GeSi Raman spectra vs. local clustering/anticlustering: Percolation scheme and ab initio calculations

Abstract

We formalize within the percolation scheme that operates along the linear chain approximation, i.e., at one dimension (1D), an intrinsic ability behind Raman scattering to achieve a quantitative insight into local clustering/anticlustering in an alloy, using GeSi as a case study. For doing so, we derive general expressions of the individual fractions of the six GeSi percolation-type oscillators [1×(Ge-Ge), 3×(Ge-Si), 2×(Si-Si)], which monitor directly the Raman intensities, via a relevant order parameter κ. This is introduced by adapting to the 1D oscillators of the GeSi-diamond version of the 1D-percolation scheme, i.e., along a fully consistent 1D treatment, the approach originally used by Verleur and Barker for the three-dimensional (3D) oscillators of their 1D-cluster scheme applying to zincblende alloys [H. W. Verleur and A. S. Barker, Phys. Rev. 149, 715 (1966)], a somehow problematic one in fact, due to its 3D–1D ambivalence. Predictive κ-dependent intensity-interplays between the Ge0.5Si0.5 Raman lines are confronted with existing experimental data and with ab initio Raman spectra obtained by using (32-atom) disordered supercells matching the required κ values, with special attention to the Ge-Si triplet and to the Si-Si doublet, respectively.