Composition dependence of atomic order in strain-relaxed, metastable GeSn alloys

Extended x-ray absorption fine structure (EXAFS) measurements of single-crystal Ge/GeSn radial heterostructure nanowires are used to examine the effects of composition on both short-range order (SRO) and longer-range disorder in GeSn alloys. GeSn has prompted significant interest because it can achieve a direct band gap for sufficient Sn concentrations beyond the equilibrium solid solubility limit in an all-group IV system. Short-range order in this material is particularly interesting as it has been predicted to affect the band gap independent of average composition or strain effects. By independently controlling the Sn composition and GeSn thickness during chemical vapor deposition of misfitting GeSn shells around ultrathin, elastically compliant, Ge core nanowires, the elastic misfit strain in the GeSn is minimized for Sn compositions over the studied range $\ensuremath{\approx}\mathrm{G}{\mathrm{e}}_{0.96}\mathrm{S}{\mathrm{n}}_{0.04}$ to $\mathrm{G}{\mathrm{e}}_{0.88}\mathrm{S}{\mathrm{n}}_{0.12}$. The degree of SRO was found to decrease with increasing Sn composition. Additionally, damping of the EXAFS signal was observed as the Sn content increased, particularly for increasingly distant atomic shells about the absorbing atom, even for scattering paths not involving Sn atoms. This result is quantified as an increase in the mean-squared relative displacement parameters of the shells. These measurements reveal the accommodation of local strain due to the presence of the highly size-mismatched Sn atoms in the Ge diamond cubic lattice ($\ensuremath{\approx}14%$), which may have effects on the band structure of the material in addition to the influence of short-range atomic order. Comparison among the nanowire samples allows for calculation of the topological rigidity parameter, $\phantom{\rule{4pt}{0ex}}{a}^{**}$, for the first-neighbor bond lengths. These exhibit chemically distinct values for Ge-Ge, Ge-Sn, and Sn-Sn, and they are consistent with the value ${a}^{**}=\phantom{\rule{0.16em}{0ex}}0.75\ifmmode\pm\else\textpm\fi{}0.07$ confirming the general applicability of the model to alloys with both large amounts of natural misfit strain and the potential for short-range order.