Thermoelastic analysis of periodic thin lines deposited on a substrate

Thermoelastic stresses and curvatures arising from patterned thin lines on initially flat isotropic substrates are analyzed. A connection is made betw een substrates with patterned lines and laminated anisotropic composites co ntaining transverse matrix cracks. Using this analogy along with anisotropi c plate theories, approximate analytical expressions are derived for volume -averaged stresses as well as curvatures along and normal to the lines, for any thickness, width and spacing of the lines. The predictions of the anal ysis are shown to compare favorably with finite element simulations of stre sses and curvatures for Si substrates with Al, Cu or SiO2 lines. The predic tions also match prior experimental measurements of curvatures along and no rmal to patterned SiO2 lines on Si wafers, and further capture the general experimental trends reported previously for curvature evolutions in Si wafe rs with Al lines. The model presented here thus provides a very convenient and simple analytical tool for extracting stresses in thin lines on substra tes from a knowledge of experimentally determined film stress, thereby circ umventing the need for detailed computations for a wide range of unpassivat ed line geo metries of interest in microelectronic applications. (C) 1999 E lsevier Science Ltd. All rights reserved.