Field enhancement factors of random arrays of carbon nanotubes

Field enhancement factor and field emission from a hemi-ellipsoidal metallic needle

“…Instead of (12) we should use (31), (32), and (36). So, the parameter η = L/H in the force and emission current formulas (17), (18), (25), and (26) should be included only through the field enhancement factor β = β(L/H, H/ρ).…”

“…Various theoretical approaches based on both analytical solutions and numerical simulations have been reported. [18][19][20][21][22][23][24] Analytical solution was obtained for a hemisphere on a plane, a floating sphere at the emitter-plane; a hemi-ellipsoid on a plane [18], and a sphere-on-cone model [19]. Usu- * Electronic address: azhbanov@gate.sinica.edu.tw ally only the apex field enhancement factor is calculated when dealing with a hemi-ellipsoid on a plane [18].…”

“…Influence of the anode-cathode distance within a floating sphere model was investigated in [20]. The model of a hemisphere on a post for CNT emitters was used in numerically simulations and reported in many papers [21][22][23][24]. Calculation difficulties in these numerical methods arise due to the large nanotube aspect ratio and very long distance between cathode and anode in comparison with emitter height.…”

“…Calculation difficulties in these numerical methods arise due to the large nanotube aspect ratio and very long distance between cathode and anode in comparison with emitter height. Usually, these numerical results were generalized and simple fitting formulas of field enhancement factor for individual nanotube [21,22,25,26], for nanotube in space between parallel cathode and anode planes [27][28][29][30], and for a nanotube surrounded by neighboring nanotubes with a screening effect [31][32][33][34][35] were suggested.…”

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

“…The field enhancement factors computed by this treatment are compared with theoretical or modeling estimates, relating them to relevant geometrical parameters such as aspect ratio and surface density. [21][22][23] Effective emission areas and current densities are also calculated from the present treatment and compared with older approaches. 9,24,25 General conclusions regarding the interpretation of FE data from random or ordered arrays of ZnO nanostructures are drawn.…”