Field emission in ordered arrays of ZnO nanowires prepared by nanosphere lithography and extended Fowler-Nordheim analyses

A multistage chemical method based on nanosphere lithography was used to produce hexagonally patterned arrays of ZnO vertical nanowires, with 1 μm interspacing and aspect ratio ∼20, with a view to study the effects of emitter uniformity on the current emitted upon application of a dc voltage across a 250 μm vacuum gap. A new treatment, based on the use of analytical expressions for the image-potential correction functions, was applied to the linear region below 2000 V of the Fowler-Nordheim (FN) plot and showed the most suitable value of the work function φ in the range 3.3–4.5 eV (conduction band emission) with a Schottky lowering parameter y ∼ 0.72 and a field enhancement factor γ in the 700–1100 range. A modeled γ value of ∼200 was calculated for an emitter shape of a prolate ellipsoid of revolution and also including the effect of nanowire screening, in fair agreement with the experimental value. The Fowler-Nordheim current densities and effective emission areas were derived as 10¹¹ Am⁻² and 10⁻¹⁷ m², respectively, showing that field emission likely takes place in an area of atomic dimensions at the tip of the emitter. Possible causes for the observed departure from linear FN plot behavior above 2000 V were discussed.