Tip Cooling Effect and Failure Mechanism of Field-Emitting Carbon Nanotubes Wei Wei, † Yang Liu, ‡ Yang Wei, † Kaili Jiang,* ,† Lian-Mao Peng,* ,‡ and Shoushan Fan* ,† Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua UniVersity, Beijing 100084, China, and Key Laboratory for the Physics and Chemistry of NanodeVices and Department of Electronics, Peking UniVersity, Beijing 100871, China Received August 23, 2006; Revised Manuscript Received October 31, 2006 ABSTRACT The cooling effect accompanying field electron emission has been considered for a single carbon nanotube (CNT) used as a field emission (FE) electron source. An improved model for the failure mechanism of field emitting CNTs has been proposed and validated. Our model predicts a maximum temperature (T-max) located at an interior point rather than the tip of the CNTs, and the failure of the CNT emitters tends to take place at the T-max point, inducing a segment by segment breakdown process. A combination of Joule heating and electrostatic force effect is proposed responsible for initiating the failure of the field emitting CNT and validated by in situ FE observation. Carbon nanotubes (CNTs) are promising field emission electron sources with advantages of high brightness, high monochromaticity, and low power consumption, 1 which can be applied in various devices such as flat panel displays, 2 electron guns, 3,4 X-ray sources, 5 etc. The field emitting materials, however, are requested to withstand the high- temperature caused by Joule heating and the high tensile stress exerted by the electric field (E-field) to avoid device failure. 1 In the case of CNTs, both the high temperature 6 and tensile stress 7 have been measured during FE. Device failures due to both effects have been intensely investigated. 6,8-13 Concerning the temperature effect, Vincent et al. have proposed a model to calculate the temperature distribution along CNTs during FE, 8 which predicts a maximum tem- perature at the CNT’s tip. Later, this model was slightly modified by Huang et al., which predicts that the tip temperature will go to infinity when the emission current is above a critical value. 9 If the maximum temperature is located at CNT’s tip, a gradual shortening is expected to occur at the tip of the CNT when it reaches the critical current. In many cases, however, the CNTs are shortened segment by segment, rather than shortened gradually, according to in situ transmission electron microscopy (TEM) observations by Wang et al. 10 and Doytcheva et al. 13 To solve this puzzle, we conducted both theoretical modeling and a series of experiments. We found that this phenomenon can be well interpreted by considering the heat taken away by emission electrons, which was further verified by our experimental results. On the basis of this model, the failure mechanisms of the CNT emitters were proposed and validated. More than 100 years ago, Richardson theoretically pre- dicted the cooling effect in thermionic emission; 14 that is, the evaporation of electrons from the surface of a hot conductor is very similar to the evaporation of molecules from a liquid, causing a cooling of the surface. 15 In his paper, 14 Richardson argued that the cooling effect induced by electron emission is less prominent than that by thermal radiation for metals at less than 2000 K, but in the case of carbon, the cooling effect became prominent at temperatures above 2000 °C. As is well-known, FE is a quantum tunneling process, implying no energy loss when electrons pass through the cathode-vacuum barrier. When an electron is field emitted from a cathode at temperature T, it will take away an energy of about (3/2)k B T, inducing a cooling effect. For FE from CNTs, Vincent et al. have measured a tip temper- ature of about 2000 K at an emission current of 2 µA. 8 On the basis of their data, a rough estimation indicates that the energy loss due to electron emission is more than 4600 times that due to thermal radiation, which shows the cooling effect in FE is much more prominent than that in thermionic * Corresponding authors. E-mail: jiangkl@tsinghua.edu.cn, lmpeng@ pku.edu.cn, and fss-dmp@tsinghua.edu.cn. † Department of Physics and Tsinghua-Foxconn Nanotechnology Re- search Center, Tsinghua University. ‡ Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics, Peking University. NANO LETTERS 2007 Vol. 7, No. 1 64-68 10.1021/nl061982u CCC: $37.00 © 2007 American Chemical Society Published on Web 12/01/2006