Hexagonal [0001] nonpassivated ZnO nanowires are studied with density functional calculations. The band gap and Young's modulus in nanowires which are larger than those in bulk ZnO increase along with the decrease of the radius of nanowires. We find ZnO nanowires have larger effective piezoelectric constant than bulk ZnO due to their free boundary. In addition, the effective piezo-electric constant in small ZnO nanowires doesn't depend monotonously on the radius due to two competitive effects: elongation of the nanowires and increase of the ratio of surface atoms. PACS numbers: 77.65.-j,62.25.+g,73.22.-f,61.46.-w ZnO[1] is one of the most important materials due to its three key advantages: semiconducting with a direct wide band gap of 3.37 eV and a large excitation binding energy (60 meV), piezoelec-tric due to non-central symmetry in the wurtzite structure, and biocompatible. Recently, a diversity group of ZnO nanostructures including nanowires[2], nanobelts[3], nanosprings[4], nanocombs[5], nanorings[6], nanobows[7], and nanohelices[8, 9] have been synthesized under specific growth conditions. ZnO nanos-tructures could have novel applications due to their unique physical and chemical properties arising from surface and quantum confinement. In particular, ZnO nanowires with relatively simple structures are important one-dimensional (1D) nanostructures. Experimentally , the group of Wang had synthesized well-aligned [0001] ZnO nanowires enclosed by facet {10 ¯ 10} surfaces [10, 11]. Room-temperature ultraviolet lasing[12] and piezoelectric nanogenerators based on ZnO nanowire arrays have been demonstrated[13]. Rectifying diodes of single ZnO nanobelt/nanowire-based devices [14] and a ZnO nanowire photodetector[15] were fabricated very recently. Although many studies on ZnO nanowires have been conducted, there are some important issues remained to be addressed. First, the mechanical properties, especially the Young's modulus of ZnO nanowires are on debate in the literature[16, 17, 18, 19, 20]. For instance, Chen et al. [16] showed that the Young' modulus of ZnO nanowire with diameters smaller than about 120 nm is significantly higher than that of bulk ZnO. However, the elastic modulus of vertically aligned [0001] ZnO nanowires with an average diameter of 45 nm measured by atomic force microscopy was found to be far smaller than that of bulk ZnO[17]. The second issue is about the elec-tromechanical coupling in ZnO nanowires. The effective piezoelectric coefficient of individual (0001) surface dominated ZnO nanobelts measured by piezoresponse force microscopy was found to be much larger than the value for bulk wurtzite ZnO[21]. In contrast, Fan et al. showed that the piezoelectric coefficient for ZnO nanopillar with the diameter about 300 nm is smaller than the bulk values[22]. They suggested that the reduced electrome-chanical response might be due to structural defects in the pillars[22]. Whether the electromechanical coupling is enhanced or depressed in defect-free ZnO nanowires is not clear. Thirdly, although ...
