Derivation of film chracteristic constants by using governing parameter for electromigration damage in passivated bamboo line

The governing parameter for electromigration damage in the passivated bamboo lines, called AFD*_li, was recently formulated by considering the divergence of atomic flux due to electromigration. The formulation was based on the parameter AFD_li previously introduced in our studies. The parameter AFD_li has been identified as the governing parameter for electromigration damage in unpassivated bamboo lines through experimental verification process. On the other hand, metal lines used in integrated-circuit (IC) products are covered with passivation or dielectric layer. A mechanical stress (atomic density) distribution induced by electromigration appears in such lines and plays an important role in the electromigration mechanism. The parameter, AFD*_li , was formulated by adding the effect of the atomic density gradient to AFD _li. By the way, it is known that the displacement of line edge appears at the cathode end of via-connected line as a result of electromigration. So far, the velocity of the edge displacement, the so-called drift velocity, was expressed by using AFD*_li to construct an AFD*_li-based method for determination of film characteristics. In this study, the film characteristic constants in AFD*_li are experimentally determined from the measurement of the drift velocity, where two kinds of metal lines with different line-lengths are treated. Some of the unknown film characteristics do not depend on the line-length and others depend on the length. The film characteristic constants included in AFD*_li are obtained for two metal lines so that the drift velocity calculated by AFD*_li agrees with measured one. Through the discussion on the validity of the obtained constants, it is shown that the AFD*_li-based method can determine both the film characteristics independent of the line-length and another constant depending on the line-length appropriately.