Calculating the Field Emission Current from a Carbon Nanotube

The purpose of this work is to present elements of a design tool for field emission displays using carbon nanotubes as emitters. We use a continuum model to describe the carbon nanotubes and we use a locally one-dimensional approximation to calculate the emission current. We investigate the emission current to voltage characteristic, screening effects and the lateral spread of the emission current as a function of the height and radius of the nanotube. We also present a set of results pertaining to the electrostatic properties of a carbon nanotube immersed in a uniform electric field. We show that the field enhancement factor at the apex of the nanotube increases linearly with the aspect ratio in the parameter region of interest to field emission applications. We have also found that the relative variation of the field enhancement factor along the cap of the nanotube only depends on the radius and not on the height of the nanotube.