Reliability limits of the Maxwell–Garnett–Mie model for gold nanoparticle-doped silicon nanocomposites

Abstract The Maxwell–Garnett–Mie (MGM) model is widely used for rapid estimation of the optical response of nanoparticle-doped semiconductors, although its quantitative reliability becomes uncertain when local particle arrangement and electrodynamic interactions become significant. In this work, the reliability limits of the homogenized MGM description are systematically assessed for gold nanoparticle-doped silicon nanocomposites by benchmarking against full-wave finite-difference time-domain (FDTD) simulations. Particle diameter, particle population, and interparticle spacing are varied to distinguish finite-size effects from geometry-dependent interactions. The results show that the quantitative agreement between the homogenized MGM description and explicit-particle FDTD simulations depends not only on particle size and nominal volume fraction, but also on the particle population and interparticle spacing of the explicit nanoparticle assembly. For three-particle assemblies, the 80 nm case remains predominantly within the high-confidence regime, with maximum spectral differences below 5% over the investigated gap range, whereas the 40 nm case is predominantly classified as low confidence with deviations exceeding 15%. Increasing the particle population from three to five substantially reduces the high-confidence region, indicating greater sensitivity to geometry-dependent electrodynamic interactions. Based on the maximum wavelength-dependent spectral discrepancy between the two approaches, a reliability map is established to identify parameter regimes in which the homogenized description provides an accurate approximation to explicit nanoparticle assemblies. These findings demonstrate that nominal volume fraction alone is insufficient to assess the applicability of effective-medium descriptions, since different nanoparticle configurations with the same volume fraction can exhibit markedly different levels of agreement with full-wave simulations. The proposed framework provides a practical guideline for selecting between rapid effective-medium modeling and rigorous full-wave simulations in nanoparticle-engineered Si photonic structures.