Importance of metallic nanotube flexibility on its field emission characteristics

Abstract

It is known that field electron emission (FE) characteristics of emitters are influenced by their flexibility, as bending under an applied electrostatic field, EP, can significantly increase their characteristic field enhancement factor and emission current. However, this effect has not been thoroughly studied. In this Letter, a numerical algorithm is developed to investigate the impact of electrostatic forces on the FE properties of a flexible metallic carbon nanotube (CNT), classically modeled as a cylinder with a hemi-spherical cap, as a function of EP, its sharpness aspect ratio, and its initial (assumed to be fixed) angle θ0 of inclination with the substrate, i.e., the horizontal emitter's plate. Our numerical simulations are based on an iterative process to include the mechanical stress problem and resulting bending of the CNT, taking into account its finite Young's modulus and the electrostatic problem due to the redistribution of surface charges on the emitter until a convergent solution is found. The process is repeated as a function of EP. Importantly, it is found that the emitted current of the bendable CNT can be several orders of magnitude larger than those for the case when the emitter is modeled as a rigid body. Moreover, the curvatures of the Murphy–Good plots predicted theoretically align with those observed experimentally in FE from carbon-based materials under the high EP limit, where protrusion deflection effects are likely to influence emission. Therefore, our findings highlight the necessity of considering the flexibility of nanoscale field emitters to accurately interpret their FE characteristics.