The exceptional electronic, optical and chemical properties of two-dimensional materials strongly depend on the 3D atomic structure and crystal defects. Using Re-doped MoS2 as a model, here we develop scanning atomic electron tomography (sAET) to determine the 3D atomic positions and crystal defects such as dopants, vacancies and ripples with a precision down to 4 picometers. We measure the 3D bond distortion and local strain tensor induced by single dopants for the first time. By directly providing experimental 3D atomic coordinates to density functional theory (DFT), we obtain more truthful electronic band structures than those derived from conventional DFT calculations relying on relaxed 3D atomic models, which is confirmed by photoluminescence measurements. We anticipate that sAET is not only generally applicable to the determination of the 3D atomic coordinates of 2D materials, heterostructures and thin films, but also could transform ab initio calculations by using experimental 3D atomic coordinates as direct input to better predict and discover new physical, chemical and electronic properties.
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