Backside Absorbing Layer Microscopy: Monolayer Counting in 2D Crystal Flakes

The properties of two-dimensional (2D) material stacks critically depend on the number of monolayers (m) in the stack. It is therefore important to quantify this number, which is a local quantity since 2D stacks are essentially heterogeneous. Optical interferential techniques based on contrast-enhancing surfaces may be sensitive enough to visualize m variations but the experimental determination of m requires heavy and unstable comparisons with multiparameter numerical models. Focusing on the recent backside absorbing layer microscopy, the most sensitive to date among interferential techniques, a self-calibrating method is demonstrated allowing instantaneous monolayer counting all over the sample surface which does not require the knowledge of the instrumental parameters, the sample or ambient refractive indices or the detailed structure of the contrast-enhancing layer. This method is introduced step by step using examples of hexagonal boron nitride (hBN) stacks with increasing complexity. Exact monolayer counting up to 36 hBN monolayers is obtained using basic image analysis.