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 thickness profiles. Current thickness profiling methods for 2D material (e.g., atomic force microscopy and ellipsometry) are limited in measurement throughput and accuracy. Here we present a novel high-speed and high-precision thickness profiling method, termed Transmission-Matrix Quantitative Phase Profilometry (TM-QPP). In TM-QPP, picometer-level optical pathlength sensitivity is enabled by extending the photon shot-noise limit of a high sensitivity common-path interferometric microscopy technique, while accurate thickness determination is realized by developing a transmission-matrix model that accounts for multiple refractions and reflections of light at sample interfaces. Using TM-QPP, the exact thickness profiles of monolayer and few-layered 2D materials (e.g., MoS2, MoSe2 and WSe2) are mapped over a wide field of view within seconds in a contact-free manner. Notably, TM-QPP is also capable of spatially resolving the number of layers of few-layered 2D materials.