MEMS Gyroscope Design and Simulation

MEMS gyroscopes (gyros) are one of the most exciting growth areas for the MEMS industry, with deployment in smart phones leading the way. Yole Development predicts that MEMS gyros will be built into in nearly 500 million smart phones by 2015. Other well established and still growing uses of MEMS gyros include stability control in automobiles, image stabilization in digital cameras, and motion sensing in gaming systems. As the applications for MEMS gyros increase, so does the competition among MEMS manufacturers to win their share of this valuable, high-growth market.

MEMS gyroscopes

Penetration of motion sensors in mobile phones, courtesy Yole Development.

Design Challenges

MEMS gyro fabricated in SOIMUMPS, courtesy M. Sharma and E. Cretu, U. British Columbia.

Successful gyro designs must:

  • Provide high sensitivity and low drift,
  • Maximize sensing bandwidth,
  • Maximize signal-to-noise (SNR) ratio,
  • Minimize cross-axis sensitivity,
  • Minimize quadrature error,
  • Provide stable response vs. temperature,
  • Reject external vibrations,
  • Survive shocks from impacts,
  • Minimize parasitic cross-coupling, and
  • Minimize power consumption.

Designers of MEMS gyroscopes know that it’s extremely difficult to satisfy all of these requirements, especially for consumer electronics applications where cost and time to market are also key considerations. Being able to rapidly explore design trade-offs while accurately accounting for all physical effects is critical to their success. A new design methodology is required.

New Methodology for MEMS Gyroscope Design

In partnership with leading MEMS companies and software vendors, Coventor has developed a new methodology for gyro design. The methodology, shown in the diagram below, supports all phases of product development, from initial proof of concept studies through final functional verification. Coventor MEMS+ and CoventorWare together provide a platform for MEMS designers, enabling them to accurately simulate their designs and to deliver accurate models to their counterparts in system and IC design. The methodology supports simulation at different levels of abstraction on the system side, in the tools of choice throughout the MEMS industry: MathWorks Simulink for control system design and Cadence Virtuoso for analog/mixed-signal design.

MEMS gyroscopes

Coventor software provides a platform for all phases of MEMS design as well as MEMS+IC integration

Design Tasks

MEMS gyroscopes

Gyroscope design implemented in MEMS+

MEMS designers assemble a design by combining elements from the parametric library that’s included with MEMS+. Typically, the proof mass is modeled by combining rigid plate segments (which may have perforations for release etches) while the suspension is modeled with beams or flexible plates. The mechanical components can be supplemented with electrostatic components such as top, bottom and side electrodes, and electrostatic comb drives. Each component has a 3D view as well as an associated behavioral or high-order finite-element model.

Matching Sense and Drive Mode Frequencies

MEMS gyroscopes

Gyro frequency response, simulated in MATLAB using a MEMS+ model, showing nearly matching actuation and sense mode frequencies

Most gyro designs depend on matching the frequencies of the sense and drive modes. In practice, despite careful design, the modal frequencies may differ slightly due to manufacturing effects. Mismatch between the drive and sense mode frequencies can be compensated by adjusting the DC bias voltage on the actuation or sensing comb drives. Determining how much the DC bias affects the modal frequency depends on accurately simulating a second-order effect known as electrostatic spring softening. Both MEMS+ and CoventorWare can accurately simulate electrostatic spring softening.

MEMS gyroscopes

Shift in sense mode resonant frequency due to DC bias.

Manufacturing Sensitivity

Sensitivity and cross-axis sensitivity can be affected by manufacturing effects such as variation in sidewall angles across a wafer. MEMS+ models can easily account for these real-world effects, as shown in these simulation results.

MEMS gyroscopes
MEMS gyroscopes
MEMS gyroscopes

Sensitivity change and cross-axis sensitivity as a function of sidewall angle.

Gas Damping Analysis

Gas damping is the primary damping mechanism in MEMS gyros, and affects the sensitivity and power consumption of the device. Gas damping effects must be included in simulations of the gyro alone and together with control and sensing circuitry. The CoventorWare MemDamping module includes two solvers for computing gas damping: a Reynolds equation solver for squeeze-film and slide-film damping between parallel surfaces, and a Stokes equation solver for general geometry. Typical gyro designs require use of both solvers to compute the damping of drive and sense modes.

MEMS gyroscopes

Decomposition of gyro design for gas damping simulations

MEMS gyroscopes

Stokes solver simulation results for electrostatic comb drives: convergence graph above, fluid force contours below.

MEMS + IC System Simulation

Integrating the 3D MEMS device with the sensor conditioning circuit is critical to bringing MEMS gyroscopes to market, but all too often happens late in the product development cycle. With MEMS+, designers can hand off a MEMS+ model to their counterparts in system design and IC design early in the design process, exposing integration issues sooner rather than later. MEMS+ models are compatible with two widely used simulation environments, Simulink and Cadence.

MEMS gyroscopes

Circuit schematic of MEMS gyro with synchronous demodulator

A Complete Platform for MEMS Gyroscope Design

Coventor provides a complete platform for designing and simulating MEMS gyros. MEMS+ enables designers to rapidly explore design concepts in the familiar and powerful MATLAB environment. Rather than spending months developing their own analytical or numerical model of a particular design, MEMS teams can rapidly assemble a fully parametric design using the proven building blocks in Coventor’s MEMS component library. The resulting MEMS+ models capture not only basic behavior of the gyro, but higher-order physical effects such as electrostatic spring softening, quadrature error, and substrate deformation due to temperature changes. Furthermore, the MEMS+ models can be verified and supplemented with simulations in CoventorWare’s best-in-class field solvers. These solvers have been optimized to address simulation challenges that are specific to MEMS gyros, such as electrostatic fringing fields, non-linear electro-mechanical coupling effects, gas damping, and anchor losses. Because the simulations with MEMS+ models run very fast, typically in minutes versus hours or days for conventional FEA simulations, designers can now explore the parametric nature of MEMS+ models and perform automated optimization and manufacturing variability studies. Thus, MEMS+ and CoventorWare together provide the best of both worlds: the speed of behavioral modeling with the accuracy of FEA.

Coventor’s platform goes far beyond the design of the electro-mechanical gyro. Coventor enables a true top-down design methodology for MEMS-enabled systems. To collaborate with their colleagues in system and IC design, MEMS designers no longer need to devote weeks or months to hand crafting reduced-order models based on analytical expressions and/or FEA extractions. Instead, they can immediately hand over MEMS+ models for simulations of the complete system, i.e. the MEMS sensing element plus electronics. Not only does this save valuable engineering time, but it eliminates manual hand-off as a potential source of errors. More importantly, the MEMS+ models fully capture the complex physical behavior of gyros so that the surrounding electronics do not have to be over designed to compensate for unknown effects. MEMS+ models can be used early on, for algorithmic and control system design in Simulink, and for circuit design in Cadence. MEMS+ models can also be used for final design verification in Cadence prior to tape out.

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