Damping Mechanisms

Full analysis of a MEMS design requires simulating energy loss mechanisms such as gas damping, thermo-elastic damping and anchor losses. Whether simulating the transient response of an accelerometer or estimating the Q factor of a resonator, getting the damping right is a crucial. MEMS designers have traditionally relied on simple analytical formulae or experimental data to estimate damping coefficients. With CoventorWare, it’s possible to simulate energy loss mechanisms and accurately predict damping coefficients.

Gas Damping
Moving MEMS devices transfer energy to surrounding air or gas through their motion. The resulting “gas damping” plays a desirable role some devices, such as accelerometers, microphones, display mirrors and switches, and an undesirable role in others. In sensors, gas damping contributes to signal-to-noise ratio. While it is possible, in principle, to simulate gas damping with a general-purpose fluid dynamics field solver, such a brute-force approach is generally not practical. CoventorWare’s DampingMM module includes two specialized solvers that can be used separately or in combination to accurately and efficiently simulate gas damping.

The DampingMM module in CoventorWare contains two solvers that are suitable for computing the damping of different regions of typical MEMS devices such as this accelerometer.

Anchor Losses
MEMS devices such as gyroscopes and resonators that rely on continuous vibration for operation lose energy through their anchors. In fact, anchor losses may be the dominant energy loss mechanism in devices that are hermetically packaged. CoventorWare’s MemMech solver includes a “quiet” boundary condition that can be used to predict elastic energy that is transmitted via the anchor to the substrate.

CoventorWare simulation of acoustic waves propagating in the substrate, with quiet boundary condition at the exterior perimeter of the substrate. This simulation predicts energy loss via the anchors of a resonator.

Thermoelastic Damping
A vibrating structure generates heat as the material is alternately compressed and tensioned. Dissipation of this heat is known as thermo-elastic damping (TED). For hermetically packaged MEMS that rely on bulk acoustic modes for operation, TED may compete with anchor losses as the dominant energy loss mechanism. TED can be reduced by careful design and placement of perforations in the vibrating devices, but such design can only be done with the help of accurate TED simulations.

CoventorWare simulation of thermal field generated by a resonator

The following table shows simulated Q values for the resonator with and without perforations, indicating a desirable increase in Q when perforations are included.

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