Ponderomotive forces effect on the field emission of carbon nanotube films

Field emission from strained carbon nanotubes on cathode substrate

“…1) is dependent on the electromechanical forces. Based on the studies reported in published literature, it is reasonable to expect that a major contribution is by the Lorentz force due to the flow of electron gas along the CNT and the ponderomotive force due to electrons in the oscillatory electric field [24]. In addition, the electrostatic force and the van der Waals force are also important.…”

Carbon Nanotube Field Emitters

“…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 (Edgcombe & Valdrè, 2001;Edgcombe & Valdrè, 2002;Shang et al, 2007), for nanotube in space between parallel cathode and anode planes (Bonard et al, 2002a;Filip et al, 2001;Nilsson et al, 2002;Smith et al, 2005), and for a nanotube surrounded by neighboring nanotubes with a screening effect (Jo et al, 2003;Glukhova et al, 2003;Nilsson et al, 2000;Wang et al, 2005) were suggested. The main problem for such algebraic fitting formulas is the lack of a definitive proof of their accuracy.…”

“…When we chose logarithmic scale for  and  / H with logarithmic steps we obtain a set of nearly straight isolines with equal distances in the plot. We think that under the action of ponderomotive forces in the external electric field, carbon nanotubes that are even chaotically located on the substrate straighten and become oriented (Musatov et al, 2001;Glukhova et al, 2003). …”

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

“…Therefore for the force and emission current we may use the above derived formulas. 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).…”

“…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.…”