Effects of line and passivation geometry on curvature evolution during processing and thermal cycling in copper interconnect lines

Abstract

A simple theoretical analysis for curvature evolution in unpassivated and passivated copper interconnect lines on a silicon substrate is proposed. A layer consisting of copper and oxide lines is modeled as a homogenized composite that has different elastic moduli and thermal expansion coefficients in two different directions, i.e. along and across the lines, due to the anisotropic line geometry. These effective thermoelastic properties of the composite layer are approximated in terms of volume fractions and thermoelastic properties of each line using standard composite theory. This analogy facilitates the calculation of curvature changes in Damascene-processed copper lines subjected to chemical–mechanical polishing and/or thermal cycling. The effects of line height, width and spacing on curvature evolution along and across the lines are readily extracted from the analysis. In addition, this theory is easily extended to passivated copper lines irrespective of passivation materials by superimposing the curvature change resulting from an additional layer. Finite element analysis has been used to assess the validity of the theoretical predictions; such comparisons show that the simple theory provides a reasonable match with numerical simulations of curvature evolution during the Damascene process in copper interconnects for a wide range of line and passivation geometry of practical interest.