Peak-Decomposition-Free Inverse Metrology of Hyperspectral Moir\'e Photoluminescence

Abstract

Hyperspectral photoluminescence (PL) of moir\'e transition-metal dichalcogenide heterobilayers encodes spatially varying exciton landscapes, but extracting that information is hampered by the ambiguity of multi-peak spectral decomposition. Here we develop a peak-decomposition-free inverse framework for quantitative optical metrology of effective disorder coordinates. From the raw cube $I(x,y,E)$ we construct physically motivated descriptor maps -- centroid energy, dominant emission energy, spectral width, low/high spectral-weight ratio, and dominant--centroid offset. Their spatial autocorrelation hierarchy and covariance structure form a robust descriptor fingerprint of multi-scale disorder-sensitive spectral statistics. By matching these descriptor summary statistics to a minimal smooth-plus-trap generative model through a grid-Bayesian inverse, we infer effective disorder coordinates $\Thetaeff=\{\Ws,\xis,\Wt,\nt\}$ with explicit uncertainties. Using synthetic PL cubes generated from controlled multi-scale landscapes, we recover the well-identified smooth-disorder coordinates and constrain the trap sector up to a strength--density degeneracy. We report this degeneracy explicitly as an intrinsic identifiability limit rather than a deficiency of the method, and map four canonical disorder regimes onto a disorder-coordinate diagram. The descriptor statistics are stable against shot noise and pixel pitch, and behave predictably under optical-resolution and energy-window changes. The same pipeline ingests experimental cubes without modification, making it directly applicable to two-dimensional and moir\'e materials. Our results establish descriptor-based hyperspectral PL as a practical, minimal-assumption route to optical disorder diagnostics and provide the validated core of a reusable analysis workflow (\texttt{HyperPL-Diag}) for moir\'e exciton systems.