Transcript “MEMS Resonator Simulation.”

MEMS Resonator Simulation
(RTH46/JD)
David S. Bindel, Emmanuel Quevy, Tsuyoshi Koyama
Sanjay Govindjee, James W. Demmel, Roger T. Howe
©2005 University of California Prepublication Data Spring 2005
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
©2005 University of California Prepublication Data Spring 2005
Loss Model of a Disk Resonator
Device micrographs (top) and schematic (bottom)
©2005 University of California Prepublication Data Spring 2005
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
©2005 University of California Prepublication Data Spring 2005
Basic Loss Mechanism
Displacement and mean energy flux at resonance
• Dominant mode is not purely radial!
©2005 University of California Prepublication Data Spring 2005
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
©2005 University of California Prepublication Data Spring 2005
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)
©2005 University of California Prepublication Data Spring 2005
Thermoelastic Damping
• Compute thermoelastic interactions from coupled PDEs
– Matches Zener’s formula on a beam geometry
– Works more generally than Zener’s formula
©2005 University of California Prepublication Data Spring 2005
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
©2005 University of California Prepublication Data Spring 2005
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
©2005 University of California Prepublication Data Spring 2005
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.
©2005 University of California Prepublication Data Spring 2005