Analysis of average thermal stresses in passivated metal interconnects

Volume-averaged thermal stresses in passivated metal interconnects on Si su bstrates are derived for situations where the thickness to width ratio of t he interconnect lines is "small" or "large." The analysis provides differen t components of volume-averaged stresses for the most general case of therm al and elastic anisotropy in the passivation layer, the interconnect line, and the substrate. It is shown that the theoretical predictions, particular ly those for the hydrostatic stresses, are in agreement with detailed finit e element calculations for a wide range of line and passivation geometries of practical interest. The theoretical predictions of average hydrostatic s tresses are also found to be in reasonable agreement with available experim ental results for thermal stresses derived from x-ray diffraction measureme nts on passivated Cu lines. The present theoretical results are shown to be far more accurate than prior stress analyses for periodic passivated lines based on Eshelby's theory of inclusions. (C) 1999 American Institute of Ph ysics. [S0021-8979(99)09623-1].