Research ArticleAPPLIED PHYSICS

Electrically tunable single- and few-layer MoS2 nanoelectromechanical systems with broad dynamic range

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Science Advances  30 Mar 2018:
Vol. 4, no. 3, eaao6653
DOI: 10.1126/sciadv.aao6653
  • Fig. 1 Nanomechanical resonances in atomically thin MoS2 drumhead membranes: Excitation, detection, tuning, and DR.

    (A) Illustration of ultrasensitive optical interrogation of the motions of drumhead-structured MoS2 resonators. A 633-nm red laser is used to probe both the undriven thermomechanical motions and the driven vibrations excited by an amplitude-modulated 405-nm blue laser. (B) Schematic of the measurement system and scanning electron microscopy images of arrays of single- and few-layer MoS2 resonators with different drumhead diameters. Scale bars, 1 μm. Two electrical configurations (① and ②) are available, respectively, for driven resonance and undriven thermomechanical noise floor measurements. BS, beam splitter; LPF, long-pass filter; PD, photodetector. (C) Illustration of DR for a generic transducer. (D) Two types of frequency tuning (fres versus Vg) curves expected in NEMS resonators with electrostatic gate tuning.

  • Fig. 2 Resonance characteristics of 1L, 2L, 3L, and 4L MoS2 membranes vibrating at very high frequencies.

    (A to D) Measured nanomechanical resonance (left panel) and PL (right panel) for 1L to 4L MoS2 resonators with diameter D = 1.5 μm. The vertical dashed lines in right panels of (A) to (D) indicate the indirect interband transition in 2L to 4L MoS2 crystals, which are at lower energies than the direct interband transition (which is the only visible peak in the PL data from 1L MoS2). Insets: Optical images. Scale bars, 2 μm. Both undriven thermomechanical resonances [as in (A) and (C)] and optically driven resonances [as in (B) and (D)] are shown. Red dashed lines in resonance plots are fittings to a finite Q harmonic resonator. a.u., arbitrary units.

  • Fig. 3 Very high frequency MoS2 nanoelectromechanical resonators with great electrical tunability.

    (A) Optical image of a 2L MoS2 resonator (D ≈ 1.5 μm) contacted by metal electrode. (B) Schematic of electrical tuning and driving of a MoS2 NEMS resonator. (C) Gate tuning of optically driven resonance of a 2L MoS2 resonator (D ≈ 1.5 μm), showing measured frequency response at 41 different Vg values, with data from Vg = 0, ±10, and ±20 V highlighted as examples. Colored dots represent measured peak amplitudes (and their projections onto different planes) under different Vg values. (D) Response of an electrically driven 2L MoS2 resonator (D ≈ 1.5 μm) under increasing driving amplitudes. (E) Gate tuning of electrically driven resonance of the same MoS2 resonator as in (D), with the same conventions as in (C). (F) Gate tuning of quality (Q) factors for measured resonances in (C) and (E).

  • Fig. 4 Discovering nanomechanical nonlinearity and very large DR in 1L, 2L, and 3L MoS2 resonators.

    (A) Duffing response measured from a 1L MoS2 resonator (D ≈ 1.5 μm). Solid curve: Experimental data showing hysteresis. Dashed curves: Theoretical frequency response curve of a Duffing resonator. The backbone curve, response curve under critical driving, and the critical amplitude ac are highlighted. (B) Nonlinear response of a 2L MoS2 resonator (D ≈ 1.5 μm) with increasing driving amplitude. The backbone curve and the level of ac are illustrated. (C) Measured DR of a 1L MoS2 resonator (D ≈ 1.5 μm). The DR for linear operation (green zone) is determined by the measurement noise floor and the onset of nonlinearity [0.745ac, the 1-dB compression point below ac (16)]. The DR for nonlinear operation (red zone) is limited by the fracture strength of the material. (D) Measured DR for a MoS2 resonator (3L, D ≈ 1.5 μm), with the same conventions in (C).

  • Fig. 5 Scaling of DR and resonance frequency in atomically thin MoS2 resonators.

    (A) Intrinsic DR of 1L (green), 2L (magenta), 3L (blue), and 4L (black) devices (D = 1.5 μm) as a function of measured critical amplitude ac and fres3/Q. (B) Resonance frequency scaling with device diameter D and MoS2 thickness t. Theory is shown as lines, and measured data points are sphere symbols. Dark yellow lines: fres versus D for 1L (0.7 nm) MoS2 membrane with surface tension γ = 0.5 and 0.1 N/m. Gray line: fres versus D for t = 100 nm MoS2 plate. Curves: fres versus t for tensioned MoS2 plate resonators. For D ≈ 0.5 μm (magenta curves) and 6 μm (red curves), calculations are shown for γ = 0.5, 0.2, and 0.1 N/m. For devices with 1.5-μm diameter (blue curves), additional tension values of γ = 0.05, 0.02, and 0.01 N/m are also shown. Spherical symbols show the measured fres values for 1L (green), 2L (magenta), 3L (blue), and 4L (black) devices (D ≈ 1.5 μm). Data for thicker devices with D ≈ 6 μm (red) are taken from the study of Lee et al. (37).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/3/eaao6653/DC1

    section S1. Device fabrication

    section S2. Optical interferometry measurement system

    section S3. Electrical tuning of device resonance

    section S4. Power handling, mass sensitivity, and frequency stability

    section S5. Nanomechanical tuning and sensing of device strain and bandgap

    section S6. Measuring nonlinearity and estimating critical amplitude

    section S7. Translation of voltage fluctuations into frequency instability

    section S8. Comparison of DR in 1D and 2D NEMS resonators

    fig. S1. Calculated displacement versus reflectance values for 1L to 3L MoS2 resonators.

    fig. S2. Calculated displacement-to-reflectance responsivity (ℜRef) and measured displacement-to-voltage responsivity (ℜV) values for 1L to 3L MoS2 resonators.

    fig. S3. Thermomechanical resonance with qualify (Q) factor exceeding 1000.

    fig. S4. Thermomechanical vibrations with distinct signatures of digitized thicknesses (number of layers) as a function of fres and Q.

    fig. S5. Electrical gate turning of higher-mode resonances.

    fig. S6. FOM for frequency tuning: Comparison across reported 2D NEMS devices.

    fig. S7. Schematic for calculating the total surface area on a deformed membrane.

    fig. S8. Measured DR in 1D and 2D resonators operated at room temperature.

    fig. S9. Resonance frequency scaling with device diameter D and MoS2 thickness t.

    table S1. FOM for frequency tuning.

    table S2. List of devices with measured nonlinear characteristics.

    table S3. DRs measured in 1D and 2D resonators.

    References (6880)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Device fabrication
    • section S2. Optical interferometry measurement system
    • section S3. Electrical tuning of device resonance
    • section S4. Power handling, mass sensitivity, and frequency stability
    • section S5. Nanomechanical tuning and sensing of device strain and bandgap
    • section S6. Measuring nonlinearity and estimating critical amplitude
    • section S7. Translation of voltage fluctuations into frequency instability
    • section S8. Comparison of DR in 1D and 2D NEMS resonators
    • fig. S1. Calculated displacement versus reflectance values for 1L to 3L MoS2 resonators.
    • fig. S2. Calculated displacement-to-reflectance responsivity (ℜRef) and measured displacement-to-voltage responsivity (ℜV) values for 1L to 3L MoS2 resonators.
    • fig. S3. Thermomechanical resonance with qualify (Q) factor exceeding 1000.
    • fig. S4. Thermomechanical vibrations with distinct signatures of digitized thicknesses (number of layers) as a function of fres and Q.
    • fig. S5. Electrical gate turning of higher-mode resonances.
    • fig. S6. FOM for frequency tuning: Comparison across reported 2D NEMS devices.
    • fig. S7. Schematic for calculating the total surface area on a deformed membrane.
    • fig. S8. Measured DR in 1D and 2D resonators operated at room temperature.
    • fig. S9. Resonance frequency scaling with device diameter D and MoS2 thickness t.
    • table S1. FOM for frequency tuning.
    • table S2. List of devices with measured nonlinear characteristics.
    • table S3. DRs measured in 1D and 2D resonators.
    • References (68–80)

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