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We formalize within the percolation scheme, that operates along the linearchain approximation, namely at one dimension (1D), an intrinsic ability behindRaman scattering to achieve a quantitative insight into local clustering oranticlustering in an alloy, using SiGe as a case study. For doing so, we derivegeneral expressions of the individual fractions of the six SiGepercolation-type oscillators [1(Ge-Ge), 3(Si-Ge), 2(Si-Si)], which monitordirectly the Raman intensities, via a relevant order parameter k. This isintroduced by adapting to the 1D oscillators of the SiGe diamond version of the1D percolation scheme, namely along a fully consistent 1D treatment, theapproach 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 onein fact, due to its 3D vs. 1D ambivalence. Predictive k-dependent intensityinterplays between the SiGe (50 at.%Si) Raman lines are confronted withexisting experimental data and with ab initio Raman spectra obtained by usinglarge (32 atom) disordered supercells matching the required k values, withspecial attention to the Si-Ge triplet and to the Si-Si doublet, respectively.

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