Transmission-Matrix Quantitative Phase Profilometry for Accurate and Fast Thickness Mapping of 2D Materials

The physical properties of two-dimensional (2D) materials may drastically vary with their geometric thickness profiles. Current profiling methods for 2D are limited in measurement throughput and accuracy. Here, we present a novel high-speed high-precision method, termed transmission-matrix quantitative phase profilometry (TM-QPP). In TM-QPP, picometer-level optical pathlength sensitivity is enabled both temporal spatial domains by extending the photon shot-noise limit high-sensitivity common-path interferometric microscopy technique, while accurate determination ∼10 pm precision realized developing model that accounts multiple refractions reflections light at sample interfaces. Using exact profiles monolayer few-layered (e.g., MoS2, MoSe2, WSe2) mapped over wide field view within seconds contact-free manner. Notably, TM-QPP also capable spatially resolving number layers materials.