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Introduction:. Perfectly Matched Layers:. High frequency surface-micromachined MEMS resonators have many applications Filters, frequency references, sensors Need high quality factors Difficult to predict analytically Existing tools predict frequency, but not Q

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Introduction:

Perfectly Matched Layers:

  • High frequency surface-micromachined MEMS resonators have many applications
    • Filters, frequency references, sensors
  • Need high quality factors
    • Difficult to predict analytically
    • Existing tools predict frequency, but not Q
  • Anchor loss is a major damping source
    • Simulate anchor loss with perfectly matched layers
    • Illustrate anchor loss in disk resonators
    • Predict surprising sensitivity to geometry
  • Assume waves from the anchor are not reflected (i.e. the substrate is semi-infinite).
  • Add damping at the boundaries to absorb waves
    • Implemented in standard FEA codes using a complex-valued change of coordinates
    • Effectively change properties smoothly for perfect matching of mechanical impedance

Basic Loss Mechanism:

Model of a Disk Resonator:

Device micrographs (top) and schematic (bottom)

Displacement and mean energy flux at resonance

  • Simulated and built poly-SiGe disk resonators
    • 31.5 and 41.5 micron radii, 1.5 micron height
    • Post is 1.5 micron radius, 1 microns height
    • Fabricated dimensions vary from nominal
  • Axisymmetric finite element model, bicubic elements with 0.25 micron node spacing
  • Dominant mode is not purely radial
    • Includes a small bending motion
    • Vertical motion at post pumps elastic waves into the substrate
    • More bending motion when “radial” and “bending” modes are close in frequency

Conclusions:

Design Sensitivity:

  • Anchor loss is complicated even for disks!
    • Surprising dips in Q from interacting modes
    • Poisson coupling is important: acoustic approximations are inadequate
  • Need CAD tools to predict damping
    • Simulate wafer with a perfectly matched layer
    • Have integrated anchor loss and thermoelastic damping models into HiQLab simulator
    • http://www.cs.berkeley.edu/~dbindel/hiqlab/

Simulated Q for two modes (solid lines, left) at different film thicknesses matches lab measurement (dots). The behavior is explained by the interaction of two complex frequencies near a critical geometry.