MEMS resonator: Thermo-Elastic Damping and Anchor Loss models

 

Resonator Design In CoventorWare

One of the design consideration for MEMS Resonators is the Quality Factor (Q). This is the ratio of the total stored energy to the energy dissipated in a single cycle. At a particular oscillation frequency, a higher Q indicates a lower rate of energy dissipation and oscillations die out more slowly.

Numerous physical loss mechanisms contribute to overall Q and can be expressed as:

QGAS

Air Damping: Squeeze film or Stokes
Minimized by operating in a vacuum
Coventor's Solution: Rayleigh Damping Coefficients

QTED

Thermoelastic Damping: As a vibrating body is strained, the temperature changes in proportion to the strain; when temperature gradients occur, heat conduction causes irreversible energy loss
Coventor's Solution: Thermoelastic Damping Option

QANCHOR

Anchor Loss: A fraction of elastic energy propagates into the surrounding support structure
Also referred to as support loss, clamping loss, or attachment loss
Coventor's Solution: QuietBoundary Surface Boundary Condition

QOTHER

Other Loss Mechanisms: Including structural dissipation (crystallographic defects) and surface effects
Coventor's Solution: Rayleigh Damping Coefficients
Thermoelastic Damping
The Thermoelastic Damping can contribute significantly to Q in MEMS resonators operating in vacuum. CoventorWare-ANALYZER's MemMech module calculates the energy lost to heat conduction caused by strain-induced temperature gradients. This direct harmonic analysis simulate in 32-bit mode and requires material properties such as thermal expansion coefficient (TCE Integral Form), thermal conductivity and specific Heat.

Temperature distribution during Thermo-Elastic Damping Simulation

TED Energy Distribution during Thermo-Elastic Damping Simulation

The graph below shows a comparison between a Thermo-Elastic Damping model that has been implemented in CoventorWare-ARCHITECT, Finite Element results from ANALYZER and analytical models.

 

Losses

Anchor losses result when anchors are stressed as a result of resonator displacement. A fraction of the vibration energy is lost from the resonator though elastic wave propagation into substrate. In MEMS structures we usually assume all elastic energy transferred to the substrate is lost, although the mechanism is not fully understood. Anchor losses can be significant if contributions from other loss mechanisms are negligible. Having a simulation tool provides the ability to investigate optimal anchor placement.

Acoustic waves propagate through the substrate causes energy loss at the anchor

The anchor loss can be calculated by modeling the resonator and a fictitious substrate, these are linked together in the simulation automatically (this avoids overly fine meshes). In addition a so called "QuietBoundary" boundary condition is applied which models elastic waves propagating to infinity in the substrate, eliminates the reflection of the elastic waves impinging on the boundary or excitation origin.

The results can be analyzed by plotting the harmonic displacement to identify the harmonic frequency closest to resonance. The Q factor and Harmonic Energy values can then be determined as can be seen in the result graph below:

Determining the Q factor from anchor loss calculations

Nombre: Lenny D. Ramirez C.
Asignatura: CRF
Dirección: http://info.coventor.com/memsahead/bid/34328/MEMS-resonator-Thermo-Elastic-Damping-and-Anchor-Loss-models
Ver blogg: http://lennyramirez-crf3.blogspot.com/