SUPPLEMENTARY INFORMATION DOI: 10.1038/NNANO.2014.309 Observation of piezoelectricity in free-standing monolayer MoS 2 Authors: Hanyu Zhu 1,, Yuan Wang 1,, Jun Xiao 1, Ming Liu 1, Shaomin Xiong 1, Zi Jing Wong 1, Ziliang Ye 1, Yu Ye 1, Xiaobo Yin 1,2 and Xiang Zhang 1,2,* Supplementary Fig. 1: A side view and a tilted view of a single layer of MoS 2. Supplementary Fig. 2: Raman and photoluminescence spectrum of few-layer MoS 2. Supplementary Fig. 3: Polarization dependent second harmonic mapping of a large exfoliated monolayer. Supplementary Fig. 4: Angular dependence of second harmonic generation from MoS 2. Supplementary Fig. 5: Schematics of sample fabrication. Supplementary Fig. 6: Non-contact AFM imaging of freestanding membrane. Supplementary Fig. 7: Finite element calculation of the mechanical response of suspended MoS 2 devices. Supplementary Fig. 8: Simulation of the angular dependence of the piezoelectric response in MoS 2 devices. Supplementary Method: Electrical setup NATURE NANOTECHNOLOGY www.nature.com/naturenanotechnology 1
Supplementary Fig. 1: A side view and a tilted view of a single layer of MoS 2. a, A side view and b, a tilted view of a single layer of MoS2 consisting of S-Mo-S stacking. From the side view each unit cell consists of two sulphur atoms (yellow) and one molybdenum atom (blue), and therefore the crystal breaks the inversion symmetry in XY plane but preserves mirror symmetry in Z direction.
Supplementary Fig. 2: Raman and photoluminescence spectrum of few-layer MoS 2. a, Raman spectrum and b, Photoluminescence of 1-, 2-, 3-layer MoS 2. c, the comparison of Raman spectrum and d, photoluminescence of a monolayer before and after suspension. Our MoS 2 flakes were obtained by exfoliating natural 2H crystals (SPI Supplies ) on polymer stacking, which consisted of 270-nm-thick poly-methyl-methacrylate (PMMA, 950k in anisole from Microchem), 50nm water-soluble polymer (aquasave from Mitsubishi Rayon America INC.) and another PMMA layer on top of silicon substrate. The top PMMA layer is released in water and transferred onto hydrogen silsesquioxane (450nm FOX -15 from Dow Corning) spin-coated on silicon substrate with 270 nm thermal oxide. The thickness of the flake was inferred from Raman spectrum and photoluminescence S1, S2.
To speed up searching monolayer samples, scanning photoluminescence (PL) microscopy (Nikon Eclipse TE2000, excited at 488nm) was employed to provide both the total intensity of PL (cut off with 650nm long-pass filter) that unambiguously highlights monolayer from thicker ones (the signal of which is more than 5 times stronger than bilayers), and the intensity of reflection that gives distinctive contrast for up to 5-layer flakes. We used both Raman and photoluminescence (PL) spectra to verify that fabrication does not degrade the quality of MoS 2 crystal. The position and linewidths of Raman peaks do not change before and after fabrication. The PL spectrum peak after suspension is boosted by 4 times with a smaller FWHM of 20 nm, in agreement with the results of Mak et al S3.
Supplementary Fig. S3: Second harmonic generation from MoS 2 devices. a, Optical image of the device. b, Angular dependence of SHG intensity, where θ is the angle between the polarization of incident light and the direction of electric field in piezoelectric measurement. The maximum of sinusoidal fitting was θ=2, meaning the E field was parallel to the armchair direction in the crystal. We measured the azimuthal angle by second harmonic generation (SHG), since the nonlinear susceptibility χ (2) of a material has the same symmetry as its piezoelectric constant. The MoS 2 film was pumped with a pulsed laser centred at 1340 nm and SHG signals were collected around 670 nm. The polarization of pumping light and signal detection was fixed at the same direction while the sample was rotated. The measured angular dependence of SHG intensity confirmed that the applied electric field through electrodes was aligned with the armchair direction of the crystal. Our exfoliation method on PMMA substrate can routinely yield large flakes with length exceeding 50 μm. For long monolayers we obtained, we also used SHG mapping to verify that they were single crystal.
Supplementary Fig. S4: Polarization dependent second harmonic mapping of a large exfoliated monolayer. a, The x-polarized SHG emission and b, y-polarized SHG emission. The uniformity of the SHG intensity and the absence of boundaries within the domain demonstrated that the membrane has one single orientation.
Supplementary Fig. S5: Schematics of sample fabrication. a, MoS 2 flakes were exfoliated on top of PMMA/Aquasave/PMMA stacking which could be released by water immersion. b, The MoS 2 /PMMA stacking was transferred onto HSQ and exposed by electron beam. c, The PMMA layer was developed to open the windows for electrodes. d, MoS 2 flakes were suspended after lift-off of Au and development of HSQ. Electrodes and pillars of the MoS 2 devices were patterned with electron beam lithography (EBL, 2000μC/cm 2 at 50keV). A small projection outside the electrode was added to mark the centre of the film. After exposure the chips were developed in MIBK:IPA 1:3 solution and metalized with Cr/Ti/Au (0.5/5/90 nm), during which the HSQ layers were kept intact underneath PMMA. Then the samples were lifted off in acetone, transferred to aquatic KOH/NaCl solution (0.25mol/L and 0.5mol/L respectively) for thorough development of HSQ S4 and dried using critical point dryer. Finally the chips were wirebonded (dual in-line ceramic package, DIP24) and connected to voltage sources. The
fabrication preserved the quality of the film as inspected through Raman spectrum, photoluminescence and SEM.
Supplementary Fig. S6: Non-contact AFM imaging of freestanding membrane. a, SEM image of the hemispherical tip. The white dash line was used to determine the radius of the tip. Scale bar: 200 nm. b, Tapping image of freestanding membrane between Au electrodes. The flatness of surface suggested tensile stress inside the film. Scale bar: 500 nm; color bar: 0-200 nm. c, Cross-section of device obtained under tapping mode from the projection on the side of one electrode across the membrane to the opposite electrode. AFM images and force curves were acquired from Dimension 3100 scanning probe microscope with home-made hemispherical tips based on silicon nitride contact probes. The spring constant of cantilevers was chosen as a balance between high force-sensitivity (soft cantilever) and sufficient indentation (hard cantilever). To reduce the peak stress in the indented membrane and the tip, the radius of tips was increased to 200 nm by uniformly depositing Al 2 O 3 through atomic layer deposition (ALD). 20-nm Palladium was evaporated over the cantilever to provide conductivity. Finally the cantilevers were inspected with SEM and calibrated against a standard cantilever. The resonant frequency (85 khz) was doubled after deposition due to increased stiffness of cantilever (1.0 N/m), allowing the tip to work also in tapping mode.
The freestanding membrane was first imaged using tapping mode. To avoid disturbing the fragile free edge we controlled the tip to approach the centre of membrane from the side of the clamp marked with a projection. A cross-section image was obtained at the position of projection to verify suspension. Flat image indicates good clamping and absent of defects, while loose or broken membrane can cause sharp oscillation of height profile under the same scanning condition. We found the distance between clamping as seen by AFM image agrees with our EBL mask design. The force characterization was performed after the position of the tip across the trench was fixed within 100 nm from the centre. The position along the trench was determined by the projection to be within 500 nm from the film centre. Before indentation, the setup was stabilized for 12 hours until the relative drift was below 2 nm/min. The scanning speed of Z-piezo tube was 10 nm/s to ensure quasi-static measurement.
Supplementary Fig. 7: Finite element calculation of the mechanical response of suspended MoS 2 devices. a, The numerical factors of the load-indentation equation were determined by finite element calculation of the load-indentation curve. b, Determination of the numerical factor of the piezoelectric response. The change of load was proportional to the perturbation of piezoelectric stress. We use Abaqus CAE to calculate the mechanical and piezoelectric response of the film. Theory of elastic mechanics in membrane dictates that the load-indentation curve has the form S5 : F = C 1 σ 2D d + C 2 (ν)y 2D d 3 /L 2 (Eq. S1) where C 1 and C 2 are two geometric-dependent numerical factors. Here we took the Poisson s ratio ν = 0.25 since the different values of ν among literature would affect the results by less than ±5%. Thus only the values of C 1 and C 2 needed to be determined by finite element calculation.
The model was built with a shell domain and calculated by stationary solver. The displacement of one pair of edges (along y-axis) was set to zero while the other pair was left free. Isotropic Young s modulus and pre-stress were assigned to the membrane. The shell was indented by a hemisphere with a radius of 200 nm at the centre of the domain. The calculated load-indentation curve and its fitting agreed very well with the linear elastic theory. We used the decoupling approximation to calculate the piezoelectric response S6. The distribution of electric field in the membrane was determined by the distribution of resistance rather than capacitance, since the RC constant in our devices was estimated to be ~ 1 µs while the period of voltage oscillation was ~ 100 µs. The piezoelectric stress was included in the calculation through a uniform anisotropic change of pre-stress. With the values of pre-stress and Young s modulus derived from experimental indentation curve, we calculated the piezoelectrically induced load. The load was proportional to the anisotropic stress, as expected from small perturbation, and approximately to the depth of indentation. Since the load was primarily determined by the stress of the film close to the tip, the numerical coefficients in Eq. 3 and Eq. 4 approached the values of infinitely wide film when the width was much larger than the electrode distance, which was also confirmed in our FEA calculation. The values of these coefficients were derived from the simulation results of 6-by-2-µm membrane, which was our average sample geometry. The deviation of load and piezoelectric response for our samples with different geometry (width ranging from 4 μm to 10 μm) were found to be smaller than 5% and 15%, respectively, which are
the primary sources of error. They are insensitive to the geometry because the reaction force from the clamps is concentrated near the centre.
Supplementary Fig. S8: Simulation on angular dependence of piezoelectric response of MoS 2, showing the 3-fold rotational symmetry of piezoelectric response. The amplitude ranges from -1 to +1. When crystal is rotated by an angle θ with respect to the electric field, the piezoelectric stress in the original coordinate system is transformed accordingly: 11 21 12 cos 3 sin 3 e 11E1 (Eq. S2) 22 sin 3 cos 3 We simulated the piezoelectric force as a function of angle at fixed depth and electric field by defining the pre-stress accordingly. The result bears the expected 3-fold symmetry, with maximum of amplitude at 0 and minimum at 30. The perturbation of shear stress has no effect on the load because of the mirror symmetry in the XZ and YZ plane of our device. After reflection transformation the shear stress reverses sign, while the reaction force on the tip in Z direction should not change sign. Therefore the change of load on the probe from shear stress term must be zero, and then the piezoelectric response comes only from normal stress. In the same way we found the
reaction force on the tip in X and Y direction must be zero from all components of stress. Thus in the experiment the deflection of cantilever could be attributed to Δz without Δx or Δy components. As long as the sign of e 11 is given, our approach can unambiguously distinguish a crystal from its inverse structure without resorting to TEM-resolution techniques. It is challenging to transfer the fabricated devices to be inspected by TEM, but if this can be done, one could experimentally verify the sign of e 11.
Supplementary Method: Electrical setup Square wave was applied to the electrode as the source of electromechanical modulation. The reference signal was generated by the internal oscillator of lock-in amplifier (Stanford Research 830) and fed into delay generator (Stanford Research DG535) that provided two out-of-phase square waves with tunable amplitude and DC offset to the opposite electrodes of the MoS 2 device. The induced piezoelectric force in the form of bending of cantilever was detected by the photodiode of the AFM as shift of output voltage, which was monitored by the lock-in amplifier through signal access module (Nanoscope SAM). The force sensitivity S was first calibrated with a force gauge (GlobalSpec ) at near-zero frequency. Then the tip was held above a conducting surface with alternating potential that electrostatically drove the cantilever with a constant force, thus yielding the frequency characteristics of the system. Due to the electronics of our AFM setup (a nominal 19 khz low-pass filter in the SAM channel) the amplitude and phase read-outs must be adjusted to recover the raw data. At our operating frequency ~10 khz, the real amplitude is 15% higher than the read-out and the real phase is 30 in advance. The displacement sensitivity is calibrated similarly. The relative errors of force sensitivity (from the gauge) and displacement sensitivity (from the piezo tube) were below 5%. Since the resonant frequency of the tip is much higher than the oscillation of the electric field, the mechanical response of the tip and the film can be treated quasi-static: ΔF = (k t + k f )Δz (Eq. S3)
where k t is the stiffness of the cantilever, k f is the spring constant of the film, and z is the bending of cantilever. The electrically induced force has several contributions, but only the signal proportional to the applied voltage is read by lock-in amplifier at the same frequency S6 : ΔF = V ac (d eff k f + A(V f -V s ) + B(V t -V av ) ) (Eq. S4) where V ac is the voltage across the film, d eff is the effective piezoelectric constant of the film (see next section), V f -V s is the bias between the film and the substrate, V t -V av is the bias between the cantilever and the average potential of the device. Factor A and B are related to the capacitance between the film and the substrate, and between the cantilever and the device respectively. To eliminate the third term the tip bias V 1 is adjusted such that force signal is reduced below noise lever when the tip approaches the film. Then the second term is eliminated by adjusting the substrate bias V 2 so that force signal is reduced below noise level when the tip adheres with the film yet without indentation. Therefore during indentation the observed force signal can only come from piezoelectric response of the film.
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