2.2 Moleculardynamicsmodelingofsixmaterialpairs

The wire bonding process with six material pairs (Cu-Cu, Ag-Ag, Au-Au, Cu-Ag, Cu-Au, and Ag-Au) are investigated using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) ^[21] . The Open Visualization Tool, which is three-dimensional (3D) visualization software designed for postprocessing atomistic data obtained from MD, is used for analysis ^[22] .

The frequently used embedded atom method (EAM), which is developed by Daw and Baskes ^{[23, 24]} , can govern interactions among atoms. In this work, the EAM is used as the force field. The total energy E of a single atom i is defined as follows:

where the embedding energy F is a function of the atomic electron density ρ ; The single pair potential interaction is defined as ϕ ; while the element types of i and j atoms are defined as α and β , respectively. On the right side of Equation (2-1), the summations are calculated over all the neighbors of atom within the cutoff distance.

All simulations use the same EAM potential parameters developed by Zhou et al. ^[25] for Cu-Ag-Au. For each simulation, a view of the wire and substrate is extracted to observe microweld formation and breakage processes ^[26] . Fig. 2-1(a) shows the MD simulation model of different material pairs, which consists of the wire and substrate parts. The lower layer of the wire part and the upper layer of the substrate are defined as the Newton layer. The upper layer of the wire part and the lower layer of the substrate are defined as the fixed layer, and the middle layer of the substrate is defined as the thermo layer ^[11] .

The Newton layer is the main interaction area during the simulation, where in the NVE ensemble is used. The fixed layer is set to fix the other layers on their bottoms. In the wire part, the fixed layer is used to push the Newton layer (indenter) such that it moves forward at a stated velocity. While in the substrate, the fixed layer is used to fix the low end of the substrate by setting the fixed layer velocity to 0 m/s. The thermo layer plays a role in controlling the temperature in which the NVT ensemble is used ^[17] . The thermo layer is set to the constant temperature (0.1 K) during the whole process, which prevents the drastic fluctuations of atomic displacement and stress ^[27] .

As shown in Fig. 2-1(b), the velocity of the wire part is set to 10 m/s ^[10,28] . Before the microscale contact process begins, the system has a relaxation of 100 ps to release energy. After relaxation, the wire part moves along [001] towards the substrate for 25 Å during the loading process. Afterward, the wire part retracts from the substrate in the opposite direction [00-1] with the same speed for 25 Å during the unloading process. Due to the constant velocity of the wire part, the force between the wire and substrate equals the loading force. The atomic stress analysis is calculated based on spatial and temporal ensemble averages of the atomic virial stress, and the results are shown in the form of the six components of the atomic stress tensor ^[27-29] :

where σ _mn is the atomic stress component in the order of m , n ( x , y , or z ); mv _m v _n is the kinetic energy contribution; is the pairwise energy contribution, which is associated with the surrounding atoms from n =1 to N _p . Additionally, the von Mises stress is adopted to present the atomic stress distribution, as shown in Equation (2-3):

where σ _vm ( i ) is the von Mises stress of atom i ; σ _mn ( i ) is the atomic stress tensor in the order of m , n ( x , y , or z ). 1UZE8bldJ3nK2x0GhF6i859yPWugoEshufDdWFfyZofRX364paJlOg247uTFSgqn