Finite Element Analysis of Electromigration and Stress Induced Diffusion in Deformable Solids
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ABSTRACT With a view to analyzing failure mechanisms in interconnects, we have developed a finite element method that may be used to compute the effects of diffusion and deformation in an electrically conducting, deformable solid. The analysis accounts for large changes in the shape of the solid due to surface diffusion, grain boundary diffusion, and elastic or inelastic deformation within the grains. To illustrate the capabilities of the method, we have analyzed void migration and collapse due to current induced surface diffusion; the drift of a strip of conducting solid on a substrate; and have calculated intergranular stresses and plastic deformation induced by electromigration in a passivated, polycrystalline interconnect line. INTRODUCTION Interconnect lines are susceptible to several types of mechanical failure. Voids and cracks may form in the lines, causing open circuits; or the material surrounding the line may crack and damage devices near the line. As the dimensions of microelectronic circuits have been reduced, such failures appear to have become more common. There is therefore considerable interest in understanding the mechanisms responsible for the damage, and in finding ways to constrain them. When a microelectronic circuit is cooled to room temperature after manufacture, severe thermal stresses are induced in the interconnect lines [1]. This is one cause of mechanical failures. The stresses are large enough to cause significant plastic deformation in the solid, and as a result, voids tend to nucleate in regions of stress concentration near the edge of the line. Fortunately, voids which are nucleated in this way are rarely large enough to sever the interconnect, since the plastic deformation is constrained by the stiff material which surrounds the line [2,3]. Subsequently, the voids continue to grow, partly due to continued creep deformation within the line [4], and partly because the stress in the interconnect causes material to diffuse away from the surface of the void [5]. Eventually, the voids may become large enough to cause an open circuit in the line. During service, a dense electric current flows along interconnect lines. This significantly increases the likelihood of failure [6,7]. Material tends to diffuse along the line in the direction opposite to the electric current. Voids may grow as a direct result of electromigration, since the electric current may cause material to diffuse away from the voids along grain boundaries. In addition, the rate of material flow may not be uniform along the length of the line, either due to irregularities in the microstructure or geometry of the line, or due to temperature gradients. Material therefore tends to accumulate in some sections of the line, and is removed from others. This induces severe stresses in both the interconnect and the surrounding material, which increases the rate of stress induced void growth in the line, and may also cause the material surrounding the line to crack [6]. Electromigration can also cause voids to translate large distanc
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