Reflectivity-based refractive index measurement of van der Waals materials

TL;DR

This paper introduces a reflectivity-based technique for measuring the in-plane refractive index of small, exfoliated van der Waals materials without relying on spectral models, enabling characterization of tiny flakes on non-transmissive substrates.

Contribution

The method allows direct refractive index measurement from reflectivity minima without assuming spectral shapes, suitable for small flakes where traditional ellipsometry fails.

Findings

Successfully measured HfS₂ refractive index across visible spectrum.

Validated results against previous ellipsometry data.

Applicable to small exfoliated vdW flakes on various substrates.

Abstract

We present a reflectivity-based method for measuring the in-plane refractive index of transparent van der Waals (vdW) materials. The approach enables the characterization of as small as $3 \times 3$~{\textmu}m$^2$ exfoliated flakes on a non-transmissive substrate without assuming any specific spectral shape of the refractive index. Exfoliated flakes are most commonly obtained through mechanical exfoliation, which generally produces vdW flakes with tens-of-micron lateral dimensions. As a result, conventional ellipsometry - which depends on large, uniform areas and specific spectral models - becomes challenging to apply. Our method determines the refractive index directly from the spectral position of reflectivity minima, provided the flake thickness and the substrate complex refractive index are known. We demonstrate the technique on hafnium disulfide (HfS$_2$), a vdW semiconductor with high refractive index and low absorption, retrieving its in-plane refractive index across the visible range. The results both validate previous ellipsometry measurements and establish this method as an accessible and spectral-model-free alternative for refractive index characterization of vdW materials.