Highly accurate determination of heterogeneously stacked Van-der-Waals materials by optical microspectroscopy.

The composition of Van-der-Waals heterostructures is conclusively determined using a hybrid evaluation scheme of data acquired by optical microspectroscopy. This scheme deploys a parameter set comprising both change in reflectance and wavelength shift of distinct extreme values in reflectance spectra. Furthermore, the method is supported by an accurate analytical model describing reflectance of multilayer systems acquired by optical microspectroscopy. This approach allows uniquely for discrimination of 2D materials like graphene and hexagonal boron nitride (hBN) and, thus, quantitative analysis of Van-der-Waals heterostructures containing structurally very similar materials. The physical model features a transfer-matrix method which allows for flexible, modular description of complex optical systems and may easily be extended to individual setups. It accounts for numerical apertures of applied objective lenses and a glass fiber which guides the light into the spectrometer by two individual weighting functions. The scheme is proven by highly accurate quantification of the number of layers of graphene and hBN in Van-der-Waals heterostructures. In this exemplary case, the fingerprint of graphene involves distinct deviations of reflectance accompanied by additional wavelength shifts of extreme values. In contrast to graphene, the fingerprint of hBN reveals a negligible deviation in absolute reflectance causing this material being only detectable by spectral shifts of extreme values.