Supporting Online Material for

Transcription

1 Supporting Online Material for Piezoelectric Nanogenerators Based on Zinc Oxide Nanowire Arras Zhong in Wang* and Jinhui Song *To whom correspondence should be addressed. Published 14 April 6, Science 31, 4 (6) DOI: 1.116/science.1145 This PDF file includes: Figs. S1 to S6 Table S1 Movies S1 and S SOM Text

2 Suplimentar materials for: Piezo-Electric Nano-Generators Based on Zinc Oxide Nanowire Arras B Zhong in Wang * and Jinhui Song Fig. S1: TEM images of ZnO nanowires showing no gold caps or with small gold caps at the growth fronts. Note the hespherical shape of the gold particles at the tips Au Au (striped off from the tip) Au 1 nm

3 Fig. S: Three different perspectives of outputting the data shown in Fig. B to clearl image the sharp piezoelectric voltage peaks. 5 µm 5 µm x 5 µm x 5 µm 5 µm x 5 µm

4 Fig. S3: Piezoelectic output voltage received at a higher scan frequenc at a small scan region, showing the shape of the discharge peaks. The output voltage peak is as high as mv.

5 Fig. S4: To ensure the voltage output signal in Fig. B is due to piezoelectric induced charging effect rather than friction or contact potential, we immediatel scanned the AFM tip at a side area covered b a metal film of the sample under exactl the same experimental conditions used for acquiring Fig. B. The output morpholog image (A) and the voltage signals (B) of the metal film are displaed as the following. The output voltage shows no peaks but remains at the noise level, indicating that a metal film even with a different contact potential does not produce the observed discharge process. The data rule out the possibilit of friction or contact potential being the cause of the observed charging event. (A) Morpholog image (B) Output voltage image

6 Fig. S5: To ensure the voltage output signal in Fig. B is due to piezoelectric induced charging effect rather than friction or contact potential, we carried out similar experiments using aligned carbon nanotubes. (A, B) Side and top views of aligned carbon nanotubes. (C) The output voltage image shows no peaks but noise, indicating that carbon nanotubes do not produce the discharge process presented in Fig. B for ZnO nanowires. The data rule out the possibilit of friction or contact potential being the cause of the observed discharging event. (A) 6 m (B) m (C)

7 Fig. S6: To ensure the voltage output signal in Fig. B is due to piezoelectric induced charging effect rather than friction or contact potential, we carried out similar experiments using aligned WO 3 nanowires. The output voltage image shows no peaks but noise, indicating that WO 3 nanowires do not produce the discharge process presented in Fig. B. The data rule out the possibilit of friction or contact potential being the cause of the observed discharging event for ZnO nanowires. (A) SEM image of WO 3 nanowires 1 m (B) Voltage output image

8 Table S1: The efficienc of converting elastic deformation energ into piezoelectric energ. The Young s modulus of ZnO NWs is 9 GPa (J.H. Song, X.D. Wang, E. iedo and Z.. Wang, Nano etters, 5, 1954 (5). ); piezoelectric coefficient 1 pm/v, NW size 6 nm. NW NW length (m) Max. Bending m (m) Max. output voltage V (V) Voltage peak width (s) Elastic Def. Energ (J) Piezoelectric energ (J) Efficience of energ conversion (%) 1 5.6E E E E E E E E E E E E E-7 8.8E E E E-17.76E E-7 8.8E E-3 3.7E E E E E E-3 7.9E E-16.98E E E E-3 3.1E E-17.39E+1

9 Analtical analsis of the bending induced piezoelectric voltage drop across a ZnO nanowire For the following calculation, we consider the in-plane bending of a nanowire b an external point force F perpendicular to the nanowire. For a short segment of nanowire, the local bending can be approximated b a small arc characterized b a small angle and a local curvature of radius (see Fig. S7), the local strain is H G HG H G HG ( ) HG EF (A) (B) z F E F G H E G F H Fig. S7: (A) A segment of a nanowire for calculating the bending induced piezoelectric potential across the two side surfaces. (B) The definition of coordination sstem under an external displacement force F. Using the stress and strain relationship, we have: Y Y (1) where Y is the elastic modulus. In the static state of the sstem the moments are balanced. The total moment of the bent nanowire is 1

10 B using Eq. (1) we have M Y M da M I da Y da Y I Y () From the geometr shown in Fig. S7(B), we have the following results under small angle approximation: d dz tan 1 d d d d d thus ( ) ds dz dz dz dz In combining with Eq. (), 1 M YI d dz M d 1 dz dz (3) YI B the principle of balancing of moment: internal moment = external moment M d YI dz F ( z) d M F ( z) (4) dz YI YI where the external force is assumed to act approximatel perpendicular to the nanowire at the top and is the nanowire length. Equation (4) determines the bending of the nanowire under the deflection of an external force at the front end. Appendix 1: Piezoelectric induced potential Now we calculate the potential produced b piezoelectric effect. From the definition of the piezoelectric coefficient (d): d, the corresponding electric field along z-axis is E E z (5) d d Equation (5) is given b ignoring local polarization (or dielectric screening) for simplification of the analtical derivation. For simplicit of analtical calculation and to illustrate the phsical principle, we consider the potential at the side surface a along the entire length of the nanowire: a E z (6) d

11 V E ds a d 1 ds a d 1 ds a d d (7) Using Eqs. (3) and (4), Eq. (7) gives V a M a F ( z) af af dz dz z dz d ( ) (8) YI d YI dyi dyi Together with the relationship between the maximum deflection m and the applied force: 3YIm F (see next section), we have the potential induced b piezoelectric effect: 3 3am V (9) d It must be pointed out that this is a qualitative estimation of the potential induced b PZ effect for understanding the phsical process. Numerical calculation with considering the boundar conditions and dielectric screening is required to get quantitative results. Appendix : Deflection of the nanowire under external force We now consider the deflection of the nanowire under an externall applied force F perpendicular to the nanowire. From Equation (4) and boundar conditions: d( z ) ( z ) ; (1) dz Under small deflection and assuming that F is constant, integrating Eq. (4) gives d dz F 1 ( z z ) (11) YI and m F ( z z ) z (1) YI 6 For z, m o F z 3 F 3YIm m F (13) 3 3YI The mechanical work done b the external force for bending of the nanowire: 3

12 W m m 3YI F dl F( ) d d 3 3YI 3 m (14) Appendix 3: Discharge of an C circuit As shown in the diagram on the right-hand side: 1 idt( I) i C (15) i C di ( I ) dt (16) C I i i t ( ) C I I e (17) For initial condition: t, i V I, we have t V I C i ( ) e (18) r The deca time constant = ( )C I The electric power consumed b the resistor (the output work): W PZD i dt V ( ) V C ( ) I I e t ( I ) C dt For I << V C W PZD (19) Appendix 4: The elastic deformation energ of the nanowire dissipated in the first ccle of the resonance 4

13 To calculate the energ loss after a single ccle of vibration, we assume that the amplitude of the nanowire resonance decas with time as described b: t / t m moe () where mo is the maximum deflection pushed b the AFM tip, and t o is the deca constant of the vibration amplitude. Therefore, the elastic energ at a subsequent vibration from Eq. (14) is 3YI 3YI W e / t t o ED 3 m 3 m (1) The energ dissipated after one ccle of vibration is YI W e t () ED 3 / t to 3 m t First the ccle: t and 1 t : f 3YI W ED 3 m t 1 f (3) Under the first order approximation (.P. Gao, Z.. Wang*, Z.G. Bai, W. de Heer,. Dai and M. Gao, Phs. ev. etts., 85 () 6-655), the life time of the resonance t o is related to the qualit factor Q and resonance frequenc f b Therefore t 3Q (4) f 3YI W W (5) ED 3 m max Q 3 Q 3 For ZnO nanobelts in a vacuum of 1-7 torr, Q 6 (X.D. Bai, P.X. Gao, Z.. Wang and E.G. Wang, Appl. Phs. etts., 8, 486 (3)), the efficienc of energ transform b the NW is / W. W PZD ED 5