Raman spectroscopy of group-IV Ge1−xSnx alloys: Theory and experiment

Ge1−xSnx alloys are a promising candidate material to realise direct-gap group-IV semiconductors for applications in Si-compatible electronic and photonic devices. Here, we present a combined theoretical and experimental analysis of Raman spectroscopy in Ge1−xSnx alloys. We describe liquid-vapour-solid growth and structural characterisation of Ge1−xSnx (x ≤ 8%) nanowires displaying high crystalline quality, and investigate the structural and vibrational properties of the nanowires using Raman spectroscopy. Our theoretical analysis is based on a fully analytic anharmonic 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 elastic constants and, as a consequence, the zone-centre transverse optical phonon mode frequency and its hydrostatic and axial strain dependence. We compute bulk elastic properties via density functional theory to parametrise the VFF potential for Ge1−xSnx alloys, and apply the VFF potential to explicitly compute the Raman spectra of realistic, disordered Ge1−xSnx alloy supercells. Our atomistic theoretical calculations quantitatively capture: (i) the evolution of the measured Raman spectra with Sn composition x, (ii) demonstrate explicitly that the presence of short-range alloy disorder can significantly impact the shift coefficients a and b that respectively describe the dependence of the Raman shift on Sn composition and pseudomorphic strain, (iii) elucidate the origin of the so-called “disorder activated” 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 this emerging material system. © 2021, CC BY.