3.3.6 Void Nucleation

As described in Section 2.6, the void nucleation condition represents the transition from the first to the second phase of electromigration failure [25]. From the early days of electromigration modeling, the void nucleation condition has been derived from careful investigations based on the classical nucleation theory [63,64,59,36]. In particular, the authors of the nucleation theory have determined the cause for void nucleation by the tensile stress σ_thr reaching a threshold value at those sites of the interconnect where the adhesion between the metal and passivation layers is weak. The expression for the threshold stress for void nucleation [36] is given by

\[\begin{equation} \sigma_\text{thr}= \cfrac{2\gamma_\text{$m$}\sin\theta_\text{c}}{R_\text{p}}, \end{equation}\] (3.72)

where γ_m is the interfacial free energy of the metal, θ_c is the critical contact angle, and R_p is the radius of the adhesion-free patch.  (3.4) shows the time evolution of the stress build-up caused by electromigration. If the stress is below the threshold value (σ≤σ_thr), the energy barrier for stable void formation exists. The stress build-up increases with time until it reaches the threshold value for void nucleation. For σ≥σ_thr, the energy barrier decreases leading to the nucleation of a stable void at the interface between the metal and the passivation layer. The void nucleation condition is therefore useful to determine the time needed to nucleate a stable void. By assuming the adhesion-free patch with a radius of 10nm in a typical copper interconnect, the stress needed to nucleate a void in the interconnect is in the order of 330MPa, and can already be reached by the thermal stress alone [25]. Lower threshold stresses, which can be reached by electromigration, are obtained by considering bigger patch radii.

Figure 3.4: Time evolution of the stress build-up due to electromigration in a copper interconnect. Two different threshold tensile stresses for differing patch radii R_p are presented.