©2005 University of California Prepublication Data Spring 2005

RTH46/JDMEMS Resonator SimulationDavid S. Bindel, Emmanuel Quévy, Tsuyoshi Koyama Sanjay Govindjee, James W. Demmel, Roger T. Howe

Introduction: Perfectly Matched Layers:

Basic Loss Mechanism:

Design Sensitivity: Conclusions:

Model of a Disk Resonator:

Displacement and mean energy flux at resonance

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

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

Device micrographs (top) and schematic (bottom)

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

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.