Characterizing Curvatures and Stresses in Thin-Film Structures on Substrates having Spatially Non-Uniform Variations
AssigneeCalifornia Institute of Technology
InventorsAres Rosakis, Yonggang Huang
Life of this patent
Estimating the term…
Abstract
Techniques and devices are described to use spatially-varying curvature information of a layered structure to determine stresses at each location with non-local contributions from other locations of the structure. For example, a local contribution to stresses at a selected location on a layered structure formed on a substrate is determined from curvature changes at the selected location and a non-local contribution to the stresses at the selected location is also determined from curvature changes at all locations across the layered structure. Next, the local contribution and the non-local contribution are combined to determine the total stresses at the selected location.
Claims16
A computer-implemented method for determining stresses at a location on a layered structure comprising at least one film formed on a substrate, comprising:
- applying a spatially varying structural condition in the layered structure to computation of stresses at a selected location in the layered structure from curvatures at all locations of the layered structure, wherein the spatially varying structural condition in the layered structure comprises at least one of (1) the film covers only a portion of the substrate, (2) the film has a film thickness that varies from one location to another across the film, and (3) the substrate has a substrate thickness that varies from one location to another;
- determining in the computation under the spatially varying structural condition a local contribution to stresses at the selected location on the layered structure from curvature changes at the selected location;
- determining a non-local contribution to the stresses at the selected location from curvature changes at all locations of the layered structure;
- and
- combining the local contribution and the non-local contribution to estimate the total stresses at the selected location.
A device for charactering stresses in a layered structure, comprising:
- an optical module to project an optical probe beam to a layered structure and to obtain a full-field curvature map of a surface on the layered structure;
- a processor in communication with the optical module to receive data of the full-field curvature map, the processor comprising:
- means for applying a spatially varying structural condition in the layered structure to computation of stresses at a selected location in the layered structure from curvatures at all locations of the layered structure, wherein the spatially varying structural condition in the layered structure comprises at least one of (1) the film covers only a portion of the substrate, (2) the film has a film thickness that varies from one location to another across the film, and (3) the substrate has a substrate thickness that varies from one location to another;
- means for determining in the computation under the spatially varying structural condition a local contribution to stresses at the selected location on the layered structure from curvature changes at the selected location;
- means for determining a non-local contribution to the stresses at the selected location from curvature changes at all locations of the layered structure;
- and
- means for combining the local contribution and the non-local contribution to estimate the total stresses at the selected location.
Dependencies are inferred from the claim text.