# Temperature Comparison of Looped and Vertical Carbon Nanotube Fibers during Field Emission
## 1 Introduction  
Carbon nanotube (CNT) fibers [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12] have demonstrated significant promise as field emission (FE) cathodes due to their large aspect ratios and high electrical and thermal conductivities. They can potentially be used as FE cathodes in a wide range of applications, including compact radiation sources [13; 14; 15; 16], electron guns for ring and linear accelerators [17], and vacuum nanoelectronics [18; 19; 20; 21; 22]. CNT fibers are also extremely flexible [5; 12] and do not lose conductivity when bent [5]. This allows for their arrangement in various cathode geometries other than the typical free standing vertical emitter. CNT fiber emitters are typically mounted vertically on a substrate [3; 5; 6] in order to take advantage of the high field enhancement factor due to their high aspect ratio. The tips of the fibers are cut either mechanically or by a laser [23]. The mechanically cut tips usually introduce rough edges with dangling fibrils (Figure 1). Laser cutting largely reduces the tip roughness, however, the fiber tips are still spread out at the edge. These rough edges and tip spread out are undesirable. They lead to non-uniform emission and uneven temperature distribution and hotspots at the fiber tip. To avoid these problems that are introduced by the fiber tips, we take advantage of the high flexibility of the CNT fiber to form an emitter by looping it (Figure 2), where electron emission occurs from a well-rounded fiber loop, instead of a rough tip edge. Another issue with vertical fiber emitters is their limited heat conduction and poor thermal management because of the single contact point to the cathode base (Figures 1 and 2a). In order to produce stable, high current beams, it is important to develop cathodes with improved thermal management properties, including reliable thermal stability, better thermal conduction and circulation, and reduced temperature during current emission. Despite their exceptional thermal conductivity, the maximum temperature of individual CNT field emitters can reach 2000 K near the emitter tip during field emission [24; 25] because of joule heating. For CNT fiber based cathodes, a temperature of \(>\)500 \({}^{\circ}\)C can be reached routinely during mA level current emission [3; 23; 26]. The high temperature could potentially increase the resistance of the emitter, degrade the performance of the emission, limit the stability and reliability, and eventually lead to the failure of the field emitters [26; 27]. It is thus highly desirable to explore a new configuration of CNT fiber emitters with better thermal handling capabilities. A looped fiber emitter is one such candidate since it provides an additional heat conduction path to the cathode base (Figure 2b). There are ongoing efforts to better understand the heating and temperature distribution of CNT fiber field emitters, including direct Infrared (IR) imaging [23], a multiscale model of heat dissipation [26], coupled electrical-thermal conduction with the effects of temperature dependent electrical and thermal conductivities [27], morphology dependent field emission [3], and the effects of contact resistance [6; 28]. In this paper, we study field emission from a looped CNT fiber emitter and compare the temperature distribution with a single vertical CNT fiber emitter (Figure 2). Because of the additional heat conduction path to the cathode base, the looped emitter is expected to reach a lower temperature during field emission. Direct IR imaging shows that the maximum temperature of the looped fiber (\(\sim\)300 \({}^{\circ}\)C) is significantly lower than that of the vertical fiber (\(\sim\)600 \({}^{\circ}\)C) at the same emission current of 3 mA. The experimentally measured temperature distribution is compared with  
Figure 1: Scanning electron microscope (SEM) image of a typical single vertical carbon nanotube (CNT) fiber. Inset: the fiber tip after cutting by razor blade.