Universal Thickness-Dependent Absorption in Solids at the Nanoscale: Anomalous Enhancement in the Ultrathin Limit

Abstract

Through systematic experimental and theoretical studies of layer-thickness-dependent absorption in semiconducting MoSe$_2$ and WS$_2$ across the visible to near-infrared spectral range, we demonstrate a universal absorption behavior in solids at nanoscale thicknesses. With increasing thickness, a non-monotonic evolution of absorption integrated over the measured spectral region is revealed which is accompanied by pronounced oscillatory features. This shows a strong deviation from the expected Beer-Lambert law. Below 10 nm, we observe a sharp anomalous increase in absorption, with deviations from Beer's law exceeding 50% in layered semiconductors. Our conclusions hold irrespective of the presence of any optical resonances such as excitons or plasmons within the spectral window. The observed behavior has origins in the electromagnetic interference effects taking place between the two surfaces of the thin crystals. The present work on 2D semiconductors is extendable to all kinds of solids such as conventional semiconductors (e.g. Si, GaAs, GaN, InP), (semi) metals (e.g. Al, Ag, Au, c-HOPG) and 2D magnetic materials (e.g. CrSBr and NiPS$_3$). Our results provide fundamental insights into light-matter interactions in solids at the nanoscale and are vital for optimally designing the new generation of absorption-based flexible optoelectronic devices.