13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- process of large amounts of individual nanowires. Basically, due to the limit of the properties of current sources, it is difficult to observe the trend of (I) in Fig. 4 (c) and (d) in which both melting current and voltage decrease. Consider a system composed of an Ag nanowire mesh and current source, the corresponding melting behavior can be predicted. As a representative illustration, Fig. 5 is given. For the mode of current-controlled current source (CCCS) in Fig. 5a, such regions with the decrease of current and the subsequent recovery (e.g., the area surrounded by dash rectangular) is difficult to be reproduced in experiment. The dashed arrows indicate the predicted variation of melting current and voltage during experimental melting process of the system. The rightwards dashed arrow means that at a constant current, several mesh segments melt simultaneously leading to the increase of resistance and therefore the increase of the voltage. This phenomenon is defined as local instability, which is a jump (e.g., from point PA to point PB in Fig. 5a) when compared to the melting current-voltage curve during numerical melting. The north east dashed arrow indicates that the increase of current is necessary for the further propagation of melting. This behavior is called stable melting. Moreover, the existence of the maximum melting current, marked by a circle in Fig. 5a, tells that if the input current is high enough, the mesh segments will melt simultaneously until the circuit of mesh is open. This phenomenon is denoted as global instability. On the other hand, for the mode of voltage-controlled current source (VCCS) in Fig. 5b, such regions with the decrease of voltage and the subsequent recovery (e.g., the area surrounded by dashed rectangular in the enlarged part) are difficult to realize experimentally. The dashed arrows indicate the predicted variation of melting current and voltage during experimental melting process of the system in a similar strategy with that for the mode of CCCS. There is the repetition of the vertical descent stage and the ascent stage until the circuit of mesh is open. The downwards dashed arrows indicate the vertical descent stages, where the melting of several mesh segments will happen simultaneously at a constant voltage, which shows local instability (e.g., the jump from point PC to point PD in Fig. 5b). The north east dashed arrows show the ascent stages, where the increase of voltage is requisite for the melting propagation, which shows stable melting. The only difference from that of CCCS mode is that there is no global instability for VCCS. 4. Conclusions In the present work, the electrical breakdown of a metallic nanowire mesh induced by Joule heating is investigated by solving the corresponding electro-thermal problem, where the effect of electromigration is neglected for simplicity. A numerical computational program is developed to determine the temperature profile in the mesh, and the melting current triggering the melting of mesh segment. The structural melting of a metallic wire mesh is investigated by clarifying the variation of melting current with regard to the melting propagation of mesh segments. The melting behavior of a system of the mesh equipped with current source in real experiments can then be predicted, in which two modes of current source are discussed in detail. Local instability and stable melting will occur in spite of the mode of current source. Moreover, global instability only happens at the mode of current-controlled current source. This finding deepens the understanding of the electrical breakdown behavior of a metallic nanowire mesh, and may therefore contribute to the development of nanowire-based devices with high reliability. Acknowledgements The authors are grateful to be partly supported by Tohoku Leading Women’s Jump Up Project for 2013 (J120000428) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.
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