Research ArticleMATERIALS SCIENCE

Building and exploring libraries of atomic defects in graphene: Scanning transmission electron and scanning tunneling microscopy study

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Science Advances  27 Sep 2019:
Vol. 5, no. 9, eaaw8989
DOI: 10.1126/sciadv.aaw8989
  • Fig. 1 STEM data: Original and processed by neural networks.

    (A) STEM overview image. Brighter areas typically correspond to amorphous Si-C regions, from which Si atoms can be dispersed into clean graphene lattice, leading to various Si defect structures (in terms of number of Si atoms and their bonding to each other and to nearby lattice atoms). (B) Results of applying a defect sniffer (deep neural network followed by density-based spatial clustering) to data in (A). White markers show regions of interest as identified by a defect sniffer. Notice that it ignores amorphous Si-C regions and returns information on the location of point Si defects, only (C) 2 nm by 2 nm area cropped around one of the identified defects [white box in (B)]. This cropped image serves as an input to atom finder model. (D) The output of an atom finder network for the image in (C), where red blobs correspond to C lattice atoms and a green blob is associated with Si impurity.

  • Fig. 2 Evaluation of accuracy in finding the atomic positions via a deep learning model for different levels of noise.

    (A) The deviation of the predicted positions (average value for all atoms in the image) from the ground truth positions of atoms for different combinations of noise (λ′) and blurring (σ′). The λ′ and σ′ are the scaled parameters of Poisson and Gaussian distributions, respectively. See the Supplementary Materials for the details and code of how the noisy data were created and analyzed. (B) Simulated image of graphene lattice associated with the red cross in (A). (C) Same image overlaid with atomic coordinates. Different colors of circular markers show different degrees of atomic positions displacement from ground truth coordinates. (D) The histogram showing atomic displacements for every atomic position displayed in (C). Most of the deviations are below 10 pm, which is within instrumental uncertainty for atomic position extraction.

  • Fig. 3 Constructing libraries of defects from STEM data on graphene with Si impurities via deep learning–based analysis of raw experimental data.

    (A and B) Defects containing a single three-fold coordinated Si atom (count, 465) (A) and a single four-fold coordinated Si atom (count, 16) (B). (C and D) Histograms of Si─C bond lengths (C) and Si─C bond angles (D) for three-fold Si defect. (E and F) Examples of distorted threefold Si defect located next to a multivacancy (E) and at topological defect (F). The number of distorted (SD s = ( ∑ dx2/n)1/2 in C─Si─C bond angles above 15) and undistorted three-fold Si defects was 231 and 234, respectively.

  • Fig. 4 Atomic defects containing two and more Si atoms.

    (A to F) Defects with two Si atoms. Si dimer structures with each Si having two C in its first coordination sphere (count, 6) (A and D); one Si having three C atoms and another one having two C atoms (count, 4) (B); each Si having two C atoms plus one “shared” C atom (count, 3) (C); each Si connected to three C atoms (count, 5) (F); nondimer structure, where two Si atoms are connected via C atom (count, 3) (E). (G to I) Defects with three and more Si atoms: three Si (count, 50) (G), four Si (count, 6) (H), and five or more Si (count, 56) (I).

  • Fig. 5 STM experiment on the same sample.

    (A) Large-scale STM image of a relatively large area of the graphene sample from the STEM experiment. (B) Magnified view of an atomic defect highlighted by the white rectangle in (A). Tunneling conditions Vbias = 0.1 V and Isetpoint = 55 pA.

  • Fig. 6 Comparison of STM data on point impurities with DFT calculations.

    (A) Experimental STM data on a single impurity obtained under tunneling conditions Vbias = 0.1 V and Isetpoint = 55 pA. (B) DFT-simulated STM images of Si1C3 defect for two bands below (EV1 and EV2) and above (EC1 and EC1) the Fermi level. (C) Experimental STM data on a dimer-like impurity obtained under tunneling conditions Vbias = 0.3 V and Isetpoint = 55 pA. Inset shows a line profile along the A and B points. (D) DFT-simulated STM images of Si2C6 defect for two bands below (EV1 and EV2) and above (EC1 and EC1) the Fermi level.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/9/eaaw8989/DC1

    Fig. S1. DFT-simulated distribution of electronic charge density for Si1C4 defect.

    Fig. S2. DFT-simulated distribution of electronic charge density for Si2C4 defect.

    Fig. S3. DFT-simulated distribution of electronic charge density for Si2C5 (type 1) defect.

    Fig. S4. DFT-simulated distribution of electronic charge density for Si2C5 (type 2) defect.

    Fig. S5. Strain analysis for S1C3 defect.

    Fig. S6. More complex defect structures observed in the STM experiment on STEM sample of graphene.

    Jupyter notebook (atom-finding accuracy versus noise)

  • Supplementary Materials

    The PDF file includes:

    • Fig. S1. DFT-simulated distribution of electronic charge density for Si1C4 defect.
    • Fig. S2. DFT-simulated distribution of electronic charge density for Si2C4 defect.
    • Fig. S3. DFT-simulated distribution of electronic charge density for Si2C5 (type 1) defect.
    • Fig. S4. DFT-simulated distribution of electronic charge density for Si2C5 (type 2) defect.
    • Fig. S5. Strain analysis for S1C3 defect.
    • Fig. S6. More complex defect structures observed in the STM experiment on STEM sample of graphene.

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    Other Supplementary Material for this manuscript includes the following:

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