A Universal Approach to Determine the Atomic Layer Numbers in Two-Dimensional Materials Using Dark-Field Optical Contrast

Two-dimensional (2D) materials possess unique properties primarily due to the quantum confinement effect, which highly depends on their thicknesses. Identifying the number of atomic layers in these materials is a crucial, yet challenging step. However, the commonly used optical reflection method offers only very low contrast. Here, we develop an approach that shows unprecedented sensitivity by analyzing the brightness of dark-field optical images. The brightness of the 2D material edges has a linear dependence on the number of atomic layers. The findings are modeled by Rayleigh scattering, and the results agree well with the experiments. The relative contrast of single-layer graphene can reach 70% under white-light incident conditions. Furthermore, different 2D materials were successfully tested. By adjusting the exposure conditions, we can identify the number of atomic layers ranging from 1 to over 100. Finally, this approach can be applied to various substrates, even transparent ones, making it highly versatile.