5.6.3 Sites of Void Nucleation

Figure 5.37 shows the vacancy distribution in a bamboo-like interconnect via. The current flows from right to left, driving vacancies towards the via. Vacancies concentrate at this site, because the barrier layer blocks further vacancy diffusion into the upper metal line. Thus, the maximum vacancy concentration is located underneath the via. However, as already pointed out, grain boundaries also act as fast diffusivity paths. Consequently, vacancy diffusion along grain boundaries is an important transport mechanism, which leads to higher vacancy concentration along the grain boundary planes, as shown in Figure 5.37.

Figure 5.37: Vacancy distribution in a bamboo-like interconnect line (in cm$^{-3}$).

According to the grain boundary model presented in Section 3.4.1, once the vacancy concentration within a grain boundary exceeds the equilibrium concentration, the grain boundary is able to trap the excess vacancies. Therefore, the trapped vacancy concentration within the grain boundaries increases, as shown in Figure 5.38.

The rate at which vacancies are trapped/released from the grain boundary corresponds to an annihilation/generation term, as given in equation (3.50). In turn, generation/annihilation processes lead to production of mechanical stress, according to (3.42). Thus, the stress build-up closely follows the trapped vacancy concentration and develops at grain boundaries, as can be seen in Figure 5.39.

Figure 5.38: Trapped vacancy concentration (in cm$^{-3}$). Vacancies are trapped at grain boundaries, once the vacancy concentration within a grain boundary exceeds the equilibrium value.

Figure 5.39: Hydrostatic stress distribution in a simulated interconnect (in MPa). Mechanical stress develops at grain boundaries as a result of vacancy trapping/release events.

These results are crucial in order to explain the void nucleation at sites away from the cathode end of the line [27]. Void nucleation observed at the copper/capping layer away from the cathode end is only possible provided there is an available site where flux divergence occurs and, at the same time, is a site of weak adhesion. Grain boundaries are the only features which can provide such sites. Since triple points formed by the intersection of grain boundaries with the copper/capping layer interface are natural places of flux divergence and weak adhesion [31], the development of mechanical stress at these sites, as shown in Figure 5.39, can explain void nucleation in the middle of the line.

The introduction of the grain boundary network into the simulations, together with the consideration of material interfaces as fast diffusivity paths, represents a significant improvement of the developed model, so that the most common experimental observations regarding electromigration induced void nucleation can be explained.