  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
piezoelectric 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.
