2.5 Stress Build-up due to Electromigration

In Section 2.3, it is shown that the vacancy flux induced by the electromigration driving force results in a redistribution of the vacancy concentration in the metal line. Furthermore, vacancies are created or annihilated at those locations which act as vacancy sources or sinks in the line. In the absence of sources and sinks of vacancies, vacancy accumulation should rise at the cathode end of the line (2.2). In turn, at the anode end of the line, vacancy depletion occurs [40].

Figure 2.2: Stress build-up due to vacancy accumulation and depletion in a passivated metal line. Tensile stresses lead to void formation.

When an atom moves to the end of the line under the influence of electromigration, it leaves behind a vacancy at the opposite side [148]. Similar to the thermal expansion-induced stress, volumetric relaxations occur in the lattice site due to differences between the atomic volume and the vacancy volume [20]. Consequently, at the cathode end of the line, vacancy accumulation produces a volume contraction of the line due to the relaxation of the neighboring atoms surrounding the vacancy. At the same time, vacancy depletion creates a volume expansion of the line. In confined metal interconnects deposited on a silicon substrate and covered by different passivation layers (2.2), the response of the metal to these volumetric changes results in the development of mechanical stresses in the line. Because of the mechanical constraints imposed by the surrounding layers, volume contraction is not accommodated, and the metal line is under tension with a tensile stress at the cathode end. The vacancy accumulation, and the consequent tensile stress development, leads to the formation of a void at the cathode end. At the opposite side, compressive stress arises resulting in the creation of a hillock.

The stress generated due to electromigration influences the driving force for vacancy transport, and its incorporation into the electromigration model should solve the shortcoming regarding the criterion for void nucleation. Different approaches for the analysis of the effect of the stress during electromigration were proposed in literature.