Modeling the Field Emission Enhancement Factor for Capped Carbon Nanotubes Using the Induced Electron Density

摘要

In many field electron emission experiments on single -walled carbon nanotubes (SWCNTs), the SWCNT stands on one of two well separated parallel plane plates, with a macroscopic field FM applied between them. For any given location "L" on the SWCNT surface, a field enhancement factor (FEF) is defined as F-L/F-M, where F-L is a local field defined at "L". The best emission measurements from small -radii capped SWCNTs exhibit characteristic FEFs that are constant (i.e., independent of F-M). This paper discusses how to retrieve this result in quantum -mechanical (as opposed to classical electrostatic) calculations. Density functional theory (DFT) is used to analyze the properties of two short, floating SWCNTs, capped at both ends, namely, a (6,6) and a (10,0) structure. Both have effectively the same height (similar to 5.46 nm) and radius (similar to 0.42 nm). It is found that apex values of local induced FEF are similar for the two SWCNTs, are independent of F-M, and are similar to FEF values found from classical conductor models. It is suggested that these induced-FEF values are related to the SWCNT longitudinal system polarizabilities, which are presumed similar. The DFT calculations also generate "real", as opposed to "induced", potential-energy (PE) barriers for the two SWCNTs, for Fm values from 3 V/mu m to 2 V/nm. PE profiles along the SWCNT axis and along a parallel "observation line" through one of the topmost atoms are similar. At low macroscopic fields, the details of barrier shape differ for the two SWCNT types. Even for F-M = 0, there are distinct PE structures present at the emitter apex (different for the two SWCNTs); this suggests the presence of structure -specific chemically induced charge transfers and related patch-field distributions.