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

Abstract

The physical properties of two-dimensional (2D) materials may drastically vary with their geometric thickness profiles. Current thickness profiling methods for 2D materials 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 in both temporal and spatial domains by extending the photon shot-noise limit of a high-sensitivity common-path interferometric microscopy technique, while accurate thickness determination with ∼10 pm precision 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 geometric thickness profiles of monolayer and few-layered 2D materials (e.g., MoS 2 , MoSe 2 , and WSe 2 ) 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.