## 4 Mechanism of the Copper Particles in the FR4 during CAF  
Due to the presence of moisture and an electric field, copper ions will migrate along the glass fiber. This is a well-established phenomenon in PCBs known as CAF. As copper ions move, and as it is known that conductive particles exposed to an applied electric field will be charged [13; 14], these copper ions will also be charged. As the charged particles move, they also induce a current through the external circuit [15] and, in the case of partial discharge (which will be described later), a very short pulse of current will be induced as there will be a charge transfer between the particle and the facing electrode, which is the cathode [16].  
Generally, conductive particles in the presence of an electric field and fluid such as water will be subjected to various forces including a drift electric force, fluid force, and gravity force. The fluid force includes a mass force, drag force, and Basset force. For a detailed study of the forces, one may refer to the work by [PERSON] et al. [17]. Although the work by [PERSON] is for conductive particles in liquids, several of the underlying physical mechanisms considered can be applied. In the situation studied in this work, due to its mass and density, the copper particles were only subjected to the drift electric force and no rebound between the two electrodes occurred.  
As the conductive particles are close to the cathode as driven by the electric field from the anode to the cathode, partial discharge can occur due to the intensification of the electric field between them [17]. It has been found that the electric field is enhanced by 4.2 times for a spherical particle [16]. In the presence of multiple conductive particles, as in our case, the frequency of the partial discharge can be much higher, as shown by [PERSON] et al. [18].  
However, partial discharge does not necessary lead to the breakdown of the dielectric but it will lead to the reduction of its breakdown voltage. As the size and concentration of the particles increase, the insulating performance of the dielectric is further inhibited [19; 20; 21]. With the reduction in the insulating performance, a leakage current can flow through the FR4 and generate heat. It is worth noting that if the temperature around the FR4 exceeds more than 65 \({}^{\circ}\)C, heat dissipation becomes a major issue for the FR4; beyond this temperature, the failure mechanism changes to a thermal breakdown from an electric breakdown [2].  
When the particle concentration is relatively high, the formation of a particle bridge is possible. It was found that a DC field is beneficial to such a formation, as shown by the work by [PERSON] et al. [22].  
After a partial discharge, it is suspected that a short carbonization path is formed that connects the conductive particles to the nearby electrode [23; 2]. In a sense, the electrode is now extruded. Hence, the conductive particles that are further away can now also have a partial discharge with the subsequent formation of a carbonization path. When the resistance reduces to a certain value that corresponds with an increase in the leakage current, the Joule heating can drive out the surrounding moisture and an increase in resistance can be expected, as was observed in our experiments (shown later in Section 7) However, the charge relaxation on the conductive particles may also be reduced and thus the movement of the charged conductive particles can move further. At the same time, this localized heat enlarges the crack. Hence, external moisture can now diffuse further and in a greater amount into the FR4. As the conductive particles move closer to the extruded electrode, partial discharge occurs again. This iteration continues until the effective distance between the extruded electrode and the anode becomes so close that the field between them is so high, it exceeds the breakdown field of the FR4, which is already reduced due to the presence of conductive particles and carbonization.