Modeling and simulation for the field emission of carbon nanotubes array

Abstract

To optimize the field emission of the infinite carbon nanotubes (CNTs) array on a planar cathode surface, the numerical simulation for the behavior of field emission with finite difference method was proposed. By solving the Laplace equation with computer, the influence of the intertube distance, the anode–cathode distance and the opened/capped CNT on the field emission of CNTs array were taken into account, and the results could accord well with the experiments. The simulated results proved that the field enhancement factor of individual CNT is largest, but the emission current density is little. Due to the enhanced screening of the electric field, the enhancement factor of CNTs array decreases with decreasing the intertube distance. From the simulation the field emission can be optimized when the intertube distance is close to the tube height. The anode–cathode distance hardly influences the field enhancement factor of CNTs array, but can low the threshold voltage by decreasing the anode–cathode distance. Finally, the distribution of potential of the capped CNTs array and the opened CNTs array was simulated, which the results showed that the distribution of potential can be influenced to some extent by the anode–cathode distance, especially at the apex of the capped CNTs array and the brim of the opened CNTs array. The opened CNTs array has larger field enhancement factor and can emit more current than the capped one.

Introduction

Carbon nanotubes (CNTs) are considered as one of the best electron-emitting materials available because high-field enhancement is expected due to the high aspect ratio of the length to the diameter. Recent experiments and theoretical calculations have already shown that CNTs have excellent field emission properties with high emission current density at a low electric field [1], [2], [3], [4]. CNTs offer promising device applications such as flat panel displays, field emission electron source, microwave power amplifiers and so on [5], [6], [7].

Studies have shown that many parameters, including the aspect ratio of CNTs, the anode–cathode distance, the intertube distance, the opened/capped CNT and so on, can influence the field emission properties of the CNTs [8], [9], [10], [11], [12], [13], [14]. But for field emission devices, CNTs are not individual but grown in arrays or entangled with others. Their field emission properties should be influenced due to the electrostatic interaction between the CNTs. Many experiments had also proved that the intertube distance critically affects the field enhancement factor [11], [12], [13], [14]. Mayer et al. [15] used the scattering calculations and a transfer-matrix methodology to consider the field emission from several metallic (5,5) CNTs, and found the enhancement factor of individual CNT is larger than that of CNTs array for the electrostatic interactions between CNTs, and the opened CNTs have the better field emission performance. Buldum and Lu [2] obtained the local potential energy by solving Laplace's equation numerically and calculating the effective electronic potential of individual CNT using self-consistent field-pseudopotential electronic structure calculation method. But it could not explain the above behavior of field emission from CNTs array in experiments.

Although lots of researches on the field emission from CNT in experiment and theory have been developed, the mechanism of the behavior of field emission used CNTs array as emitter are still unclear. Some researches have shown that the traditional F–N theory could not well explain the field emission for CNTs array [1], [2], [15]. Thus, the field emission from CNTs array requires further modeling and calculation in order to understand their field emission mechanism. Numerical methods (for solving Laplace equation) are successful in calculating the field distribution and the field enhancement factor in various cases, which would be useful for future application of nanotube-based field emission display.

The previous research [16], [17] shows that the intertube distance could critically influence the properties of field emission from CNTs array with the floating sphere model. In order to verify the theoretical conclusion and clarify the mechanism of individual CNT and CNTs array, the field emission from the infinite CNTs array was studied by solving the Laplace equation numerically. The influence of the intertube distance, the anode–cathode distance and the opened/capped CNT on the field emission of CNTs array was taken into account, and the results accord well with the experiments and theoretical calculation. Due to the enhanced screening of the electric field, the enhancement factor of CNTs array decreases with decreasing the intertube distance, and the field emission can be optimized when the intertube distance is close to the tube height. Further study shows that the anode–cathode distance hardly influences the field enhancement factor, but the threshold voltage decreases with the anode–cathode distance. Finally, the field emission from the opened CNT and capped CNT was compared, and the results show that the opened has larger field enhancement factor and can emit more current than the capped.