Universality Encoded in Fano Lineshapes: A Decoupled Phonon Framework for Rapid Raman Parameter Extraction

Fano resonances frequently emerge in Raman spectra of metals and doped semiconductors; however, extracting the relevant microscopic parameters typically requires nonlinear fitting procedures that obscure physical insight and increase the computational cost. Here, we demonstrate that a universal geometric feature is encoded in renormalized Fano lineshapes and can be revealed through an angular parametrization that exposes intrinsic symmetries and spectral invariants. Within this representation, extremal separations and nodal points have analytically been related to key underlying variables with a direct physical significance. We have successfully interpreted the dimensionless Fano profile within a many-body framework in terms of isolated dressed single-phonon dynamics associated with corrected Raman vertices, effectively decoupled from purely electronic contributions. A comparison with reported Raman data on doped silicon demonstrates a substantial reduction in computational complexity, thereby enabling efficient and physically transparent material characterization without reliance on resource-intensive modeling platforms.