FINITE-ELEMENT ANALYSIS OF THE EFFECTS OF GEOMETRY AND MICROSTRUCTUREON ELECTROMIGRATION IN CONFINED METAL LINES

A simple mathematical model based on atomic drift and diffusion is adv anced to describe electromigration-induced stress in confined metal li nes. Using a finite element approach, a MATLAB program was developed t o simulate stress evolution in lines with variable geometry and micros tructure under different boundary conditions. The simulation results s how that the contact pads connected to the line end in the National In stitute of Standards and Technology (NIST) test structure postpone the stress buildup in a microstructurally homogeneous line and the time t o reach a certain stress is proportional to the pad sizes when the pad s are much wider than the line. Subtractive defects are not the prefer red failure sites when the defects fall on a wide polycrystalline line or a bamboo structure line. In a narrow polycrystalline conductor wit h a distribution of grain size, a subtractive defect may result in an abrupt change in the effective diffusion coefficient (blocking effect) along the line and quick buildup of the stress at the defect site. Th e stress at a center blocking site in a 190 mu m line reaches maximum in 146 h, under 1 MA/cm(2) and at 200 degrees C. Electromigration life time is most sensitive to distribution of grain size and variation of the linewidth when the linewidth is a few times average grain size. Fo r a near bamboo structure Line, the evolution of the stress after loca l quasisteady state is affected by line end conditions as well as by d istribution of the polygranular clusters, Under a constant source boun dary condition, the maximum stress at final steady stare depends on th e length and distribution of individual polygranular clusters in a lin e. Under blocking end conditions, the stress distribution in final glo bal steady state (if it exists) is determined by electrical current de nsity and is independent of microstructure of a line, The cluster/bamb oo juncture is the most severely stressed site in the early stages, an d the blocking line end will finally become the most severely stressed site if the Line does not fail at an early time. The magnitude of the maximum stress at the cluster/bamboo juncture at the local steady sta te depends on the ratio of the effective diffusivity of the cluster to that of the bamboo segment, D-g/D-b, as well as on the cluster length and current density. (C) 1998 American Institute of Physics.[S0021-89 79(98)05807-1].