Residual Stress in a Thin Film Resonator
• 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.
Introduction
Model Definition – Geometry
• The resonator can have either straight or folded springs.
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.
1
Er
T
Model Definition – Boundary Conditions
• The ends of the beam springs are attached to the substrate, and thus constrained to zero movement in all directions.
• As the resonator is very thin, the mesh is scaled in the z direction.
Model Definition – Mesh
Results
• The eigenfrequencies of the folded resonator are less affected by the thermal expansion.
Top Related