The Latest Techniques that Provide Insight into Package Stress and Temperature Deformation of a MEMS-based Gyroscope

Transducers 2021 is a prestigious international conference that reviews advances in Solid-State Sensors, Actuators and Microsystems.   At this year’s conference, there were 391 papers presented from 29 different countries with more than 700 participants attending the event.  During the conference,  one particular presentation caught my attention. Sam Zhang, ADI Fellow and Director of Advanced MEMS Technologies at Analog Devices, gave a presentation entitled “High-Fidelity Modeling for High-Performance MEMS”.

Analog Devices has been a pioneer in modeling the interaction between MEMS transducers and their packages, with publications on the topic starting as early as 2007 [1]. They have used joint transducer and package modeling as a foundation of their work with MEMS-based, high-performance sensors for a number of years. Since that time, they have advanced their technique to support very sophisticated analysis.

During his presentation, Sam described how Analog Devices models the effect of package stress on the performance of a gyroscope, by coupling package stress to their Multiphysics transducer models. These models use a technique similar to that discussed in a prior publication by Coventor [2]. This is a dynamic, iterative modeling process, where Analog Device engineers simulate offset (and other performance measurements) in the device caused by package stress forces. Sam noted that “the dynamic simulation was very complicated because it’s a two-way coupled system”. In effect, the package deformation affects the MEMS device in multiple ways, due to mechanical and electrostatic coupling of the gyroscope and its package.

Figure 1: Courtesy, Sam Zhang, Analog Devices

To simulate the effect of package stress, Analog built a nonlinear, Multiphysics dynamic model of the transducer in MEMS+^®. Using this model, they applied static package deformation to the entire MEMS transducer using finite element analysis and looked at the shift in gyroscope output offset. This type of analysis starts with a designer having a good understanding of the material properties and potential process variations of their device.  Once a model of the MEMS device is built, the designer can apply environmental conditions (e.g. temperature changes) to the package and simulate and correlate package stress to changes in performance. In this analysis, Analog Devices designers used small and large signal AC analysis and transient analysis techniques. The scale of measurement in different portions of the sensor varied dramatically in these studies, from a resonator displacement of a few microns down to a substrate of hundreds of nanometers to sensor signal measurements of a few picometers. These dimensional characteristics of the design were needed to support a highly-accurate sensor with a strict dynamic range and high Signal to Noise Ratio.

AC and transient simulation of a MEMS-based gyroscope can be very computationally expensive using finite-element modeling software, due to the need to simulate many elements in the model with a large degree of freedom. MEMS+ uses reduced order models that operate up to 100 times faster than traditional finite element models, making it much more suitable to these complex, dynamic simulations.  During his presentation, Sam noted that “With this technique, actually, we really successfully simulated gyroscope and accelerometer offset over temperature, over stress performance.”

This presentation provided an excellent example of modeling complex package and temperature deformation effects, and how they can be quickly and accurately analyzed using MEMS+. Analog Devices is one of the premier manufacturers of MEMS devices, producing the most accurate sensors in the industry, and its products are used worldwide.  I enjoyed their presentation at the Transducers 2021 conference, and hope to hear more about their future successes at the upcoming 2023 Transducers Conference in Kyoto, Japan.

Learn more about how to model the interaction between MEMS inertial sensors and their packages.

References:

1. Zhang, Xin, Seungbae Park, and Michael W. Judy. “Accurate assessment of packaging stress effects on MEMS sensors by measurement and sensor–package interaction simulations.” Journal of microelectromechanical systems 16.3 (2007): 639-649.
2. A. Parent, C. J. Welham, T. Piirainen, A. Blomqvist, Thermo-Mechanical Simulation of Die-Level Packaged 3-axis MEMS Gyroscope Performance, 2017 Inertial Sensors and Systems, Karlsruhe, Germany