High-contrast optical microscopy of graphene sheets

In the way of making graphene an industry-friendly material, it must be mass-produced with high-quality and reduced cost over large areas. Assisted by machine-learning techniques, rapid, nondestructive and accurate determination of large graphene sheets on SiO₂ /Si substrates has been made possible in recent years by the optical microscopy method. Optimization of the substrate to achieve the maximum contrast can further extend the application of the optical microscopy method for quality control of the mass-produced graphene. Graphene/n₂ /n₃ three-layer structures, where n₂ and n₃ are refractive indices, are routinely used for identifying the number of graphene layers by optical reflection microscopy. In this paper, two analytical equations are derived that can be easily used for high-contrast optical imaging of graphene sheets without any need to resort to the cumbersome numerical methods. One of the equations is derived for choosing the best material with refractive index n₂ that when coated on a substrate with refractive index n₃ , maximizes the optical contrast. The other equation is derived for finding the best thickness of the SiO₂ layer in graphene/SiO₂ /Si structures, which are in common use for fabrication of graphene-based devices. The results are implemented in a MATLAB GUI, see Supporting Information, to assist the users in using the equations.