Looped carbon nanotube fibers as cathodes with giant field enhancement factors

Abstract

Structures with a sharp apex amplify an applied macroscopic field, FM, substantially and generate significant field electron emission (FE). The apex barrier field, Fa, is related to FM by the apex field enhancement factor (aFEF), γa≡Fa/FM. In this Letter, we provide a theoretical explanation for extremely high-effective FEFs (104 ≲ γeff ≲ 105) recently extracted from an orthodoxy theory analysis of the emission current–voltage characteristics of looped carbon nanotube (CNT) fibers, making them promising candidates for FE applications. In this work, we found a dependence of γa on the geometrical parameters for an isolated conductive looped CNT fiber, modeled via the finite element technique. The aFEF of looped CNT fibers is found to scale as γa=2+[hf/rfiber][ln (2h/rfiber)]−1, where f≡1+θ[rfiber/b]α[ln (2h/rfiber)−1], in which h is the height of a looped fiber standing on an emitter plate, b is its base length, rfiber is the radius of the fiber, and θ and α are fitting parameters that have a nonlinear dependence on the scaling parameter h/b. Our results show that the scaling law predicts that 10 ≲ γa ≲ 100 for looped CNT fibers with parameters: 10 μm ≤rfiber≤ 100 μm, 0.4 ≤h/b≤ 2, and d/h≥1, where d is the distance between the apex of the looped fiber and the anode. However, scanning electron microscopy images reveal the presence of microfibrils protruding from the looped CNT fiber surface close to its apex. We show that the modeling of a combined two-stage structure (looped CNT fiber + fibrils) leads to aFEF values in excellent agreement with an orthodoxy theory analysis of FE experiments performed on these fibers.