## 5 Conclusions  
We consider that field emitters can be used as an electron-emission source in CL devices. The field emitters that are used in CL devices, including lighting devices employing visible rays, X-rays, and ultraviolet radiation, suffer from the problem that the radiation from the CL device has a fluctuating output that depends on the electrical properties of the field emitters in time and space. In this study, we analyzed the fluctuation of the output when field emitters are used in a CL device, where we employed metallic SWCNTs as field emitters. The homogeneous dispersion of metallic SWCNTs with high crystallinity is one of the essential design requirements in the fabrication of the cathode in CL devices in order to obtain high output stability. However, it was difficult for the highly crystalline SWCNTs to control homogeneous dispersion into a mixture to make an FE cathode device. We have realized the homogeneous dispersion of metallic SWCNTs with high crystallinity for the first time by an agitation process with the ITO precursor solution, butyl acetate added, as is required to control the viscosity of the solution, and EC as a surfactant at a weight ratio of 1:8:600:10. It was difficult to disperse highly crystalline carbon nanotubes homogeneously, because no surfactant can combine to a surface of a nanotube with high crystallization. In this study, we succeeded to disperse the solution with the designed composition by controllable wet dispersion process. The metallic highly crystalline SWCNTs were employed as field emitters to analyze the fluctuation in the FE of conventional materials. We succeeded in constructing a physical mechanism to examine FE fluctuation. Fluctuation of the FE current was observed using the metallic SWCNTs as field emitters, which was compared with the theoretical spectra calculated using a current-fluctuation theory that incorporates a realistic power spectrum of the current fluctuation in the Fowler-Nordheim tunneling regime. Good agreement was seen between the observed and the theoretically calculated spectra of the FE current obtained using  
Figure 6: Dependence of power spectrum by simulation on the applied voltage. \(E_{0}\) indicates the original field supplied between the cathode and anode electrodes. the SWCNTs. We consider that inelastic electron tunneling causes the current fluctuation in the FE. The mechanism behind this can be explained by the superposition of the high frequency components of FE current in time and space. We also succeeded in developing a theoretical model of the flow of electrons (current) by considering the fluctuation of the tunnel current due to electrons passing through a potential barrier in the FE regime. The tunneling matrix based on the potential barrier that was obtained using the WKB approximation method is an important parameter for developing an inelastic-electron-tunneling model, and was used to obtain the power spectrum in this study. The FE model was obtained by combining the Fowler-Nordheim tunneling model with the power spectrum obtained using the tunneling matrix. From the above results, the use of metallic SWCNTs with high crystallinity as field emitters was found to generate a fluctuating FE current, where the fluctuation originated from inelastic electron tunneling. We have provided a brief explanation of the FE current fluctuation of metallic SWCNTs in terms of their electrical conductivity, and described the development of a conduction model for electrons that passed through a potential barrier. Highly crystalline SWCNTs are expected to be used as field emitters with stable FE. This work was supported in part by DOWA Holdings Co. Ltd., Tokyo, Japan. The authors would like to thank the co-researchers from DOWA for the discussions and suggestions, and are grateful for the technical instructions provided during the device-assembly process and the assembly work.