Supporting Inormation or: Piezoelectric Nanoribbons Printed onto Rubber or Flexible Energy Conversion Yi Qi, Noah T. Jaeris, Kenneth Lyons, Jr., Christine M. Lee, Habib Ahmad, Michael C. McAlpine *, Department o Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544 Department o Electrical Engineering, Princeton University, Princeton, NJ 08544 Division o Chemistry and Chemical Engineering, Caliornia Institute o Technology, Pasadena, CA 9115 * Corresponding author, Telephone number: (609) 58-8613, Fax number: (609) 58-1918, e- mail: mcm@princeton.edu Department o Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544 Department o Electrical Engineering, Princeton University, Princeton, NJ 08544 Division o Chemistry and Chemical Engineering, Caliornia Institute o Technology, Pasadena, CA 9115
For characterizing the undamental piezoelectric perormance o the PZT ilm as well as the PZT nanoribbons, the piezoelectric charge constants d were measured. This value represents the polarization generated per unit o mechanical stress applied to a piezoelectric material, or, conversely, the mechanical strain experienced per unit o electric ield applied. The piezoelectric charge coeicient is a tensor, with components d ij, where i indicates the direction o polarization generated in the material when the electric ield is zero (or the direction o the applied ield strength), and j is the direction o the applied stress (or the induced strain). I. d 31 Measurement The most practical o the piezoelectric constants is d 31, the transverse operation mode. To determine d 31 o the PZT thin ilm, we utilized the waer lexure approach. Figure S1 illustrates the basic coniguration o the experiment, consisting o a uniorm pressure rig (diameter 39 mm, depth mm). A PZT/Pt/MgO waer with Au/Cr top electrode is sandwiched between the top and bottom halves o the rig to orm a closed chamber system. To orm the waer with bottom and top electrode, 80 nm Pt bottom contact electrode was deposited via e-beam evaporation and then post annealed at 600 ºC or 1 hour, prior to PZT thin ilm deposition. Au (10 nm) / Cr (30 nm) top contact electrodes with an area ~ mm were deposited at the waer center using e-beam evaporation. The PZT thin ilm was synthesized using the sputtering procedure described in the manuscript. A pipette bulb connected to the rig was used to apply an oscillating planar stress, which subjects the waer to controlled bending. Assuming the bending o the ilm is slight, small delection plate theory may be used to determine the principal stresses, which can be determined by direct calculation rom the read-out o a pressure transducer (Omega PX09, 30 psi ull
scale). Generated charge is collected rom the top electrode on the PZT ilm and converted to an RMS voltage via a charge integrator circuit. Figure S1. Measurement apparatus used or d 31 measurement. The induced charge was measured via a charge integrator circuit between the contact electrodes, while the pressure is measured with a pressure transducer. The principal stresses near the center o the waer were calculated rom the pressure readings via classical mechanical plate theory according to: (1) E 1 ν PZT MgO 3Pa σ 1 + σ EMgO 1 ν PZT 4t Where σ 1 and σ are the radial and tangential principal stresses applied to the ilm, E is Young s modulus (E MgO 49 GPa, E PZT 101 GPa), ν is Poisson s ratio (ν MgO 0.18, ν PZT 0.3), P is the uniorm pressure as measured by the transducer, t 0.5 mm is the thickness o the waer, and a 19 mm is the inner radius o the pressure rig. The piezoelectric coeicient is inally calculated according to the ollowing, where D 3 is the induced dielectric displacement: () d 31 D3 σ + σ 1 3
II. d 33 Measurement To determine the piezoelectric coeicient d 33, piezoresponse orce microscopy (PFM) was used, in which an AC bias voltage was applied with amplitude U (V). The sample displacement or tip vibration is measured as the piezoresponse amplitude P (pm), which is the product o the vertical delection signal V (V) and sensitivity δ (pm/v). The slope o piezoresponse vs. applied AC voltage is calculated as the eective piezoelectric coeicient d e.. (3) d e P U V δ U Because the electric ield under the tip is not uniorm, the eective piezoelectric coeicient d e is not necessarily the same as true piezoelectric coeicient o the ilm d 33. Kalinin et al (see reerence 35 in the main text) provides a theoretical explanation o the tip-surace interaction. Generally, a blunt tip and an intermediate orce are required to ensure that the measured signal is electromechanical response dominated. As a control or our experimental conditions, a PPLN crystal standard sample was measured with a tip o radius 50 nm and an applied orce o 000 nn (Fig. S). The measured curve is linear and corresponds to an eective piezoelectric coeicient d e 7.7 pm/v, which is in good agreement with the known d 33 value o PPLN (7.5 pm/v). These results conirm operation in the strong-indentation limit or the thin ilm PZT samples on the MgO host substrate. 4
Figure S. PFM measurement on a standard PPLN sample. The slope o the linear piezoresponse vs. applied voltage was calculated as d e. 5