Energy scavenging based on a single-crystal PMN-PT nanobelt

Self-powered nanodevices scavenging mechanical energy require piezoelectric nanostructures with high piezoelectric coefficients. Here we report the fabrication of a single-crystal (1 − x)Pb(Mg1/3Nb2/3)O3 − xPbTiO3 (PMN-PT) nanobelt with a superior piezoelectric constant (d33 = ~550 pm/V), which is approximately ~150%, 430%, and 2100% of the largest reported values for previous PMN-PT, PZT and ZnO nanostructures, respectively. The high d33 of the single-crystalline PMN-PT nanobelt results from the precise orientation control during its fabrication. As a demonstration of its application in energy scavenging, a piezoelectric nanogenerator (PNG) is built on the single PMN-PT nanobelt, generating a maximum output voltage of ~1.2 V. This value is ~4 times higher than that of a single-CdTe PNG, ~13 times higher than that of a single-ZnSnO3 PNG, and ~26 times higher than that of a single-ZnO PNG. The profoundly increased output voltage of a lateral PNG built on a single PMN-PT nanobelt demonstrates the potential application of PMN-PT nanostructures in energy harvesting, thus enriching the material choices for PNGs.


Section 2: Importance of PMN-PT nanostructures
The piezoelectric coefficient (d33), which represents the ability of piezoelectric materials to convert mechanical deformation into an electric signal, plays a key role in the device performance. BaTiO3 and NaNbO3 based piezoelectric nanocomposites have limited output voltage and current due to their relatively low piezoelectric coefficients. Materials with high piezoelectric constants are highly desired for applications of piezoelectric materials. One such material is the lead-based relaxor ferroelectric (1−x) Pb(Mg1/3Nb2/3)O3− x PbTiO3 (PMN-PT), which exhibits strain levels and piezoelectric coefficients 5 to 10 times higher than bulk PZT ceramics and a large electromechanical coupling coefficient of k33 ~ 0.9 15,16 . PMN-PT bulk was reported to have a d33 up to 2500 pm/V 17 , which was almost 30 times higher than that of BaTiO3 (approximately 85.3 pm/V 18 ) and 4 times higher than that of PZT bulk material. For PMN-PT nanowires, d33 was measured as 371 pm/V 3 , which was over 13 times higher than that of BaTiO3 nanoparticles (28 pm/V 19 ) and 90 times higher than that of NaNbO3 nanowires (4 pm/V 20 ), respectively.
A theoretical prediction 8 has suggested that PMN-PT nanowires could generate high output power with higher efficiency than other piezoelectric nanostructures. This is because the ultrahigh dielectric constants lead to a large intrinsic capacitance, such that only a small external resistant load is needed to extract the power out.
Furthermore, nanostructures can undergo large deformation 21,22 due to their excellent mechanical properties (e.g. the maximum strain for ZnO Nanowire is ~7.7% 23 , while the maximum strain for bulk ZnO material is ~0.2% 24 ), thus producing larger electric charges and higher output power, rendering them attractive for energy applications. The high flexibility and strain tolerance of nanostructures can effectively reduce the risk of potential fracture or damage of piezoelectric materials under high-frequency vibration conditions, thus broadening their safety vibration frequency and amplitude range 25 . As electromechanical systems move to nanoscale, the dense integration of nanoscale devices to provide novel system functionality is highly desired. The mechanical systems are required to be controlled by low voltage signals provided by small, cheap, densely integrated analog or digital circuits 26 . Owing to the small size and high flexibility of nanostructures, the nano-devices based on them are very sensitive to small-level mechanical disturbances and are ideal for powering wireless sensors, microrobots, NEMS/MEMS, and bioimplantable devices 11,27 .  The piezoelectric properties of PMN-PT nanostructures depend on both intrinsic (stoichiometry, orientation) and processing-related (phase purity, defect density) factors.
(1-x)PMN-xPT crystal is a complex solid solution of relaxor ferroelectric PMN and normal ferroelectric PT. The structure of (1-x)PMN-xPT crystal transforms from rhombohedral to tetragonal phase, depending on the composition x at room temperature. When PT concentration (x) is below 30%, PMN-PT has a rhombohedral (3m) structure, while at PT concentrations larger than 35%, the crystal exhibits the tetragonal (4mm) symmetry.
When PT content is located within the range of 0.30-0.38, which is the so-called morphotropic phase boundary (MPB) region, a monoclinic phase exists 28 . PMN-PT exhibits its strongest piezoelectric effects when the composition is situated near MPB between two distinct crystalline structures 29 .
Apart from composition, another important parameter influencing the piezoelectric properties of PMN-PT nanostructures is crystal orientation, which will be described in

<100> polarized PMNPT:
In contrast, the domain configuration of <001> polarized rhombohedral crystals was found to be stable 14 . At room temperature, rhombohedral PMN-PT phase with 3m symmetry has eight possible dipole orientations along the body diagonal directions (< 111> family). When an electric poling field is applied to the crystals along <001> of the cubic axes, a multi-domain configuration can be produced consisting of four degenerate states and charged domain walls, i.e. <001> poled crystals have the configuration that each domain has one of four possible polar directions <111>, <-111>, <1-11>, and <-1-11>.
During hydrothermal synthesis, potassium reacts with niobium and produces KNbO3 3 , which is also a well-known piezoelectric material, but with piezoelectric constants (d33= 7.9 pm/V 35 ) much smaller than that of PMN-PT. Consequently the piezoelectric properties of PMN-PT nanowires with potassium residue were degraded.
(2): Crystal structure may be distorted by impurity atoms. Impurity (potassium) atoms diffused into the nanowire under high temperature and high pressure environment 3 , thus the crystal structure may be distorted, though the major lattice remained unchanged. Since the piezoelectric effect originates from the special crystal structure of ferroelectric materials, the distortion of crystal structure by impurity atoms will degrade the piezoelectric properties too.
(3): Defect density may increase due to lattice distortion.
As impurity atoms occupy substitutional or interstitial positions in the lattice, they turn into point defects in the hydrothermally synthesized PMN-PT nanowires. Also linear defects (such as edge dislocations and screw dislocations) and planar defects (such as twins and stacking faults) will be introduced if the concentration of impurity atoms reachs a certain level.  Similarly as pointed out in point (4), the precise control of shape and size of an individual nanowire is also impossible for a bottom-up method, such as hydrothermal synthesis.

(6): PMN-PT composition may be influenced by excess chemical reaction products.
According to the quantitative analysis of hydrothermally synthesized PMN-PT nanowires 3 , the ratio of PMN and PT in nanowires is about 1.82, lower than the designed composition of 1.86 (65/35). The ratio between magnesium and niobium (4.10/8.89) is lower than 1:2, with the loss of magnesium. Furthermore, the concentration of lead is less than that in the precursor.  shows its length and width to be ~22 µm and ~6 µm, respectively. The line profile ( Figure   S2b) derived from Figure S2a shows an average thickness of 300nm for the nanobelt.

Section 6: SEM characterization of FIB-cut nanostructures
The FIB-cut nanostructures were further studied by SEM for microstructural and compositional analyses. Figure S4a shows the morphology of the (011)c surface dominated PMN-PT nanobelt, which has a well-chiseled rectangular shape with sharp contours. The length and width of the nanobelt are measured from the SEM image to be ~19.8 and ~4.6 µm, respectively, corresponding well to the confocal microscopy results. Combining the line profile ( Figure S2b) with SEM observation, the width-to-height and length-to-width ratios are obtained as ~ 15:1 and ~4.3:1, respectively. The energy dispersive spectrum (EDS) generated from the pink box in Figure S4a is shown in Figure S4b    where Xi is the strain tensor, dki is the piezoelectric tensor, and Ek is the electric field tensor. CPE describes how an applied electric field will create a strain, leading to a physical deformation of the material. In order to separate the low level signal from random noise, the deflection of the probe cantilever is detected by a standard photodiode detector and then demodulated using a lock-in amplifier. In our case, the reference oscillatory AC signal applied between the AFM tip and the Au surface during scanning is: Where ω is the frequency of the reference signal, and the induced sample signal is: where φ is any phase shift between the two signals. Therefore the demodulator output (tip vibration signal) is obtained by multiplying the two signals together: The AC component has a frequency of twice the original reference signal and the DC component is related to both the amplitude and phase of the input signal. The demodulator output is sent through a low-pass filter to remove the 2ω component and leave the DC component, and then the signal is integrated over a period of time. When the tip is scanned above the PMN-PT nanobelt, the responsive piezoelectric strain in the nanobelt will cause the displacement of the cantilever: = dc + ( , ac , )cos( + ) Where φ is any phase shift between the reference and input signals. When the voltage is driven at a frequency (ѡ) well below the contact resonance of the cantilever, the above expression converts to: Therefore the local piezoelectric response will be detected as the first harmonic  Figure S6).
When the ramp-plot function is used to ramp the applied voltage from -10 to 10 V and to generate a piezoelectric displacement vs voltage sweeping curve, the piezoelectric displacement (Af in unit of nm), was obtained by multiplying the deflection signal (Vf in unit of mV) with the calibration constant (δ in nm/V) of the photodetector sensitivity, which is determined from the slope of the force−distance plot. We thus have: In which 16 is the gain factor used by the instrument. In our case, δ is measured to be ~50 nm/V.

Section 8: AFM height map and PFM phase map of 001NB
The simultaneously obtained AFM height map and PFM phase map of 001NB are shown in Figure S6a and b, respectively. The surface oscillations inside the nanobelt region is in phase with the tip voltage, which means φ = 0, (φ is the phase of the electromechanical response of the sample, see supplementary information section 7). Outside the nanobelt region, φ is random such that the contrast between the regions inside and outside of 001NB is obvious in phase map.    Figure S10 and can be divided into the following four steps: First of all, the (001)c surface-dominated PMN-PT substrate (5mm in length, 5mm in width, 0.5mm in thickness) was put onto a SEM sample stub, which was electrically conductive and used as one electrode later during poling. A rubber ring (~15mm inner diameter, ~3mm in height) was then placed onto the SEM sample stub so that the PMN-PT substrate was in the center of the ring. The rubber ring placed here to isolate the two electrodes (the top sample stub and the bottom sample stub) because it is insulating.
Sequentially, another sample stub was put onto the rubber ring, working as the other electrode during poling.
Then the two electrodes (the top stub and the bottom stub) were connected to a highvoltage power supplier, so that the (001)c PMN-PT substrate was in a uniform electric field of ~5kV/cm. The whole system, include the inside region between two electrodes, was immersed in silicon oil to avoid electric breakdown in air.
Last but not least, the hot plate under the poling system was heated up to above 100 °C during the poling. The high temperature will assist the realignment of dipoles within each unit cell of the PMN-PT crystal. The poling was maintained in this configuration for 24 hours. substrate, fixed by silver paste on both ends and capped with a thin layer of polydimethylsiloxane (PDMS), the whole system can be regarded as a compact, unidirectiontal nanobelt-enforced entity. The modulus E11 of the whole composite can be calculated as following: Where EPMNPT(18Gpa) 15 , EPI (2.5 GPa) 38 and EPDMS (500 KPa) 39 are the Young's moduli of PMN-PT nanobelt, PI substrate, and PDMS. VPMNPT and VPI are the concentrations of PMN-PT nanobelt and PI substrate: Where A is net cross-sectional area for PMN-PT nanobelt, PI substrate and the whole composite. The major Poisson's ratio can be given as Where νPMNPT (0.37) 40 , νPI (0.34) 41 Since the potential generated from the PMN-PT nanobelt between the two electrodes is given by: Where l is the length of the nanobelt across two electrodes, and g33 is the piezoelectric voltage constant (38.8 x 10 -3 V m/N) 43 . The output voltage can be written as: