Figure 2

Sketch for the modeling process and the solution of the “charge disc” model.

(a), The hexagonal pyramid-shaped ZnO-nanotaper (left) is simplified into a cone-shaped nanotaper (right). (b), The simplified cone with a rounding-top in a uniform electric field F₀. (c), The surface charge density distribution of the nanotaper (h = 2 μm, R₀ = 200 nm) under the applied field 20 V/μm. (d), The disc radius R is determined by the top radius r₀ and the bottom radius R₀ of the ZnO-nanotaper. (e), The constructed charge disc (above the cathode) and image charge disc (below the cathode) model on the opposite side of the cathode. (f), Three-dimensional (3D) surface for the relationship among θ, h and γ_C-array of the ZnO-nanotaper arrays, for clarity the inset is the back view of the diagram.