Invisible N-layer graphene

The detection of graphene layers on Si substrates is a common task, but has the aspect of being a nontrivial scientific problem. In visual detection of graphene, the difference between the reflectance of light from the substrate and that from graphene on it must be sufficiently large for increasing their contrast. It is known that Si substrates with a SiO₂ surface layer of a certain thickness have an advantage[1]. Namely, when the optical thickness of SiO₂ is a quarter or three quarters of the light wavelength used, the reflectance from the substrates is minimized and the contrast takes a maximum. What happens to the contrast if the number of graphene layers on the substrates increases?

We found that the reflectance can vanish for a normal incident light with a specific N (≈20) and wavelength (≈590 nm) when SiO₂ thickness is 300 nm. The zero-reflectance cannot occur without the surface layer[2], and it is inherent to a strange interference effect between the substrates and N-layer graphene. We will show experimental data that partly confirm the calculations, where the N value was determined by atomic force microscopy, and discuss how to determine the N-value from the optical contrast. 

[1] Blake et al., APL 91, 063124 (2007). [2] Kumar et al., Nanotechnology 24, 165402 (2013).