Research ArticleCONDENSED MATTER PHYSICS

Determination of band offsets, hybridization, and exciton binding in 2D semiconductor heterostructures

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Science Advances  08 Feb 2017:
Vol. 3, no. 2, e1601832
DOI: 10.1126/sciadv.1601832
  • Fig. 1 Bands and hybridization in graphene-encapsulated WSe2 measured by μ-ARPES.

    (A) Optical image and (B) schematic cross section of an exfoliated WSe2 flake with monolayer (1L), bilayer (2L), and bulk regions partially capped with monolayer graphene (G) and supported by a graphite flake on a doped silicon substrate. (C) Angle-integrated spectra from each region in (A). (D) Map of the energy of peak emission, showing contrast between 1L, 2L, and bulk regions. (E) Momentum slice through the graphene K point, showing that EF is at the Dirac point. (F) Momentum slice along Γ − K (WSe2) in the 1L region. The intensity is twice-differentiated with respect to energy. Avoided crossings between the graphene valence band (white dotted line) and the monolayer WSe2 bands are indicated by white arrows. (G) Momentum slice of unprocessed (top) and twice-differentiated ARPES (bottom) along Γ − K (WSe2) in the 1L (left), 2L (middle), and bulk (right) regions. Below is the intensity twice-differentiated with respect to energy with overlaid DFT calculation (red dashed lines).

  • Fig. 2 Bands in a 2D heterostructure.

    (A) Optical image showing monolayer MoSe2 and WSe2 sheets, which overlap, with the MoSe2 on top, in an aligned heterobilayer region (H). Their boundaries are indicated with color-coded dotted lines. (B) Angle-integrated spectra in each of the three regions. (C) Map of the energy of maximum emission. (D to F) Momentum slices along Γ − K in the three regions, (top) unprocessed and (bottom) twice-differentiated, with cartoons of the structures above. The superposed dashed colored lines are DFT calculations for the MoSe2 monolayer (green), the WSe2 monolayer (red), and the commensurate heterobilayer (blue). The graphene valence band is indicated by a white dotted line. The white dashes in the lower panel of (F) indicate the valence band maxima in the MoSe2 and WSe2 monolayers and hence the valence band offset. The white dashed lines in the upper panels of (D) to (F) mark the valence band maxima in the isolated MoSe2 (M) and WSe2 (W) monolayers and in the aligned heterobilayer (H). (G) A momentum slice near Γ in another heterobilayer intentionally misaligned by about 30°. Here, only two bands are seen, indicating that the third band near Γ in the aligned heterobilayer (F) arises from commensurate domains.

  • Fig. 3 Summary of measured band parameters.

    Left: Schematic showing the definitions of parameters applicable for monolayers and aligned bilayers. Solid lines signify measured quantities, and dotted lines denote DFT calculations. Main: Graphical illustration of the positions of homologous band edges and hybridization effects. In both 2L WSe2 and heterobilayer MoSe2/WSe2, hybridization is almost undetectable at K (red) but much larger at Γ (black). Bottom: Table of quantities determined by fitting the μ-ARPES spectra shown in Figs. 1 and 2. Energies are from Lorentzian fits to the second-derivative curves. The effective masses, which are isotropic within the accuracy of the fits, are obtained from weighted parabolic fits to the above band positions in symmetric windows about K and Γ with widths of 0.08 Å− 1 and 0.15 Å− 1, respectively.

  • Fig. 4 Photoluminescence and exciton binding in aligned MoSe2/WSe2 heterobilayers.

    (A) Top: Representative photoluminescence spectrum showing peaks due to intralayer (XM and XW) and interlayer (XI) excitons (excitation of 2.33 eV at 20 μW). Bottom: Peak positions for 13 samples, implying that the energy of XI is 220 ± 20 meV below that of XM. (B) Energy diagram showing the connection between the three exciton energies and the levels derived from the MoSe2 and WSe2 conduction and valence bands at the K points.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/2/e1601832/DC1

    section S1. Fabrication of encapsulated WSe2 and additional ARPES data

    section S2. Fabrication of and further ARPES from a MoSe2/WSe2 heterobilayer structure

    section S3. Linear-scaling DFT calculations for twisted MoSe2/WSe2 heterobilayers

    section S4. Band structure of twisted monolayer MoSe2/WSe2

    section S5. ARPES of encapsulated MoSe2/WSe2 with heterotrilayer regions

    section S6. Exciton energies at lower temperatures

    section S7. DFT methodology

    fig. S1. Fabrication of a graphene, WSe2, and graphite heterostructure.

    fig. S2. Relative orientations of the graphene, WSe2, and graphite heterostructure.

    fig. S3. Fabrication of a MoSe2/WSe2 heterostructure.

    fig. S4. Relative orientations of the layers in an encapsulated MoSe2/WSe2 heterostructure.

    fig. S5. Linear-scaling DFT predictions of the band structure of the twisted MoSe2/WSe2 interface.

    fig. S6. Band structure of a twisted monolayer MoSe2/WSe2 heterostructure.

    fig. S7. Comparison between bands and hybridization in aligned and twisted heterostructures.

    fig. S8. Bands and hybridization in a MoSe2/WSe2 structure with heterotrilayer regions.

    fig. S9. Lower-temperature interlayer exciton photoluminescence.

    References (4450)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Fabrication of encapsulated WSe2 and additional ARPES data
    • section S2. Fabrication of and further ARPES from a MoSe2/WSe2 heterobilayer structure
    • section S3. Linear-scaling DFT calculations for twisted MoSe2/WSe2 heterobilayers
    • section S4. Band structure of twisted monolayer MoSe2/WSe2
    • section S5. ARPES of encapsulated MoSe2/WSe2 with heterotrilayer regions
    • section S6. Exciton energies at lower temperatures
    • section S7. DFT methodology
    • fig. S1. Fabrication of a graphene, WSe2, and graphite heterostructure.
    • fig. S2. Relative orientations of the graphene, WSe2, and graphite heterostructure.
    • fig. S3. Fabrication of a MoSe2/WSe2 heterostructure.
    • fig. S4. Relative orientations of the layers in an encapsulated MoSe2/WSe2 heterostructure.
    • fig. S5. Linear-scaling DFT predictions of the band structure of the twisted MoSe2/WSe2 interface.
    • fig. S6. Band structure of a twisted monolayer MoSe2/WSe2 heterostructure.
    • fig. S7. Comparison between bands and hybridization in aligned and twisted heterostructures.
    • fig. S8. Bands and hybridization in a MoSe2/WSe2 structure with heterotrilayer regions.
    • fig. S9. Lower-temperature interlayer exciton photoluminescence.
    • References (44–50)

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