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Residual Stress in a Thin Film Resonator
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Introduction Surface micromachined thin films are often subject to residual stress. In this model, the springs of a thin film resonator are fastened to a thick substrate. A temperature change causes thermal stress, due to the different thermal expansion coefficients in the film and the substrate. This alters the natural frequencies of the resonator.
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Model Definition – Geometry
The resonator can have either straight or folded springs.
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Model Definition – Equations
Stress-strain relation: The thermal strain equals the difference between deposition and operating temperature times the difference between the thermal expansion coefficients: The eigenfrequency equation is solved with the residual stress accounted for.
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Model Definition – Boundary Conditions
The ends of the beam springs are attached to the substrate, and thus constrained to zero movement in all directions.
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Model Definition – Mesh
As the resonator is very thin, the mesh is scaled in the z direction.
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Results The eigenfrequencies of the folded resonator are less affected by the thermal expansion.
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