Assumptions of FN theory say "flat surfaces of metals obey FN theory", but CNT do not have a flat surface.
How can we apply it in the case of CNTs?
Hi, Shama!
Use of the form factor characterizing the gain of the electrostatic field, allows you to "tune" the Fowler-Nordheim law for describing the real field of the nanostructure.
I agree. In our group we have applied different tip models to adjust FN according to the acquired data.
I think you have already answered your question. The conventional FN-theory is for planar field electron emission from a polycrystalline tungsten surface. Although it is often applied to any case dealing with field electron and field ion emission, it must be modified for various parameters. Researchers have worked over a decade modifying FN-theory for CNT. Please consult some of the contemporary literature on CNT field emission. I would suggest the work done by John Xanthakis (NTUA), Chris Edgcombe (Cambridge), and Richard Forbes (University of Surrey).
Article Field penetration into amorphous-carbon films: Consequences ...
Yes, we could successfully applied the FN theory to the carbonnanofiber emitters.
The conventional FN theory is valid for planar surfaces or surfaces of large radius of curvature R i.e. R>2onm. Furthermore the so called supply function- the number of electrons hitting the surface per unit time is assumed to be free-electron-like in FN. Both these requirements fail for small radii CNT (R=1-10nm). For THICK wall AND LARGE R CNTs the FN theory is OK if modified by the enhancement factor beta. If either the CNT are single wall or of small radius then even the beta modified FN will NOT do the job. See my JAP and JVST publications
J P Xanthakis
FN theory had been extensively applied not only to thermoionic and field emission but also to photofield emission as well as to CNT. My research group had been involved for quite sometime with the photon assisted field emissions and presently we are doing works with SWCNT.
For application of the Fowler-Nordheim (FN) theory to field electron emission from the carbon nanofibers, we have to modify the FN theory by using the enhancement factor β. The β is given by relation for the local (microscopic) electric field F by F = βE, where the quantity E is the macroscopic electric field around the emitter. In the use of the FN theory, most important procedure is how to evaluate the macroscopic field. Thus, the factor β is a correction factor for the application of the FN theory to the real emitter, which is different from the ideal metal emitter.
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