Optimized Carbon Nanotube Array Cathodes for Thermo-Field Emission in Plasmas: A Theoretical Model and an Experimental Verification

In this work we developed a 3-D theoretical model for plasma-enhanced thermo-field emission from nanostructured cathodes in the absence of significant erosion. Our first studies indicated that very dense arrays of vertically-aligned carbon nanotubes (CNT) acting as electron emitters in vacuum could sustain the temperatures resulting from very high surface-averaged current densities such as those found in the cathode spots of arc discharges on non-refractory cathodes. A comparative study of the electron emission models for cold surfaces subjected to strong electric field revealed the existence of a simple relation between the inaccurate Fowler-Nordheim (F-N) equation and the accepted result provided by the theory of Murphy and Good (M-G). We therefore proposed a parametric equation for the emitted current density which was as convenient as the F-N equation but more accurate. The use of M-G theory has also provided an explanation for the tip cooling effect described in a previous study on the destruction of field emitting CNT. We identified the source of the tip cooling effect as the Nottingham effect. For very short emitters, this particular effect heats the surface and accelerates the destruction process and for long emitters, it creates a small isothermal zone at the emitter's tip which is destroyed when it reaches a critical temperature (approximately 1850 K according to our calculations). When combined to existing data on the emitter's length, its diameter, the applied voltage and the measured current, our model can provide the emitter's work function, its room temperature resistivity and the value of the thermal contact resistance between the emitter and its substrate. Another version of this model includes a calculation of the surface electric field in the presence of a non-thermal plasma. To this end we modified the model developed by Mackeown and obtained a general result for 3-D surfaces. This general expression requires the calculation of the ion flux enhancement factor which can be obtained by solving Laplace equation above the surface of interest. This simple approach allows us to describe how the ions are redistributed within the sheath towards the tip of the CNT where the surface field increases. These theoretical predictions were tested by developing simultaneously a fabrication process for a composite electrode matching the optimized design we suggested. Anodic aluminum oxide templates were used as substrates to grow CNT arrays. In order to facilitate their large scale use we modified a standard CNT production process to allow the direct use of as anodized commercial aluminum. Our resulting electrodes were then used as cathodes in low pressure gas discharges. The operating parameters of these discharges are different from the typical voltages and current densities found in glow discharges using as electrodes bare aluminum surfaces. In fact, due to the very low work function of the sharp and relatively ordered emission sites and the simultaneous presence of a ceramic template around them, our electrodes produced very diffuse attachment points for the plasma in a similar fashion as thermionic cathodes do for high pressure arcs. They also required lower (38-140 V) sustaining voltages than what is necessary to sustain a conventional glow discharge. Our electrodes also showed the ability to sustain these low voltage discharges for as much as 500 hours if their bulk temperature was maintained below 60 Celsius and if water vapour was added to the feed gas. Our experiments in nitrogen-water mixtures demonstrated the feasibility of producing large amounts of UV photons at an operating voltage (anode, grounded cathode) of 90-100 V. These results are very promising for future applications in lighting.