1.3 Results and discussions

1.3.1 Formation and breakage processes of Cu-Cu weld

Fig. 1-2 shows an atomic (010) slice of the Cu wire and substrate during the loading and unloading processes. An attractive force between the wire and substrate is observed when the wire is close to the substrate, which displays the bulging of the substrate surface atoms under the wire tip, as shown in Fig. 1-2(a). The attraction force increases with the decrease of the distance between the substrate and wire. The substrate surface atoms are rapidly contacted by wire atoms, as shown in Fig. 1-2(b). As the wire continues to press downward, the repulsion between the substrate and wire becomes the main force. Because the substrate atoms are compressed at the lower end of the wire, the atomic lattice begins to deform and the strain energy increases. When the repulsion exceeds a certain value, the lattice structure breaks, and the substrate atoms start to rearrange and the strain energy is released, as shown in Fig. 1-2(c). During the unloading process, the main force acting on the substrate atoms changes from repulsion to attraction. Upon retraction of the wire away from the substrate surface, a small portion of the substrate atoms adhere to the indenter surface, as shown in Fig. 1-2(d). Continuing the retraction of the wire, a neckband is formed between the indenter and substrate, as shown in Fig. 1-2(e). At the time of 484 ps, the wire separates from the substrate, as shown in Fig. 1-2(f).

Fig. 1-2 Atomic (010) slice of the Cu wire and substrate during the loading and unloading processes

The variations of the Cu wire load force versus the model indentation displacement are shown in Fig. 1-3, which consists of the loading curve and unloading curve. During the initial contact stage, in which the indentation displacement is-3.6 Å, the attractive force between the wire and substrate appears, and increases significantly. This instability corresponds to the jump-to-contact (JC) phenomenon[26]. During the JC process, the kinetic temperature of the system increases due to the bulging of the surface atoms, then this temperature rise is dissipated to the ambiance through stochastic collisions. At the onset of contact formation, in which the tip approach is-0.75 Å, the maximum attractive force reaches a value of 23.5 nN. As the indentation displacement continues to increase, the repulsive force increases and becomes the main force. When the indentation displacement equals 2.32 Å, the contact load is approximately zero, the attractive and repulsive forces between the wire and substrate achieve the equilibrium point. Further indenting the wire to the substrate, the contact load increases linearly by increasing the indentation displacement. When the indentation displacement reaches 4.50 Å, it meets the yielding point and the plastic deformation starts. During the unloading process, the repulsive force considerably decreases and changes to attractive force as the indentation displacement reaches 4.57 Å. The loading and unloading curves do not coincide, the unloading curve presents hysteresis. This is explained by the wire indenter retraction away from the substrate; a neckband forms and breaks between the indenter and substrate because of the adhesion force, as shown in Fig. 1-2(f).

Fig. 1-3 The variations of the Cu wire load force versus the model indentation displacement