Electrostatic potential in a bent piezoelectric nanowire. The fundamental theory of nanogenerator and nanopiezotronics

We have applied the perturbation theory for calculating the piezoelectric potential distribution in a nanowire (NW) as pushed by a lateral force at the tip. The analytical solution given under the first-order approximation produces a result that is within 6% from the full numerically calculated result using the finite element method. The calculation shows that the piezoelectric potential in the NW almost does not depend on the z-coordinate along the NW unless very close to the two ends, meaning that the NW can be approximately taken as a “parallel plated capacitor”. This is entirely consistent to the model established for nanopiezotronics, in which the potential drop across the nanowire serves as the gate voltage for the piezoelectric field effect transistor. The maximum potential at the surface of the NW is directly proportional to the lateral displacement of the NW and inversely proportional to the cube of its length-to-diameter aspect ratio. The magnitude of piezoelectric potential for a NW of diameter 50 nm and length 600 nm is 0.3 V. This voltage is much larger than the thermal voltage (25 mV) and is high enough to drive the metal-semiconductor Schottky diode at the interface between atomic force microscope tip and the ZnO NW, as assumed in our original mechanism for the nanogenerators. Developing novel technologies for wireless nanodevices and nanosystems is of critical importance for applications in biomedical sensing, environmental monitoring, and even personal electronics. Miniaturization of a power package and self-powering of these tiny devices are some key challenges for their applications. Various approaches have been developed for harvesting energy from the environment based on approaches such as thermoelectricity and piezoelectricity. Innovative nanotechnologies are being developed for converting mechanical energy (such as body movement, muscle stretching), vibration energy (such as acoustic/ultrasonic wave), and hydraulic energy (such as body fluid and blood flow) into electric energy that will be used to power nanodevices that operate at low power. Recently, using piezoelectric ZnO nanowire (NW) arrays, a novel approach has been demonstrated for converting nanoscale mechanical energy into electric energy. 1-3 The single nanowire nanogenerator (NG) relies on the bending of a NW by a conductive atomic force microscope (AFM) tip, which transfers the displacement energy from the tip to the elastic bending energy of the NW. The coupled piezoelectric and semiconducting properties of the NW perform a charge creation, accumulation, and discharge process. Most recently, this approach has been extensively developed to produce continuous direct-current output with the use of aligned NWs that were covered by a zigzag top electrode, and the nanogenerator was driven by ultrasonic wave, establishing the platform of producing usable power output for nanodevices by harvesting energy from the environment. 4 Furthermore, based on the coupled piezoelectric and semiconducting properties of the NW, a new field of nanopiezotronics has been created, 5,6 which is the basis for fabricating piezoelectric field effect transistors, 7 piezoelectric diode, 8 piezoelectric force/humidity/chemical sensors, 9 and more. The theoretical background for the nanogenerator and nanopiezotronics is based on a voltage drop created across the cross section of the NW when it is laterally deflected, with the tensile side surface in positive voltage and compressive side in negative voltage. 1,5 It is essential to quantitatively calculate and even develop analytical equations that can give a direct calculation of the voltage at the two side surfaces of the NW, which is important to calculating the efficiency of the nanogenerator and the operation voltage of the nanopiezotronics. In the literature, numerous theories for onedimensional (1D) nanostructure piezoelectricity have been proposed, including first-principles calculations, 10,11 molecular dynamics (MD) simulations, 12 and continuum models. 13