In an aqueous solution of a zinc salt, counter, reference and working electrodes are placed, and an electric potential is applied across the working and reference electrodes. A gas including oxygen and an inert gas is introduced into the aqueous solution. Responsive to these conditions an array of zinc oxide nanostructures grows on a conductive nucleation plate that is a part of the working electrode. The nanostructures have sharp tips, have a more efficient electron emissivity than nanorods made from other materials, and can be used in fabricating field emission lamps and displays.