Stresses, curvatures, and shape changes arising from patterned lines on silicon wafers

Experimental and numerical results are presented on the evolution of stresses and the accompanying changes in the overall curvatures due to the patterning of silicon oxide lines on silicon wafers and subsequent thermal loading. The finite element analysis involves a generalized plane strain formulation, which is capable of predicting the wafer curvatures in directions parallel and perpendicular to the lines, for both the patterning and thermal cycling operations. The predictions compare reasonably well with systematic curvature measurements for several different geometrical combinations of the thickness, width and spacing of the patterned lines. The non-uniform stress fields within the fine lines and the substrate are also analyzed. It is shown both experimentally and theoretically that certain geometries of patterned lines on the substrate induce dramatic shape changes and reversals of curvature in the direction perpendicular to the lines. The mechanistic origin of this effect is identified to be the Poisson effect arising from the anisotropic strain coupling in the patterned structure.