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.
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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.