13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- A corresponding computational program is developed to solve this electro-thermal problem regarding the electrical breakdown of the metallic nanowire mesh induced by Joule heating. Note that to record precisely the melting current triggering the melting of mesh segment, the increment of current should be tuned to make mesh segment melt one by one. The corresponding simplified flow chart of this program is shown in Fig. 2. 3. Electrical Breakdown of an Ag Nanowire Mesh 3.1 Numerical Model Fig. 3 Schematic illustration of an Ag nanowire mesh (10×10) Table 1 Physical properties of Ag nanowire Melting point Tm (K) 873 [12] Thermal conductivity λ (W/µm∙K) 3.346×10-4 [13] Electrical resistivity ρ (Ω∙µm) 0.119 [14] A silver (Ag) nanowire mesh (10×10) as shown in Fig. 3a is considered here. The numbers of mesh nodes and mesh segments are 100 and 180, respectively. The pitch size is p=200µm, both the width and thickness of Ag nanowire are w=b=100nm as shown in Fig.3b. The physical properties of Ag nanowire are listed in Table 1. Note that size effect on the physical properties is taken into consideration for Ag nanowire. As shown in Fig. 3a, the external current I flows into the mesh from node (0, 0) and flows out of the mesh from node (0, 9), which means that node (0, 0) has an external input current and node (0, 9) has an external output current. For the other nodes, no any external current is given. A constant value is assigned to the electrical potential of node (9, 9). The temperature of boundary nodes (i.e., (i, 0), (0, j), (i, 9), (9, j) where i, j=0,…,9) is room temperature of T0=300K. There is no any external heat energy for all the other nodes. The developed program is employed to investigate the evolution of the melting current Im triggering the melting of the mesh segment. Here, in order to make mesh segment melt one by one as much as possible, the increment of the input current is set with a small value of 0.001mA until the melting current is reached. The corresponding melting voltage Vm ( i.e., the difference of electrical potential between node (0, 0) and node (0,9)) is also recorded in order to calculate the variation of resistance of the mesh, i.e., R, with regard to the sequential electrical breakdown of mesh segments.
RkJQdWJsaXNoZXIy MjM0NDE=