Transfer-matrix simulations of field emission from bundles of open and closed (5,5) carbon nanotubes

We present simulations of field emission from bundles of metallic (5,5) carbon nanotubes, which are either ideally open or closed. The scattering calculations are achieved using a transfer-matrix methodology for consideration of three-dimensional aspects of both the emitting structure and the surface barrier. Band-structure effects are reproduced by using pseudopotentials and enforcing the incident states to first travel through a periodic repetition of the tubes’ basic cell before entering the region containing the fields. The bundles consist of three and six identical structures, which are placed at the corners of equilateral triangles. In all cases, the closed emitters are found to emit less current than the open ones and to be more sensitive to the electric field in their response to neighboring tubes. Due to the enhanced screening of the electric field, the bundles’ emission rates are reduced compared to those of the isolated tubes. It turns out that the rates characterizing bundle and isolated emitters are related by a simple formula, whose dependence on the electric field suggests deviations from the Fowler-Nordheim equation at high fields. Finally, the position of peaks associated with quasilocalized states on top of the closed emitters appears to be a strong indicator of the tubes’ environment.