Analysis of average thermal stresses in passivated metal interconnects

Abstract

Volume-averaged thermal stresses in passivated metal interconnects on Si substrates are derived for situations where the thickness to width ratio of the interconnect lines is “small” or “large.” The analysis provides different components of volume-averaged stresses for the most general case of thermal and elastic anisotropy in the passivation layer, the interconnect line, and the substrate. It is shown that the theoretical predictions, particularly those for the hydrostatic stresses, are in agreement with detailed finite element calculations for a wide range of line and passivation geometries of practical interest. The theoretical predictions of average hydrostatic stresses are also found to be in reasonable agreement with available experimental results for thermal stresses derived from x-ray diffraction measurements 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.