Large-Area Layer Counting of Two-Dimensional Materials Evaluating the Wavelength Shift in Visible-Reflectance Spectroscopy

An advanced and highly scalable approach for determining the number of layers of two-dimensional (2D) materials via optical spectroscopy is introduced. Based on appropriate subjacent layer stacks, the reflectance spectra of the 2D material assemblies exhibit wavelength shifts in distinct minima, which are linearly related to the number of layers. A linear correlation enables straightforward data interpretation, which is essential for implementing simple and comparatively fast measurement routines for process control on wafer scale. The structure of the optical layer stacks as well as the complex refractive indices of 2D materials were found to strongly influence the spectral position of the reflectance minima as well as the magnitude and the linearity of the wavelength shifts. We experimentally prove this method to be applicable for large-area layer counting of subsequently stacked chemical vapor deposition graphene films on a layer stack consisting of silicon nitride and silicon oxide. The measurement results confirm the calculated wavelength shift of the reflection minimum around 540 nm equaling approx. 3 nm per layer. Numerical analysis shows that comparable behavior is also achievable by the tailored design of subjacent layer stacks for graphene oxide, hexagonal boron nitride, and more complex 2D materials like transition-metal dichalcogenides. For the achievement of linear relations between wavelength shifts of the respective minimum and the layer count of the 2D material, analytical design rules are derived considering the optical properties of the underlying layer stack as well as oscillator frequencies within the complex refractive index of the 2D material. The largest signal response of 12 nm per layer was calculated for MoSe2 on an optimized layer stack.