Predicting the optimal field enhancement factor during the growth of arched fibers

Abstract

Curved carbon-based fibers, in the form of looped fibers, have been investigated as promising field electron emitters with high mechanical stability. Recently, the growth of semicircular arched carbon nanofibers (structures when the arch is incomplete) has received increased attention due to their potential application in next-generation electronic devices. In this Letter, we theoretically investigate the field enhancement factor (FEF) during the growth of these structures. We found the conditions for the optimal FEF, γmax, as a function of the geometrical parameters. Our results show that the local characteristic FEF at the top of the arch obeys a scaling law, γC≈γmax×Ω[(ψ/ψ*)2], where Ω is a nearly quadratic function of (ψ/ψ*), where ψ is a normalized arch angle of the fiber and ψ* is the ψ-value when γC=γmax. Importantly, our results show a universal behavior for γmax, namely, γmax≈κ[(R/r)α−0.45]ρ (where r and R are the radii of the fiber and the arch, respectively), α≡Rrim/r (where Rrim is the radius of the rim at the fiber top), and κ and ρ are positive constants. We point out several advantages of the arched fiber over the fully looped fiber for field emission devices, particularly the mechanical stability of the two-stage arched structures. Finally, starting with the conditions for γmax inferred from an isolated arch, the effects of electrostatic depolarization in regular arrays of arched fibers are analyzed as a function of the lattice parameters.