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The physical properties of two-dimensional (2D) materials may drasticallyvary with their thickness profiles. Current thickness profiling methods for 2Dmaterial (e.g., atomic force microscopy and ellipsometry) are limited inmeasurement throughput and accuracy. Here we present a novel high-speed andhigh-precision thickness profiling method, termed Transmission-MatrixQuantitative Phase Profilometry (TM-QPP). In TM-QPP, picometer-level opticalpathlength sensitivity is enabled by extending the photon shot-noise limit of ahigh sensitivity common-path interferometric microscopy technique, whileaccurate thickness determination is realized by developing atransmission-matrix model that accounts for multiple refractions andreflections of light at sample interfaces. Using TM-QPP, the exact thicknessprofiles 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 offew-layered 2D materials.

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