Strain engineering in Sn-rich group IV semiconductors is a key enabling factor to exploit the direct bandgap at mid-infrared wavelengths. Here, we investigate the effect of strain on the growth of GeSn alloys in a Ge/GeSn core/shell nanowire geometry by controlling the Ge core diameter and correlating the results with theoretical strain calculations. Incorporation of the Sn content in the 10-20 at. % range is achieved with Ge core diameters ranging from 50 nm to 100 nm. While the smaller cores lead to the formation of a regular and homogeneous GeSn shell, larger cores lead to the formation of multifaceted sidewalls and broadened segregation domains, inducing the nucleation of defects. This behavior is rationalized in terms of the different residual strain, as obtained by realistic finite element method simulations. The extended analysis of the strain relaxation as a function of core and shell sizes, in comparison with the conventional planar geometry, provides a deeper understanding of the role of strain in the epitaxy of metastable GeSn semiconductors.

We address the role of non-uniform composition, as measured by energy-dispersive x-ray spectroscopy, in the elastic properties of core/shell nanowires for the Ge/GeSn system. In particular, by finite element method simulations and transmission electron diffraction measurements, we estimate the residual misfit strain when a radial gradient in Sn and a Ge segregation at the nanowire facet edges are present. An elastic stiffening of the structure with respect to the uniform one is concluded, particularly for the axial strain component. More importantly, refined predictions linking the strain and the Sn percentage at the nanowire facets enable us to quantitatively determine the maximum compressive strain value allowing for additional Sn incorporation into a GeSn alloy. The progressive incorporation with increasing shell thickness, under constant growth conditions, is specifically induced by the nanowire configuration, where a larger elastic relaxation of the misfit strain takes place.

Nanowires have emerged as a promising platform for the development of novel and high-quality heterostructures at large lattice misfit, inaccessible in a thin film configuration. However, despite core-shell nanowires allowing a very efficient elastic release of the misfit strain, the growth of highly uniform arrays of nanowire heterostructures still represents a challenge, for example due to a strain-induced bending morphology. Here we investigate the bending of wurtzite GaP/In _x Ga_1-xP core-shell nanowires using transmission electron microscopy and energy dispersive x-ray spectroscopy, both in terms of geometric and compositional asymmetry with respect to the longitudinal axis. We compare the experimental data with finite element method simulations in three dimensions, showing that both asymmetries are responsible for the actual bending. Such findings are valid for all lattice-mismatched core-shell nanowire heterostructures based on ternary alloys. Our work provides a quantitative understanding of the bending effect in general while also suggesting a strategy to minimise it.