4.1. Joule Heating of Silver Wire under Current Supply
The electrical–thermal field coupling simulations of silver wire were conducted under current supply with different current density. The temperature distribution of the silver wire obtained by simulation was shown in Figure 5
. The sample temperature increased to 367.8 K due to Joule heating as the room temperature was 300 K when the current density was set to be 0.6 MA/cm2
, and the temperature in the silver wire took the maximum value at the center of the narrow part and decreased towards the wider part of the structure. This trend was observed for all simulations under different current densities of 0.4~1.2 MA/cm2
and the temperature distribution along the silver wire length direction at the center line is shown in Figure 6
From the results of the electrical–thermal coupling simulations, it can be seen that a large amount of Joule heating was generated during the accelerated EM testing due to the current supply with high density, which caused a significant rise in temperature in the silver wire. The high temperature can promote the formation of more sintering necks between silver nanoparticles and increase the electrical conductivity. The experimental results shown in Figure 3
indicated that the resistances of the silver wires had descent tendency during current supply with current density of 0.6 MA/cm2
and 0.8 MA/cm2
, which can be explained by the sintering effect of Joule heating. The increased temperature of the two samples obtained by simulation were 367.8 K and 411.3 K, respectively, which are close to and over the sintering temperature (120 ℃/393 K) of the printed silver wire.
The temperature of the silver wire increased to be as high as 509 K when the current density was 1.2 MA/cm2, which is slightly lower than PET material melt temperature (~260 ℃/533 K). However, during the current supply with high density, the formation of voids by EM and TM could have increased the local current density, which enhanced the Joule heating effect and increased the local temperature and finally reached the melting point of PET and caused the failure of the silver wire.
4.2. Atomic Migration of Silver Wire by EM and TM
From the simulation results of temperature distribution of silver wire sample shown in Figure 6
, a significant temperature gradient can be observed from the transition area of narrow wire to the wide electrode part, and the gradient increased with the density of current supply. Figure 7
shows the distribution of temperature gradient along the length direction of the silver wire sample with current density of 0.8 MA/cm2
. The large temperature gradient was an important driving force of the atomic migration in the silver wire, which was known as TM.
The electron wind formed by high density current was another driving force of the atomic migration. Figure 8
shows the current density distribution in the silver wire. As the center part of narrow wire suffered current density of 0.8 MA/cm2
, the distribution of current density was not uniformly across the cross section. The maximum current density can reach as high as 0.8887 MA/cm2
at the edges where the narrow wire connected to wider part of the structure, which was the vulnerable area of the silver wire in the EM testing.
The AFD distribution calculated based on the current density and temperature gradient obtained by electrical–thermal coupling simulation result with current density of 0.8 MA/cm2
is shown in Figure 9
. The AFD caused by current shown in Figure 9
a was larger than that caused by temperature shown in Figure 9
b by about three orders, therefore, the effect of temperature gradient produced by Joule heating on the atomic migration in the silver wire could be ignored. However, it should be noted that the high temperature due to Joule heating strengthened the effective atom diffusivity significantly and accelerated the atom migration in EM testing. The total AFD distribution without taking into account the atomic concentration gradient in the silver wire is shown in Figure 9
c. The maximum value of AFD was located in the area of silver wire close to the two electrode pads. In the region nearby the positive electrode, the AFD value was negative which indicated that Ag atoms would accumulate and form hillocks in this place, and the region of silver wire nearby the negative electrode, the AFD value was positive which implied that the Ag atoms would migrate out and form voids.
shows the distribution of normalized concentration in the silver wire sample after 1 h current supply with a density of 0.8 MA/cm2
. It can be seen that the atoms accumulating in the area close to the positive electrode pad and migrating in the area close to the negative electrode pad will form hillocks and voids, respectively, causing the failure of the silver wire. The simulation result was consistent with the experimental results as shown in Figure 2
In order to investigate the EM and TM behavior of silver wire under different current density, the atomic migration behavior of silver wire was simulated with current density of 0.4~0.8 MA/cm2
. The AFD value along the silver wire with different current density at initial time is shown in Figure 11
a, and the maximum AFD value increased exponentially with the current density as shown in Figure 11
In the silver wire, the voids formation by atomic migration was the important factor that affected the electrical properties of silver wire. Figure 12
presents the variation of normalized atomic concentration in the area nearby the negative electrode pad of the silver wire during the accelerated EM testing. It showed that the atomic concentration had little change when the current density was below 0.6 MA/cm2
after 1 h testing, however, the atomic concentration increased sharply with the increase of current density.
According to the experimental and simulation results, the different behavior of silver wire on the PET substrate under accelerated EM testing with different current density is illustrated in Figure 13
. The electrical resistance and surface morphology kept almost unchanged when the current density was below 0.63 MA/cm2
. However, when the current density was larger, the Joule heating in the silver wire caused the temperature to rise by 100 ℃ which could sinter the silver wire and decreased the electrical resistance. Meanwhile, higher current density led to a significant EM phenomenon and caused failure of the silver wire. It was assumedthat no void formed in the silver wire when the normalized concentration was higher than 0.95 with the current density of ≤0.93 MA/cm2
. Voids and hillocks were formed when the normalized concentration was lower than 0.75 with current density of ≥1.1 MA/cm2
, causing an increase of local current density and acceleration of the silver wire damage, and finally breakage failure occurred in the silver wire. Thus, the current density from 0.63 MA/cm2
to 0.93 MA/cm2
can be defined as electrical sintering zone which can improve the electrical conductivity of silver wire during the current supply. A large number of voids and hillocks formed and led to the increase of silver wire electrical resistance when the current density was 0.93~1.1 MA/cm2
which could be named as the EM zone. When the current density was larger than 1.1 MA/cm2
, an open circuit occurred in the silver wire because of atomic diffusion of EM and TM or PET substrate melting due to Joule heating.