<title>Numerical calculation of the carbon nanostructure current using a three-dimensional model</title>

Abstract

Thin-film nanotube carbon structuresexhibitgood emission properties. Thusthey are employed, as a base, for creating matrix field emitter arrays, flat displays and electrovacuum's devices. To design these devices one needs, however, to take into account emission current, electrostatic field, and intensity distribution over nanotube surface. An error in the emission current calculation is defmed by the error in calculating the electrostatic potential. We have numerically calculated the electrostatic field and the potential distribution by a three-dimensional model of the nanotube structure with the use of the fmite elements method and a special technique. The enor of the method was estimated to be 9% by solving the model problems. An anode cunent of 0.1 mA was generated for thin-film nanotube structures with a height of 10 nm and a diameter of 3 nm at potentials at the cathode of 0 V and at the anode of I kV for a cathode -anode spacing of 20 mkm. The calculated intensity on the emitter tip was 4000 ky/cm. Keywords: field emitter arrays, carbon nanotube, singular points, three-dimensional model Experimental investigation has demonstrated thin carbon films containing tube-like nanoclasters (tubellenes) to be a good field emission material1 . Presently, they are used as a base to develop field emission anays for displays and devices of vacuum microelectronic. Designing the devices involving these field emiUer arrays necessitates calculation electric field strength and emission current from the carbon film. The complex structure of the tubellene film surface prevents the application of analytical methods for the calculation. An error with calculating the emission current is defmed by the enor in calculation of electrostatic potential. The error of a few percents made while calculating the strength can result in a very large error in the field emission current estimation. In this paper we propose a numerical calculation of electric field and potential distribution over the emitter surface with the use of a three-dimensional model of nanotube clusters and the finite element method. Due to the singular field behavior near the emitter tip an accurate calculation of the field strength is hindered. A special technique has been developed to overcome this difficulty.