Given an ideal crystal lattice as shown in Figure 3.2(a), the effect of introducing a vacancy which replaces an atom is schematically presented in Figure 3.2(b). It shows that, if the volume of a vacancy is different from the atom one, a change in vacancy concentration induces strain in the lattice due to its relaxation. Since in a typical interconnect structure the metal line is fully embedded in a passivation layer, this strain field cannot be accommodated, thus, leading to the development of mechanical stress.
As previously described in Section 3.2, the change in vacancy concentration at any point of an interconnect occurs either by a vacancy-atom exchange mechanism or, at interfaces, also by the production or annihilation of vacancies by a source/sink mechanism. This means that the strain induced by electromigration has two contributions: a migration component associated with the vacancy-atom exchange process, and a component related to vacancy production/annihilation.