Independent thickness and lateral size sorting of two-dimensional materials

Two-dimensional (2D) materials possess unique thickness- and lateral-size-dependent properties. Many efforts have been devoted to obtaining 2D materials with narrow structure heterogeneity while it is still challenging to independently control their thickness and lateral size, limiting their widespread applications. Here, we develop a three-step method which achieves independent thickness and lateral size sorting of 2D materials. Taking 2D h-BN flakes as an example, their thickness and lateral size are independently sorted to different fractions with thicknesses smaller than 6 nm. In addition, the 2D h-BN flakes possess narrow distributions of both thickness and lateral size. We further develop a force field extraction method and achieve scalable size sorting of 2D h-BN, which is universal for sorting other 2D materials including MoS₂ and graphene oxide. This work reports an effective method to produce structure homogenous 2D materials and will help fundamental studies and applications of 2D materials where thickness and lateral size are of concern.