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

A simple theoretical analysis for curvature evolution in unpassivated and p assivated copper interconnect lines on a silicon substrate is proposed. A l ayer consisting of copper and oxide lines is modeled as a homogenized compo site that has different elastic moduli and thermal expansion coefficients i n two different directions, i.e, along and across the lines, due to the ani sotropic line geometry. These effective thermoelastic properties of the com posite layer are approximated in terms of volume fractions and thermoelasti c properties of each line using standard composite theory. This analogy fac ilitates the calculation of curvature changes in Damascene-processed copper lines subjected to chemical-mechanical polishing and/or thermal cycling. T he effects of line height, width and spacing on curvature evolution along a nd across the lines are readily extracted from the analysis. In addition, t his theory is easily extended to passivated copper lines irrespective of pa ssivation materials by superimposing the curvature change resulting from an additional layer. Finite element analysis has been used to assess the vali dity 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 r ange of line and passivation geometry of practical interest. (C) 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.