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Ge$_{1-x}$Sn$_{x}$ alloys are a promising candidate material to realisedirect-gap group-IV semiconductors for applications in Si-compatible electronicand photonic devices. Here, we present a combined theoretical and experimentalanalysis of Raman spectroscopy in Ge$_{1-x}$Sn$_{x}$ alloys. We describeliquid-vapour-solid growth and structural characterisation ofGe$_{1-x}$Sn$_{x}$ ($x \leq 8$%) nanowires displaying high crystalline quality,and investigate the structural and vibrational properties of the nanowiresusing Raman spectroscopy. Our theoretical analysis is based on a fully analyticanharmonic valence force field (VFF) potential, which describes exactly - i.e.without recourse to numerical fitting - the second-order elastic constants,third-order bulk modulus, selected second- and third-order inner elasticconstants and, as a consequence, the zone-centre transverse optical phonon modefrequency and its hydrostatic and axial strain dependence. We compute bulkelastic properties via density functional theory to parametrise the VFFpotential for Ge$_{1-x}$Sn$_{x}$ alloys, and apply the VFF potential toexplicitly compute the Raman spectra of realistic, disorderedGe$_{1-x}$Sn$_{x}$ alloy supercells. Our atomistic theoretical calculationsquantitatively capture: (i) the evolution of the measured Raman spectra with Sncomposition $x$, (ii) demonstrate explicitly that the presence of short-rangealloy disorder can significantly impact the shift coefficients $a$ and $b$ thatrespectively describe the dependence of the Raman shift on Sn composition andpseudomorphic strain, (iii) elucidate the origin of the so-called "disorderactivated" mode identified in previous experimental investigations, and (iv)allow for detailed atomic-scale interpretation of measured Raman spectra.Overall, our analysis provides insight relevant to the characterisation of thisemerging material system.

Raman spectroscopy of group-IV Ge$_{1-x}$Sn$_{x}$ alloys: theory and experiment