Passivated metal lines, commonly used in integrated circuits, show thermally induced stresses due to the difference of the thermal expansion coefficients of the lines and their surroundings. These stresses cause voidage and plastic flow of the lines. Aim of the analysis was to derive equations connecting experimentally measured strains or stresses by the X-ray diffraction and wafer curvature techniques with the magnitude of voidage and plastic shear deformation of the lines.
Using the concepts of linear elasticity the volume averaged stresses of an array of parallel interconnects embedded in a passivation layer on a flat substrate are analysed. Equations are derived connecting the volume averaged stresses in the metal and in the passivation with the “eigen-strains” of the metal which characterize the true (stress free) thermal strains and plastic deformation strains of the metal. The coefficients entering these equations are determined from (elastic) finite element method (FEM) calculations performed for various geometries and aspect ratios of the metal lines. Choosing the proper values of the coefficients allows the eigen- strains to be determined from the experimental data.
By comparison of the evaluated eigen-strains with the purely elastic eigen-strains ΔaΔT the extent of voidage and/or plastic shear deformation of passivated metal lines caused by thermally induced stresses can be determined model independently.