Analysis of stresses in passivated metal lines

Using the concepts of linear elasticity the volume averaged stresses of an array of parallel metallic interconnects embedded in a passivation layer on a flat substrate are analysed. The calculation takes advantage of the proper boundary conditions and refers to lines with aspect ratio 1. Equations are derived which connect the volume averaged stresses in the metal and in the passivation to the so-called eigen-strains of the metal. These eigen-strains characterize the true (stress free) thermal strains and plastic deformation strains of the metal, thought to be not constrained by the surrounding passivation. The coefficients entering into these equations are determined from finite element calculations performed for various geometries and elastic properties of the passivation layer. Choosing the proper values of these coefficients allows the eigen-strains to be determined without further assumptions from experimentally measured metal X-ray stresses and from wafer curvature stresses. In this way a model inde...