Non-destructive thickness mapping of wafer-scale hexagonal boron nitride down to a monolayer.

The availability of an accurate, non-destructive method for measuring thickness and continuity of 2D materials with monolayer sensitivity over large areas is of pivotal importance for the development of new applications based on two-dimensional (2D) materials. While simple optical contrast methods and electrical measurements are sufficient for the case of metallic and semiconducting 2D materials, the low optical contrast and high electrical resistivity of wide band gap dielectric 2D materials such as hexagonal boron nitride (hBN) hampers their characterization. In this work, we demonstrate a non-destructive method to quantitatively map the thickness and continuity of hBN monolayers and bilayers over large areas. The proposed method is based on acquisition and subsequent fitting of ellipsometry spectra of hBN on Si/SiO substrates. Once a proper optical model is developed, it becomes possible to identify and map the commonly observed polymer residuals from the transfer process and obtain sub-monolayer thickness sensitivity for the hBN film. With some assumptions on the optical functions of hBN, the thickness of an as-transferred hBN monolayer on SiO is measured as 4.1 Å ± 0.1 Å, whereas the thickness of an air-annealed hBN monolayer on SiO is measured as 2.5 Å ± 0.1 Å. We argue that the difference in the two measured values is due to the presence of a water layer trapped between the SiO surface and the hBN layer in the latter case. The procedure can be fully automated to wafer-scale and extended to other 2D materials transferred onto any polished substrate, as long as their optical functions are approximately known.