Understanding Q-Factors in Gas Encapsulated MEMS Inertial Sensors

Here in the Application Team at Coventor, we are always working to improve our solutions to real-world MEMS design problems. We have a continuing interest in packaging that encapsulates MEMS transducers. Generally, the purpose of these packages is to mechanically support the transducer and allow it to access the signals of interest. At the same, the packages provide protection against the environment and can mitigate unwanted effects such as excessive temperatures or mechanical loads [1].

In MEMS, inertial sensors are generally packaged by encapsulating the sensing element in a cavity formed during fabrication. The cavity forms a hermetically sealed chamber. The gas and pressure in the chamber are normally controlled, as both strongly influence the performance of the sensor. Open loop accelerometers, for example, are generally encapsulated at higher pressures to carefully control the sensor bandwidth [2]. Gyroscopes, on the other hand, normally operate over a lower range of cavity pressures, typically less than a few mBar of pressure down to a high vacuum [3].

At this year’s MEMS IEEE Inertial conference in Avignon, France we displayed a poster that described how temperature variations can change the Q-factor of a 3-axis gyroscope. In our example, the gyroscope was encapsulated in a sealed cavity filled with an inert gas. According to the combined gas law, a change in ambient temperature will change the pressure in the cavity, which will also change the Gyroscope Q-factor.

Figure 1:   3D Gyroscope Model example with simulated pressure contours (left), and ambient cavity pressure vs. Q-factor graph with simulated and measured results (right) (courtesy: Murata)

Modeling this effect is not trivial since the Q-factor is itself dependent on the geometry of the cavity that surrounds the gyroscope, as well as the pressure and type of gas in the cavity. This effect can be seen in the simulated squeeze-film damping pressure contours of an example gyroscope model built in CoventorMP®, see Figure 1. As might be expected, the pressure on the large flat plates that form the moving sense mass is high. However, the pressure contour also bleeds over the plates edges where the cavity gas is forced into the channels between the sides of the sensing mass and the cavity.

Incidentally, the Q-factor of this gyro is dominated by the inert gas in the cavity. If there is no gas and the device operates in a high vacuum, the Q-factor is determined by thermo-elastic-damping and anchor damping – which can also be simulated in CoventorMP.

As the graph in Figure 1 shows, our simulation results in CoventorMP provide a good match to the measured data. When our measured data match the simulation results, this is a good indication that the models are working correctly. It is very important to model combined package-device interactions when designing MEMS devices, since performance issues caused by ambient temperature changes or mechanical package loads can degrade the actual performance of the MEMS device.   As seen in our example, CoventorMP can be used to accurately model MEMS device-package interactions to ensure that packaged device performance meets the targeted design specifications.

References

1. Kim, B., Park, WT. (2012). MEMS Packaging. In: Bhushan, B. (eds) Encyclopedia of Nanotechnology. Springer, Dordrecht.
2. A research on temperature dependent characteristics of quality factor of silicon MEMS gyroscope, FENG Rui, et. al. Nanjing University of Science and Technology, Nanjing, China Advanced Materials; Vol. 159, pp 399-405.
3. Damping Ratio Analysis of a Silicon Capacitive Micromechanical Accelerometer, Yuming Mo et al., China Academy of Engineering Physics, Mianyang, China, Wireless Sensor Network;  Vol. 9 No. 5, May 2017.