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US 6,781,702 B2Granted
Determining large deformations and stresses of layered and graded structures to include effects of body forces
AssigneeCalifornia Institute of Technology
InventorsAntonios Giannakopoulos, Subra Suresh, Ares J. Rosakis, Ilan Blech
Life of this patent
Estimating the term…
Abstract
Techniques for determining large deformation of layered or graded structures to include effects of body forces such as gravity, electrostatic or electromagnetic forces, and other forces that uniformly distribute over the structures, support forces, and concentrated forces. A real-time stress monitoring system is also disclosed to provide in-situ monitoring of a device based on the large deformation analytical approach. A coherent gradient sensing module, for example, may be included in such a system.
Claims21
A method, comprising:
- providing a plate structure to represent a device;
- using a first spatial-varying function that is uniform within a plane of said plate structure and varies along a direction perpendicular to said plane to represent a body force acting on said device which affects evolution of curvature of said device;
- using a second spatial-varying function that is uniform within said plane and varies along a direction perpendicular to said plane and with a temperature of said device to represent effects of thermal stresses in said device;
- using nonlinear functions of positions within said plane to represent displacements of said device within two principal directions within said plane and a third principal direction perpendicular to said plane, respectively, to include effects of large deformation;
- computing a total potential energy of said device based on said first and said second spatial-varying functions and said nonlinear functions for said displacements;
- and
- minimizing said total potential energy with respect to principal curvatures and axial stretches respectively along said two principal directions within said plane to derive analytical relationships between an effective force for causing curvature evolution of said device and principal curvatures along said two principal directions.
4 more elements
A system, comprising:
- a sample holder to hold a device with a plate structure;
- a curvature-measuring module disposed relative to said sample holder to measure curvatures of said plate structure;
- and
- a processing module receiving measured curvatures from said curvature-measuring module and operable to compute stresses in said plate structure to include an effect of a force acting on said plate structure according to analytical formula,
- wherein said processing module is programmed to perform the following operations:
- using a first spatial-varying function that is uniform within a plane of said plate structure and varies along a direction perpendicular to said plane to represent a body force acting on said device which affects evolution of curvature of said device;
- using second spatial-varying function that is uniform within said plane and varies along a direction perpendicular said plane and with a temperature of said device to represent effects of thermal stresses in said device;
- using nonlinear functions of positions within said plane represent displacements of—said device within two principal directions within said plane and a third principal direction perpendicular to said plane, respectively, include effects of large deformation;
- computing a total potential energy of said device based on said first and said second spatial-varying functions and said nonlinear functions for said displacements;
- and
- minimizing said total potential energy with respect principal curvatures and axial stretches respectively along said two principal directions within said plane analytical formulae that relate an effective force for causing derive said curvature evolution of said device said two principal directions.
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A method, comprising:
- determining a dimension of one or more features on a surface;
- selecting a wavelength of a coherent probe beam to be greater than said dimension to allow said surface to be specularly reflective to said coherent probe beam;
- illuminating said coherent probe beam onto said surface to produce a reflected probe beam,
- producing a first set of diffraction components of said reflected probe beam by using a first grating;
- producing a second set of diffraction components of said reflected probe beam by using a second grating spaced from said first grating by a predetermined distance, wherein each of first set of diffraction components is diffracted by said second grating to produce a plurality of diffraction components;
- combining two diffraction components that are produced by said second grating from diffracting two different diffraction components selected from said first set of diffraction components to produce an interference pattern;
- and
- processing said interference pattern to determine curvature information of said surface.
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Dependencies are inferred from the claim text.