Spectroscopic Ellipsometry for Two-Dimensional Materials: Methods, Optical Modeling, and Emerging Phenomena

TL;DR

The paper addresses the challenge of characterizing the complex optical response of atomically thin and multilayer 2D materials, where strong excitonic effects, anisotropy, and substrate interactions complicate conventional measurements. It provides a systematic synthesis of spectroscopic ellipsometry methods, from standard SE to Mueller Matrix Ellipsometry, detailing experimental configurations, layer-stack modeling, and advanced data-analysis approaches tailored to graphene, TMDs, and organic films. Key findings include the ability to quantify the dielectric function $\epsilon(\omega)$, resolve in-plane versus out-of-plane anisotropy, and observe phenomena such as extreme optical anisotropy and natural hyperbolic dispersion in multilayer 2D materials, as well as substrate- and growth-condition–driven spectral modifications. The review highlights methodological challenges and prospects, advocating for in-situ measurements, deterministic ellipsometry, and AI-assisted data interpretation to enable high-throughput, accurate characterization for fundamental studies and photonic-device engineering.

Abstract

Spectroscopic ellipsometry (SE) has emerged as a powerful and non-destructive optical characterization technique for probing the complex dielectric properties of two-dimensional (2D) materials. This review provides a comprehensive overview of ellipsometric methods applied to atomically thin and multilayer van der Waals materials, including graphene, transition metal dichalcogenides, and other emerging 2D systems. We discuss experimental configurations, optical modeling strategies, and challenges associated with reduced dimensionality, anisotropy, and substrate effects. Advanced techniques such as Mueller matrix ellipsometry are highlighted for their capability to resolve in-plane and out-of-plane dielectric tensor components in anisotropic and low-symmetry materials. Furthermore, we review recent discoveries enabled by ellipsometry, including extreme optical anisotropy, hyperbolic dispersion, and tunable plasmonic responses in multilayer 2D materials. These findings establish spectroscopic ellipsometry as an essential tool for both fundamental studies and photonic device engineering based on two-dimensional materials.

Figures (6)

• Figure 1: Schematic of SE measurement principle showing the transformation of polarized light upon sample reflection.
• Figure 2: Mapping of the physical MLG/Ni structure (left) to a multilayer optical model (right) for SE analysis.
• Figure 3: The real part of the optical conductivity ($\sigma_1$) for multilayer graphene on a nickel substrate. The experimental data (thick green line) shows a prominent peak at 4.38 eV, fitted with a Fano lineshape (dashed black line), representing the redshifted $\pi \rightarrow \pi^*$ transition due to strong substrate interaction. Adapted from Maulina2024.
• Figure 4: Imaginary part of the dielectric function ($\epsilon_2$) for monolayer MoS$_2$ at 300 K (top) and 68 K (bottom). The cryogenic spectrum reveals sharpened A and B excitons and their clear splitting into neutral (A$^0$, B$^0$) and charged (A$^-$, B$^-$) components, a feature dependent on growth method. Adapted from Nguyen2024.
• Figure 5: Comparative dielectric functions ($\epsilon_2$) of monolayer (colored lines) and bulk (gray lines) TMDs: MoSe$_2$, WSe$_2$, MoS$_2$, and WS$_2$. The plots highlight the minimal shift of the A/B excitons versus the pronounced blue-shift of the C/D transitions in monolayers, illustrating differential sensitivity to interlayer coupling. Adapted from Li2014.