LAUSR

It is known that complex growth environments often induce inhomogeneity in two-dimensional (2D) materials and significantly restrict their applications. In this paper, we proposed an efficient method to analyze the inhomogeneity of 2D materials by combination of Raman spectroscopy and unsupervised k-means clustering analysis. Taking advantage of k-means analysis, it can provide not only the characteristic Raman spectrum for each cluster but also the cluster spatial maps. It has been demonstrated that inhomogeneities and their spatial distributions are simultaneously revealed in all CVD-grown MoS2, WS2 and WSe2 samples. Uniform p-type doping and varied tensile strain were found in polycrystalline monolayer MoS2 from the grain boundary and edges to the grain center (single crystal). The bilayer MoS2 with AA and AB stacking are shown to have relatively uniform p-doping but a gradual increase of compressive strain from center to the periphery. Irregular distribution of 2LA(M)/E2g1 mode in WS2 and E2g1 mode in WSe2 is revealed due to defect and strain, respectively. All the inhomogeneity could be directly characterized in color-coded Raman imaging with correlated characteristic spectra. Moreover, the influence of strain and doping in the MoS2 can be well decoupled and be spatially verified by correlating with the clustered maps. Our k-means clustering Raman analysis can dramatically simplify the inhomogeneity analysis for large Raman data in 2D materials, paving the way towards direct evaluation for high quality 2D materials.