires, grown heteroepitaxially, have many unique properties compared to heteroepitaxial thin films: e.g., the possibility of lateral relaxation, high surface to volume ratio and lower strain energy. While the onset of plastic deformation in flat thin films has been studied extensively, much less is understood about this phenomenon in the nanowire geometry. Here, we report development of a continuum analytical model that predicts not only the onset of plastic deformation for core-shell structures with anisotropic slip system, but also the evolution of stress and strain fields beyond the initial yield. This is the first analytical elastoplastic study of heteroepitaxial core-shell nanowires. Our model is verified against finite element simulations. To illustrate trends predicted by the model, we choose InGaAs for core-shell system as an example. We find that most energetically favorable positions for formation of the first dislocations in the heterostructure have misorientation of 0, π/2, π, and 3/2πfrom the principal slip planes in zinc-blend structures. We demonstrate that anisotropy in slip systems of the heterostructure reduces the critical misfit strain. Finally, we find that there is a critical ratio (χ) of shell thickness to core radius that maximizes the thickness of the elastoplastic region. This critical ratio is independent of geometry and depends only on material properties such as elastic moduli and yield strength of the heterostructure.