Clustering/anticlustering effects on the GeSi Raman spectra at moderate (Ge,Si) contents: Percolation scheme vs. ab initio calculations

We test a presumed ability behind the phenomenological percolation scheme used for the basic description of the multi-mode Raman spectra of mixed crystals at one dimension along the linear chain approximation, to determine, via the Raman intensities, the nature of the atom substitution, as to whether this is random or due to local clustering/anticlustering. For doing so, we focus on the model percolation-type Ge_ySi_1−y system characterized by six oscillators ${1×(Ge−Ge),3×(Ge−Si),2×(Si−Si)}$ and place the study around the critical compositions $y$ ∼ (0.16, 0.71, and 0.84) corresponding to nearly matching of intensities between the like Raman modes from a given multiplet (⁠$Ge−Si$ triplet or $Si−Si$ doublet). The interplay between the Ge_ySi_1−y Raman intensities predicted by the percolation scheme depending on a suitable order parameter $κ$ of local clustering/anticlustering is found to be consistent with ab initio calculations of the Ge_ySi_1−y Raman spectra done with the Ab Initio Modeling PROgram code using large (64-, 216-, and 512-atoms) disordered cubic supercells matching the required $(y,κ)$ values. The actual “percolation vs. ab initio” comparative insight at moderate/dilute-(Ge,Si) limits, with an emphasis on the $κ$-induced intra-bond transfer of oscillator strength, extends a pioneering one earlier achieved at an intermediate composition (⁠$y$ ∼ 0.50) by using small (32-atom) supercells [O. Pagès et al., J. Appl. Phys. 114, 033513 (2013)], mainly concerned with the inter-bond transfer of oscillator strength, providing altogether a complete picture.