TEM bright-field images of Cu damascene; transverse and longitudinal cross-sectional view of the Cu lines with widths of (a) and (b) .
Median grain sizes as a function of the geometry of the interconnects; , , and refer to the grain sizes along the length, width, and thickness directions, respectively. The grain sizes were quantified from the cross-sectional TEM bright-field images using the median intercept grain size method
Median grain sizes of the set of narrow lines; increases most rapidly and becomes similar to for the line.
Dimensional dependence of stress in damascene Cu integrated with TEOS. , , and are the stresses along the lines, across the lines, and through the thickness, respectively. The hydrostatic stress was calculated from the principal stress components using Eq. (1).
Linewidth dependence of stress of the set of narrow lines and lines integrated with TEOS. , , and are the stresses along the lines, across the lines, and through the thickness, respectively. The hydrostatic stress was calculated from the principal stress components using Eq. (1).
Calculated thermal stress of damascene Cu lines as a function of the linewidth. Note that the level of hydrostatic stress is approximately , irrespective of the linewidth.
Linewidth dependence of grain growth-induced stress of the Cu lines calculated by the FEA.
Hydrostatic stress as a function of the linewidth: experimentally measured stress (XRD), thermal stress obtained by FEA, and grain growth stress from the grain size analysis and FEA.
Schematic drawing showing the effect of the linewidth dependence of the hydrostatic stress on stress voiding. The hydrostatic stress of the wide lines would be expected to be higher due to their grain size being larger than that of the narrow lines. Therefore, a strong stress gradient may result at the point where the wide lines and narrow lines (or narrow via) meet.
Thermomechanical properties of the materials used in the finite element calculations.
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