Nonlinear I-V behavior of CNT filled polymer composites and investigation of the mechanismJianWang,1,2 Shuhui Yu,1,a) Authors to whom correspondence should be addressed. Electronic addresses: yuushugmail.com and rong.sunsiat.ac.cn. Suibin Luo1,Baojin Chu,3 Rong Sun1,a) and Ching-Ping Wong41Center for Advanced Materials, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China2Department of Nano Science and Technology Institute, University of Science and Technology of China, Suzhou,215123, China3Department of Materials Science and Engineering, CAS Key Laboratory of Materials for Energy Conversion, University of Science and Technology of China, Hefei, 230026, China4Department of Electronics Engineering, The Chinese University of Hong Kong, Hong Kong, ChinaNonlinear current-voltage (I-V) behavior is a typical feature of polymeric composites containing conductor or semiconductor fillers, which are a desirable choice to handle the transient voltage and electrostatic discharge (ESD) of microelectronic devices. In this paper, the mechanism of nonlinear behavior of carbon nanotubes (CNT) filled polymer composites in the applied electric field was explored. The I-V curves of the composites exhibited three regions. The variation of current at low voltages (region I) is linear. Under relatively higher voltages (region II), the variation is nonlinear and grows exponentially with voltage. As the voltage is further increased, the I-V curve is also non-linear (region III), but the growth rate is significantly slowed down and the nonlinear coefficient is much smaller. The I-V characteristics at the above three regions were analyzed systematically based on the calculation of electron concentration, as well as the electron drift, diffusion and Joule-heating. With the rapid development of electronic devices, functions of the IC (integrated circuit) system become increasingly powerful. Meanwhile, in order to reduce power consumption and prolong the service life of the devices, the semiconductor components and IC systems should operate at low voltages.1 Therefore, the over-voltage protection is undoubtedly important to guarantee the reliability of the devices.Requirements of multifunction and miniaturization of the devices drive the development of system-in-package and component embedding technology.2-4 It is an effective way to improving systems integration that elements are embedded inside the IC package substrate. The traditional circuit protection components made of ceramics such ZnO varistors are not compatible with the printed circuit board (PCB) processing technology. Polymeric composites containing conductor or semiconductor fillers are a primary choice to be integrated in the organic substrate to handle the transient voltage and electrostatic discharge (ESD).5 The material should have a nonlinear voltage characteristic, which behaves like an insulator (dielectric) during normal circuit operation and becomes conductive when voltage surpasses a predefined threshold. The material becomes an insulator again after the voltage drops back below the threshold to normal operation level.Nonlinear current-voltage (I-V) behavior is a typical feature of inhomogeneous systems containing conductive particles or clusters.6-11 Gefen et al.8,9 observed nonlinear I-V characteristics of a two-dimensional (2D) system of a very thin gold film (7nm) as the film was approaching transition from insulator to metal which was carefully accomplished by film processing. Two theoretical models, the nonlinear random resistor network (NLRRN) model and the dynamic random resistor network (DRRN) model, were proposed to explain the deviation of I-V curves from linear characteristics. The first model assumes that the conducting backbone consists of microscopic components and the current-voltage characteristics of each such component contain a small nonlinear contribution. The second model assumes that in the presence of a sufficiently strong local field a non-conducting channel may become conducting. However, neither of the above models can explain why the channel is turned off at a low voltage and turned on at a high one, or why some channels are nonlinear, while others are linear. Sheng10 has investigated the electrical conduction of disordered materials, which are characterized by large conducting regions separated by small insulating barriers. He proposed a fluctuation-induced tunneling mechanism, in which the thermally activated voltage fluctuation across the insulating gaps played an important role in determining the field dependence of the conductivity. However, when the distance between conductive particles is above the cutoff distance of tunneling effect, which is 1.4 nm between two CNT, the tunneling effects are not significant.12 The effects of electron diffusion, drift and Joule-heating in insulating barriers on the non-linearity should be taken into account, which however, have