MEMS Resonator Simulation (RTH46/JD)

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MEMS Resonator Simulation(RTH46/JD)

• David S. Bindel, Emmanuel Quevy, Tsuyoshi Koyama
• Sanjay Govindjee, James W. Demmel, Roger T. Howe

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Introduction

• 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
• Loss is surprisingly sensitive to geometry
  variations
• Thermoelastic damping can also be significant

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Loss Model of a Disk Resonator
Device micrographs (top) and schematic (bottom)
Device micrographs (top) and schematic (bottom)
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Loss Model of a Disk Resonator

• 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 micron height
• Fabricated dimensions vary from nominal

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Basic Loss Mechanism
Displacement and mean energy flux at resonance

• Dominant mode is not purely radial!

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Basic Loss Mechanism

• Dominant mode is not purely radial!
• Includes a small bending motion
• Vertical motion at post pumps elastic waves into
  substrate
• More bending motion when radial and bending
  modes are close in frequency

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Design Sensitivity

• Simulated Q (solid line, left) very sensitive to
  film thickness
• Matches experimental data (dots)
• Sensitivity comes from interaction between two
  poles which come close at critical thicknesses
  (right)

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Thermoelastic Damping

• Compute thermoelastic interactions from coupled
  PDEs
• Matches Zeners formula on a beam geometry
• Works more generally than Zeners formula

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TED and Grain Boundaries

• Grain boundaries affect thermal conductivity and
  add another thermal length scale
• Working to include grain boundary effects in our
  thermoelastic damping simulations

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Conclusions

• Need CAD tools to predict damping
• Simulations of anchor losses using perfectly
  matched layers
• Simulations of thermoelastic damping through
  coupled PDEs
• Illustrated usefulness of our approach on a disk
  resonator
• Both simulation and experiment show surprising
  dips in Q from interactions between modes
• Poisson coupling is important acoustic
  approximations are inadequate to capture the
  behavior

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References

• http//www.cs.berkeley.edu/dbindel/hiqlab
• Program code is freely available
• Tutorial slides and relevant papers also
  available
• Papers
• Elastic PMLs for resonator anchor loss
  simulation. Tech report UCB/SEMM-2005/01.
  Submitted to IJNME.
• Anchor Loss Simulation in Resonators. MEMS
  2005.