Mechanism of field electron emission from carbon nanotubes

Field electron emission (FE) is a quantum tunneling process in which electrons are injected from materials (usually metals) into a vacuum under the influence of an applied electric field. In order to obtain usable electron current, the conventional way is to increase the local field at the surface of an emitter. For a plane metal emitter with a typical work function of 5 eV, an applied field of over 1 000 V/μm is needed to obtain a significant current. The high working field (and/or the voltage between the electrodes) has been the bottleneck for many applications of the FE technique. Since the 1960s, enormous effort has been devoted to reduce the working macroscopic field (voltage). A widely adopted idea is to sharpen the emitters to get a large surface field enhancement. The materials of emitters should have good electronic conductivity, high melting points, good chemical inertness, and high mechanical stiffness. Carbon nanotubes (CNTs) are built with such needed properties. As a quasi-one-dimensional material, the CNT is expected to have a large surface field enhancement factor. The experiments have proved the excellent FE performance of CNTs. The turn-on field (the macroscopic field for obtaining a density of 10 μA/cm²) of CNT based emitters can be as low as 1 V/μm. However, this turn-on field is too good to be explained by conventional theory. There are other observations, such as the non-linear Fowler-Nordheim plot and multi-peaks field emission energy distribution spectra, indicating that the field enhancement is not the only story in the FE of CNTs. Since the discovery of CNTs, people have employed more serious quantum mechanical methods, including the electronic band theory, tight-binding theory, scattering theory and density function theory, to investigate FE of CNTs. A few theoretical models have been developed at the same time. The multi-walled carbon nanotubes (MWCNTs) should be assembled with a sharp metal needle of nano-scale radius, for which the FE mechanism is more or less clear. Although MWCNTs are more common in present FE applications, the single-walled carbon nanotubes (SWCNTs) are more interesting in the theoretical point of view since the SWCNTs have unique atomic structures and electronic properties. It would be very interesting if people can predict the behavior of the well-defined SWCNTs quantitatively (for MWCNTs, this is currently impossible). The FE as a tunneling process is sensitive to the apex-vacuum potential barrier of CNTs. On the other hand, the barrier could be significantly altered by the redistribution of excessive charges in the micrometer long SWCNTs, which have only one layer of carbon atoms. Therefore, the conventional theories based upon the hypothesis of fixed potential (work function) would not be valid in this quasi-one-dimensional system. In this review, we shall focus on the mechanism that would be responsible for the superior field emission characteristics of CNTs. We shall introduce a multi-scale simulation algorithm that deals with the entire carbon nanotube as well as the substrate as a whole. The simulation for (5, 5) capped SWCNTs with lengths in the order of micrometers is given as an example. The results show that the field dependence of the apex-vacuum electron potential barrier of a long carbon nanotube is a more pronounced effect, besides the local field enhancement phenomenon.