Universal Thickness-Dependent Absorption in Solids at the Nanoscale

TL;DR

This study reveals a universal, thickness-dependent absorption behavior in nanoscale solids, driven by electromagnetic interference effects, challenging traditional Beer-Lambert law expectations and applicable across various materials.

Contribution

It demonstrates a universal absorption phenomenon in nanoscale solids due to interference effects, extending understanding beyond traditional models and applicable to diverse material classes.

Findings

Non-monotonic absorption evolution with thickness

Pronounced oscillatory features in absorption spectra

Deviation from Beer-Lambert law at nanoscale

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 strongly deviates from the expected Beer-Lambert law. 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.