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Correlating the three-dimensional atomic defects and electronic properties of two-dimensional transition metal dichalcogenides


The electronic, optical and chemical properties of two-dimensional transition metal dichalcogenides strongly depend on their three-dimensional atomic structure and crystal defects. Using Re-doped MoS2 as a model system, here we present scanning atomic electron tomography as a method to determine three-dimensional atomic positions as well as positions of crystal defects such as dopants, vacancies and ripples with a precision down to 4 pm. We measure the three-dimensional bond distortion and local strain tensor induced by single dopants. By directly providing these experimental three-dimensional atomic coordinates to density functional theory, we obtain more accurate electronic band structures than derived from conventional density functional theory calculations that relies on relaxed three-dimensional atomic coordinates. We anticipate that scanning atomic electron tomography not only will be generally applicable to determine the three-dimensional atomic coordinates of two-dimensional materials, but also will enable ab initio calculations to better predict the physical, chemical and electronic properties of these materials.

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Fig. 1: Scanning atomic electron tomography.
Fig. 2: 3D atomic coordinates in Re-doped MoS2 and 3D bond distortion induced by single dopants.
Fig. 3: Measurements of 3D atomic displacements and the full strain tensor in Re-doped MoS2.
Fig. 4: Measurements of the local strain tensor induced by single Re dopants.
Fig. 5: Electronic band structures calculated from experimental coordinates and PL measurements.

Data availability

The raw and processed experimental data and all the MATLAB source codes for the image reconstruction and data analysis will be freely available at immediately after this work is published. The experimental 3D atomic coordinates of the two data sets will be deposited in the Materials Data Bank (MDB,, with their MDB IDs provided in Supplementary Table 1.


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We thank M. F. Chisholm for support of the STEM experiment and C. Ophus for help with data analysis. This work was primarily supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), Division of Materials Sciences and Engineering under award DE-SC0010378. It was also supported by STROBE: a National Science Foundation (NSF) Science and Technology Center under award DMR-1548924, by an Army Research Office MURI grant on Ab-Initio Solid-State Quantum Materials: Design, Production and Characterization at the Atomic Scale, and by the Division of Materials Research of the US NSF under award DMR-1437263. P.M.A. acknowledges support from the Air Force Office of Scientific Research under award FA9550-18-1-0072. The STEM experiment was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility.

Author information




J.M. conceived and directed the project. Y.G. and P.M.A. synthesized the Re-doped MoS2 sample and measured the PL and Raman spectra, S.Y., X.T., D.S.K., J.C.I. and J.M. planned and/or performed the STEM experiments and X.T., D.S.K., J.M., Yongsoo Yang, Yao Yang and Y. Yuan discussed and/or performed 3D reconstruction, atom tracing and data analysis. C.J.C., B.D., P.N., D.S.K., X.T. and J.M. discussed and/or carried out DFT calculations. J.M., X.T. and D.S.K. wrote the manuscript with help and/or comments from all authors.

Corresponding author

Correspondence to Jianwei Miao.

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The authors declare no competing interests.

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Extended data

Extended Data Fig. 1 3D atomic coordinates and crystal defects in data set 1.

a, Top view of the 3D reconstruction of data set 1. The inset shows the side view of MoS2 (panel 1), MoS2 with a Re dopant and a S vacancy (panel 2), and MoS2 with 3 S vacancies (panel 3), where arrows indicate the vacancies. Scale bar, 1 nm and scale bar (inset), 2 Å. b, 3D atomic model of the bounded region in (a), consisting of 1381 S, 686 Mo and 21 Re atoms with 15 S vacancies.

Extended Data Fig. 2 3D atomic coordinates and crystal defects in data set 2.

a, Top view of the 3D reconstruction. Scale bar, 1 nm. b, 3D atomic model of the bounded region in (a), consisting of 1083 S, 531 Mo and 16 Re atoms with 4 S vacancies. c, 3D plot of the Mo/Re layer showing atomics-scale ripples, where the dots represent the Mo/Re atoms. d, Histogram of the distribution of the z coordinates of the Mo/Re atoms in data set 1 with a standard deviation (σ) of 0.16 Å.

Extended Data Fig. 3 Least square fitting to determine the 3D coordinates of the Re and Mo atoms.

a, The x and y coordinates of the Re and Mo atoms were localized from the aligned projections of each data set. b, From these 2D coordinates, the tilt angles were calibrated and the 3D coordinates of the Re and Mo atoms were determined for each data set. The 3D atomic coordinates are consistent with those obtained by sAET with a RMSD of 2 pm and 13 pm for Mo (c) and Re (d) atoms, respectively, where a total of 1176 Mo and 32 Re atoms was used in the statistical analysis. Scale bar, 1 nm.

Extended Data Fig. 4 Multislice simulation results.

a, The experiment image versus the multislice image of the same region. b and c, The intensity profiles corresponding to labelled regions 1 and 2 in (a), where the high, medium and low intensity peaks represent the Re, Mo and S atoms, respectively.

Extended Data Fig. 5 Numerical simulations on the sAET reconstruction of a MoSe2-WSe2 heterostructure with moiré patterns.

a, Top view of the 3D reconstruction of double-layered heterostructure from 15 multislice projections with a double tilt range from −25° to +25°. b, Top view of 3D atomic model obtained from (a), where a 5˚ rotational mismatch between the top and bottom layers is visible. c, 6 atomic layers of the 3D reconstruction in the square region in (a), where atomic defects in each layer are labelled as blue circles. d, 6 atomic layers of the 3D model in the square region in (b), where traced defects are shown as red circles. The RMSD between the sAET reconstruction and the original atomic model is 8 pm, 5 pm and 13 pm for Mo, W and Se atoms, respectively.

Extended Data Fig. 6 Full 3D strain tensor of data set 1 (a) and data set 2 (b).

The six strain components are shown from left to right columns, and the three atomic layers are displayed from top to bottom. Scale bar, 2 nm.

Extended Data Fig. 7 Strain tensor maps of εxx (a), εyy (b), εzz (c) of the Mo/Re layer in the four supercells used in DFT calculations.

The four 6×6×1 supercells labelled with (a), (b), (c) and (d) correspond to those in Fig. 5e. Scale bar, 2nm.

Supplementary information

Supplementary Information

Supplementary methods, refs. 59–63, Tables 1 and 2 and Figs. 1–6.

Supplementary Video 1

3D sAET reconstruction of the Re-doped MoS2 monolayer (data set 1), showing the different intensity distribution of the Re, Mo and S atoms as well as the S vacancies.

Supplementary Video 2

3D atomic model of the Re-doped MoS2 monolayer (data set 1) determined by sAET, consisting of 1381 S (in yellow), 686 Mo (in blue), 21 Re atoms (in black) and 15 S vacancies (in pink). Compared to an ideal MoS2 atomic model (in lighter colors), the experimental model shows 3D crystal defects, atomic displacements and full strain tensors of the 2D material. The local strains induced by single Re dopants are also visible.

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Tian, X., Kim, D.S., Yang, S. et al. Correlating the three-dimensional atomic defects and electronic properties of two-dimensional transition metal dichalcogenides. Nat. Mater. 19, 867–873 (2020).

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