By: Arnaud Parent

Simulation of Thermal Effects on MEMS Performances

MEMS inertial sensors, such as Accelerometers and Gyroscopes, have been commercially successful in the consumer marketplace, where reduced size and cost are more important than accuracy. These sensors are classified as commercial grade products, even though they are typically used in consumer applications. Today, MEMS inertial sensors are knocking on the door of tactical grade applications, where the requirements for accuracy are much more demanding. MEMS products may one day enter the navigation grade application space, where accuracy demands are even more stringent. To meet the enhanced accuracy and performance requirements of tactical and navigation grade inertial sensors, MEMS designers must not only consider the transducer itself but the interaction of the product with its surrounding environment (starting with the packaging). At Coventor, we have a new simulation platform that can be used to create a compact model of MEMS transducers along with their packaging, providing a method to efficiently study the overall behavior of MEMS inertial sensors.

A Design Flow for Package and Transducer Co-Simulation

The design flow we propose is based upon an important observation. In general, MEMS packages have dimensions that are an order of magnitude (or more) greater in size than the underlying transducer structures. Packages are also geometrically considerably simpler. While a package is generally cubic in shape, a modern inertial sensor can contain hundreds of connected shapes such as comb capacitors, suspension beams and inertial masses. Modeling a MEMS transducer and package together using standard Finite Element Analysis is challenging, especially when considering the coupled-physics between the components of the device.

A solution to this problem is to employ a hybrid approach (Figure 1) like the one used in CoventorMP™. In this approach, the package is simulated using standard CoventorWare® Finite Element Analysis (Figure 1, A) and coupled to a model of the transducer created in MEMS+® (Figure 1, B).  The MEMS+ model contains specialized multi physics finite elements, or “MEMS building blocks”, dedicated to MEMS transducer design. The complete model (transducer and package) can then be simulated within MEMS+ or included in a system or circuit design using MATLAB/Simulink® and Cadence/Spectre® (Figure 1, C).

Figure 1: CoventorMP MEMS design automation flow

Our Design Flow Applied to a 3-Axis Gyroscope

To obtain the thermo-mechanical behavior of a 3-axis gyroscope package, we simulate its deformation at different temperatures using a CoventorWare FEA model with 110,000 hexahedral, 27-node meshed brick elements. In parallel, we have created a behavioral model of the gyroscope transducer in MEMS+ that consists of multiple interconnected components: shell plates, Bernoulli beams, Timoshenko beams, electrostatic drive and capacitive sensing electrodes. This model is internally represented by fully coupled nonlinear system matrices that support 14k mechanical degrees of freedom (DoF), 10 electrical DoF, 3 angular velocity inputs and 9 capacitance outputs.

Figure 2: MEMS+ gyroscope and package joined – On the left, the assembled complete model (the package deformation is exaggerated) – On the right, thermal deformation results of the 3-axis gyro and die level package at -40°C (transparent package)

We then imported the package deformation data to the MEMS+ behavioral model using a specialized package modeling component. This component ensures that MEMS+ objects in contact with the package are deformed or displaced based upon the nodal, FEA-computed displacement of the package. MEMS+ objects are mechanically deformed or displaced based upon strain and stress applied by the package, and this deformation also impacts the electrostatic  behavior (forces and capacitances) of the device due to surface and gap deformations. The resulting MEMS+ model of the transducer and package is shown in Figure 2.

Figure 3: On the left, capacitance versus temperature for the x-rotation sense electrode. On the right, drive and x-rotation sense resonance frequencies versus temperature

With this model, we simulated the behavior of sense capacitances, resonance frequencies and angular velocity rate sensitivity as a function of temperature. Sense Capacitance and Resonance Frequencies show good agreement with actual measurements, while Angular Velocity was not experimentally studied or measured (see Figure 3).

Conclusion

We have presented a solution to simulate a MEMS transducer integrated into its package. This solution has been implemented using CoventorMP, a design automation platform for MEMS designers. CoventorMP enables the co-simulation of multi-physics, geometrically complex structures using an integrated combination of finite element and reduced-order modeling. It is a practical and validated solution to simulate and improve the performance of packaged MEMS products.

We published the results of this analysis at the 2017 Inertial Sensors and Systems conference [1]. If you would like to learn more, please feel free to download our paper or contact us for a demonstration. We’re also keen to hear of any simulation problem that you have – perhaps we can help?

[1] 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