Universal statistics of nanocrystal photoluminescence

Asymmetric photoluminescence (PL) lineshapes are a ubiquitous and defining feature of semiconductor nanocrystal ensembles, yet their microscopic origin has remained unresolved for decades. Here we show that ensemble PL can be quantitatively described by three statistically independent contributions: a Gaussian component encoding size dispersion, an exponential high-energy wing reflecting a Boltzmann-distributed exciton population, and a low-energy tail governed by exciton-phonon coupling and radiative recombination from disorder-localized states. This minimal formulation yields a generalized Gaussian asymmetric Laplace (GaLa) lineshape that accurately reproduces PL spectra across materials, morphologies, and temperatures. In the strongly confined two-dimensional limit, the low-energy wing transitions to a Lorentzian form, indicating the onset of a distinct exciton-phonon interaction regime captured by a second member of the same statistical family (GaLx). The parameters extracted from GaLa and GaLx provide direct, quantitative access to exciton thermodynamics and intrinsic energetic disorder from a single steady-state measurement. Together, these results establish a unifying statistical framework that reproduces the full ensemble PL lineshape from the strongly confined to the bulk-like limit, enabling predictive materials diagnostics and emission engineering across quantum-emitter platforms.