To estimate the apex field-enhancement factor associated with an array of carbon nanotubes (CNTs) on a planar cathode surface, the model of the floating spheres between parallel anode and cathode plates was proposed. An approximate formula for the enhancement factor was derived showing that the intertube distance of a CNT array critically affects the field emission. When the intertube distance is less than the height of the tube, the enhancement factor decreases rapidly with decreasing distance in qualitative agreement with the numerical simulation. Considering the field-emission current density, the field emission can be optimized when the intertube distance is comparable with the tube height, in accordance with the results from the experiments. Finally, the influence of the anode-cathode distance on the enhancement factor was also discussed, showing that the anode-cathode distance has little effect on the field emission from a CNT array. Thus, we can reduce the theshold voltage to some extent by decreasing the anode-cathode distance.

In order to study the tip field of the carbon nanotube (CNT) or CNT array standing upright on a cathode plane, we proposed a model in which the long CNT is replaced by a floating top segment at the cathode potential. Using the fictitious charge and image method, a simple approximate formula for the field enhancement factor of a single CNT linear with the height-to-radius ratio has been deduced. This result is evidently improved compared to that from the floating sphere model. The normalized field strength distribution on the top hemisphere is also calculated and plotted, with the result depending slightly on the height-to-radius ratio. An estimation shows that the field emission intensity on the cylindrical surface of CNT is negligible compared to that on the top hemisphere.

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We present a three-dimensionally configured cathode with enhanced fieldemission performance formed by combining carbon nanotube (CNT) emitters with a nickel foam (NiF) substrate via a conventional screen-printing technique. The CNT/NiF cathode has low turn-on electric field of 0.53 V lm À1 (with current density of 10 lA cm À2 ) and threshold electric field of 0.87 V lm À1 (with current density of 0.1 mA cm À2 ), and a very high field enhancement factor of 1.4 9 10 4 . The porous structure of the NiF substrate can greatly improve the field-emission properties due to its large specific surface area that can accommodate more CNTs and increase the emitter density, as well as its high electrical and thermal conductivities that facilitate current transition and heat dissipation in the cathode. Most importantly, the local electric field was also enhanced by the multistage effect resulting from the rough metal surface, which furthermore leads to a high field enhancement factor. We believe that this improved field-emission performance makes such cathodes promising candidates for use in various field-emission applications.

Integrating carbon nanotubes (CNTs) and graphene into hybrid structures provides a novel approach to three dimensional (3D) materials with advantageous properties. Here we present a water-processing method to create integrated CNT/graphene hybrids and test their field emission properties. With an optimized mass ratio of CNTs to graphene, the hybrid shows a significantly enhanced field emission performance, such as turn-on electric field of 0.79 V/μm, threshold electric field of 1.05 V/μm, maximum current density of 0.1 mA/cm2, and field enhancement factor of ∼1.3 × 104. The optimized mass ratio for field emission emphasizes the importance of both CNTs and graphene in the hybrid. We also hypothesize a possible mechanism for this enhanced field emission performance from the CNT/graphene hybrid. During the solution treatment, graphene oxide behaves as surfactant sheets for CNTs to form a well dispersed solution, which leads to a better organized 3D structure with more conducting channels for electron transport.