Thermoelastic analysis of periodic thin lines deposited on a substrate
1999 (English)In: Journal of the mechanics and physics of solids, ISSN 0022-5096, Vol. 47, no 5, 1113-1130 p.Article in journal (Refereed) Published
Thermoelastic stresses and curvatures arising from patterned thin lines on initially flat isotropic substrates are analyzed. A connection is made between substrates with patterned lines and laminated anisotropic composites containing transverse matrix cracks. Using this analogy along with anisotropic 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 analysis are shown to compare favorably with finite element simulations of stresses and curvatures for Si substrates with Al, Cu or SiO2 lines. The predictions also match prior experimental measurements of curvatures along and normal to patterned SiO2 lines on Si wafers, and further capture the general experimental trends reported previously for curvature evolutions in Si wafers with Al lines. The model presented here thus provides a very convenient and simple analytical tool for extracting stresses in thin lines on substrates from a knowledge of experimentally determined film stress, thereby circumventing the need for detailed computations for a wide range of unpassivated line geo metries of interest in microelectronic applications.
Place, publisher, year, edition, pages
1999. Vol. 47, no 5, 1113-1130 p.
thermomechanical processes, constitutive behavior principles, thermal stress, plates, residual stress
IdentifiersURN: urn:nbn:se:kth:diva-25448DOI: 10.1016/S0022-5096(98)00092-1ISI: 000080100300005OAI: oai:DiVA.org:kth-25448DiVA: diva2:358503
QC 201010222010-10-222010-10-222010-10-22Bibliographically approved