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We develop a computational database, web-apps, and machine-learning (ML) models to accelerate the design and discovery of two-dimensional (2D)-heterostructures. Using density functional theory (DFT) based lattice-parameters and electronic band-energies for 674 non-metallic exfoliable 2D-materials, we generate 226,779 possible heterostructures. We classify these heterostructures into type-I, II and III systems according to Andersons rule, which is based on the relative band-alignments of the non-interacting monolayers. We find that type-II is the most common and the type-III the least common heterostructure type. We subsequently analyze the chemical trends for each heterostructure type in terms of the periodic table of constituent elements. The band alignment data can be also used for identifying photocatalysts and high-work function 2D-metals for contacts. We validate our results by comparing them to experimental data as well as hybrid-functional predictions. Additionally, we carry out DFT calculations of a few selected systems (MoS2/WSe2, MoS2/h-BN, MoSe2/CrI3), to compare the band-alignment description with the predictions from Andersons rule. We develop web-apps to enable users to virtually create combinations of 2D materials and predict their properties. Additionally, we use ML tools to predict band-alignment information for 2D materials. The web-apps, tools and associated data will be distributed through JARVIS-Heterostructure website (https://jarvis.nist.gov/jarvish/). Our analysis, results and the developed web-apps can be applied to the screening and design applications, such as finding novel photocatalysts, photodetectors, and high-work function (WF) 2D-metal contacts.