Abstract
The present Thesis is mainly focused on three subjects. Firstly, the local extraction field at the tip of an isolated carbon nanotube is investigated. A method based on replacing the nanotube surface by an axial string of charges is developed. The method allows the reconstruction of the zero-voltage equipotential of the nanotube with high precision in the cap area, which is of main interest for field emission applications. Unlike previous methods that need either indirect validation procedures or comparison to numerical results obtained through various finite element algorithms, the presented method includes a criterion of self-validation that makes its results particularly reliable. The method was used to compute the geometric field enhancement factor for various nanotube geometries and leads to a linear dependence of this parameter on the aspect ratio, which is of particular interest for field emission practice. The problem of electron field emission from an isolated carbon nanotube is considered next. As the traditional Fowler-Nordheim theory is shown to be unable to reveal the particular aspects of field emission from carbon nanotubes and other nanometre size cathodes, a new model is constructed and applied to experimental data. The key aspects of the model are: 1) The assumption of the existence of quasi-free electrons that behave as a two-dimensional system on the nanotube and 2) The electron transfer from the nanotube into vacuum is considered through a connection condition for the corresponding local probability density. As a result, a method to compute the field emission current from a singular grounded carbon nanotube facing an anode is developed. Good agreement is obtained between the theoretical current voltage characteristics and the corresponding experimental curves. The final subject considered in this Thesis is the sequential tunnelling of electrons from nanoparticles into the vacuum. The theoretical aspects of the two-step tunnelling are first introduced and used for a setup with a nanoparticle separated from a grounded electrode by a nanometre-thin wide band gap material and subject to an electric field generated in vacuum by a distant anode. Tight confinement in the nanoparticle gives rise to well-separated energy spectrum. Moreover, due to the discreteness of the electronic states the field emission current as a function of the applied electric field presents stair-like features. The presented model was constructed to explain the appearance of such features in various field emission experiments. The experimental procedure is also detailed in this chapter and the results are found in qualitative agreement with the proposed model.