Generalized Lorentz Framework for Active Semiconductor Quantum Surface Plasmonics

Abstract

Nanostructured semiconductors provide an actively tunable platform for light-matter interactions across a broad spectral range. As feature sizes shrink to the deep nanoscale (~10 nm scale), nonclassical carrier dynamics and surface plasmonic responses become prominent, creating substantial challenges for a rigorous and efficient theoretical treatment. Here we develop a generalized Lorentz framework for quantum surface plasmonics in nanostructured semiconductors with arbitrary energymomentum dispersion relations. The framework enables efficient quantitative treatment of carrier nonlocality, carrier surface accumulation and depletion, and nonlocal damping in three-dimensional semiconductor nanostructures, under electrical tuning and across a wide range of doping densities. Building on this framework, we further establish a rigorous quasinormal-mode analysis that provides transparent physical insight into complex surface plasmonic responses of multiscale semiconductor structures. We demonstrate electrically controlled deep-nanoscale carrier accumulation and depletion in a semiconductor nanoantenna, leading to pronounced plasmonic-response modulation that can be interpreted in terms of eigenmode shifts, creation, and annihilation. By quantifying and linking complex nonclassical carrier dynamics with plasmonic eigenmodes, our work establishes a comprehensive quantitative framework for active semiconductor quantum surface plasmonics and will foster the convergence of electronics and photonics at the deep nanoscale.