During the melting process, the symmetrical mesh structures at three special moments for both meshes are compared in Figure 4. The difference in the melting pathway of both meshes can be attributed to the different ∆I for monitoring the melting of mesh segment, which are 0.1 mA for the Ag microwire mesh and 0.1 μA for the Ag nanowire

mesh. Note that such difference can be removed by employing much smaller ∆I for the Ag microwire mesh at the expense of increasing computational cost. Figure 4 Mesh structures at three special moments JQEZ5 in the melting process of both meshes. (a) The starting moment, (b) the moment with the maximum current (i.e., sudden fall of current), and (c) the ending moment. Moreover, from the present simulation results, it is believed that under constant current density (i.e., current-controlled current source), electric breakdown of the mesh will never RG7420 datasheet happen as long as the load current I does not reach the maximum value of I m (i.e., I mC) even if several mesh segments melt. This point is quite different from the reported EVP4593 manufacturer electrical failure of a random Ag nanowire network [26] under constant current density after a certain current stressing period. Such difference between experiments and present simulations also implies that the electrical failure in real

Ag nanowire mesh should be the synergy of Joule heating and some other possible causes, such as corrosion by sulfur, atomic diffusion in the nanowire itself, and Rayleigh instability [26]. Proposal of figure of merit Z To explore the intrinsic characteristics of the melting behavior of metallic microwire and nanowire meshes, it would be helpful to find a common parameter which is independent of geometrical and physical properties of the mesh. In order to deduce such a parameter, let us consider almost a simple

model of a wire subjected to a constant current as shown in Figure 2a. By neglecting the difference between T (i,j) and T (i-1,j) for simple approximation, the following equation can be easily obtained from Equation 4: (9) where T C is the maximum temperature occurring in the center of the wire with x = l/2. It indicates that j 2 l 2(ρ/λ)/(T C - T (i,j)) is independent of geometrical and physical properties of the wire. Based on the above consideration, the following dimensionless parameter Z was proposed as figure of merit of the mesh: (10) which indicates the current-carrying ability of the mesh. The variation of calculated Z during the melting process is shown in Figure 5, which was developed from the numerical results in Figure 3. Note that the maximum value of Z (i.e., Z C) corresponding to the maximum value of I m (i.e., I mC) characterizes the current-carrying capacity of the mesh, at which the mesh equipped with current-controlled current source will melt until open.