Screened field enhancement factor for a tall closely spaced array of identical conducting posts and implications for Fowler-Nordheim-type equations
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Schematic diagram (not to scale) of the floating-spheres model for a nanowire array. The substrate and counter-electrode are parallel planar plates, well separated by distance Z. A regular array of perfectly conducting spheres (of radius ρ) floats at height h above the substrate, with nearest-neighbour distance D. The spheres and substrate have the same electrostatic potential and collectively form the emitter assembly. A s is the area of substrate per sphere, called its “footprint.” A voltage generator creates positive surface charge of density σ on the counter-electrode, and corresponding negative charge, of average surface density –σ, on the emitter assembly. The model discussed applies when Z ≫ h ≫ D ≫ ρ.
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