## 1 Introduction  
Electronic packaging, although it is the last process to be done, is an indispensable part of the integrated circuit (IC) industry. It is responsible for connecting the integrated circuit with other electronic components. It also prevents the integrated circuit from being damaged by external forces, avoids chemical erosion and the influence of external noise, and increases the cooling path [1; 2; 3]. The range of packaging technology is very wide; it is applied in the fields of physics, chemistry, machinery, materials, etc. Packaging technology also uses a variety of materials, such as metals, ceramics, and polymers. Although packaging technology can prevent external forces from destroying the integrated circuit, there will always be unavoidable damage under normal use, such as joule heating damage and metal junction diffusion reaction and corrosion [4; 5; 6; 7; 8]. Joule heating occurs when the electron passes through the metal conductor inside the integrated circuit and produces lattice vibration due to collision with the atoms; the electrical energy and kinetic energy produced are converted into heat energy, which causes the solder temperature to rise. If the current passes through the metal conductor for a long time, overheating could occur, causing deformation, damage between the materials due to different expansion coefficients, and faster electromigration because of the thermal energy. The principle of electromigration dictates that when a current flows into the conductor, it moves from the anode to the cathode, while the electrons flow from the cathode to the anode. As the electronic and kinetic energy increases as the current density increases, if the energy increases over its threshold, the atoms inside could move. The atoms will then move away from the cathode, producing a void, and will accumulate on the anode, causing protrusion. This abnormal diffusion will cause the lattice to produce dislocation. Ultimately, this will reduce the reliability of the IC and cause signal delay and distortion. Electromigration was discovered by [PERSON] in 1861; since then, many people have studied this phenomenon [9; 10; 11; 12; 13]. In 1950, [PERSON] and [PERSON] indicated the relationship between the direction of current and the transport of matter. They observed that the direction of transport changes with charge carriers, so they made an indentation on the metal to observe the mass transfer of electromigration. From then on, this method has become the standard electromigration measurement method [14; 15]. Electromigration is a mixed effect of electric power and thermal energy; it is mainly caused by electrostatic force and electronic wind resulting in mass transfer. Electrostatic force and electronic wind occur in opposite directions; their relationship can be described using formula (1), and electric wind can be calculated using formula (2). \[F_{driving}=\Sigma_{i}CM_{i}F_{i}=F_{d}+F_{wind} \tag{1}\]  
where  
\(F_{d}\) is the electrostatic force of the electric field,  
\(F_{wind}\) is the force of the electronic wind,  
\[F_{wind}=Z^{*}|e|E \tag{2}\]  
where  
\(Z^{*}\) is the number of effective electrons that cause atoms to move,  
\(e\) is the electron charge,  
\(E\) is the electric field. The metal atoms move and carry energy. This energy comes from the atom itself and several external factors. As the atom moves, it may collide with other surrounding atoms, creating momentum transfer. The movement and diffusion of atoms is the main cause of electromigration effects. The drag force between electrons or electron holes and atoms also causes atoms to diffuse. Under the influence of electromigration effects, the diffusion of metal atoms can be expressed by using formula (3) [16].