MEMS Accelerometer Design

MEMS accelerometers are widely utilized in cars for airbag deployment and in consumer electronics applications such as smart phones. In addition, there is a growing demand for high-end MEMS accelerometers in industrial, aerospace and defense applications such as oil exploration, structural health monitoring for bridges, and inertial measurement units for navigation.

The Challenges of MEMS Accelerometer Design

From conceptual design, to optimization and performance enhancement, CoventorMP® can simulate a wide range of critical specifications related to successful MEMS accelerometer design. These include:

  • Proof of concept studies, to explore different device configurations
  • Sensitivity
  • Bandwidth
  • Noise
  • Linearity
  • Non linear physics, including damping and rectification error
  • Shock resistance
  • Temperature performance

By way of example, an accelerometer model constructed using the multi-physics elements in the MEMS+ module of CoventorMP® is shown below. The sensing element is comprised of a perforated shuttle mass suspended at both ends by two springs. Four comb finger capacitors are attached to the shuttle mass, two for sensing and two for force-feedback control. The model is fully parametric, so that design parameters can be varied to optimize sensitivity, linearity and bandwidth.

MEMS+ Accelerometer model showing colored highlighted inertial mass, sense and control combs, suspensions and contact bumpers.

MEMS+ accelerometer model showing colored highlighted inertial mass, sense and control combs, suspensions and contact bumpers.

The MEMS+ module has its own solvers for multi-physics simulations including static, modal, linear and non-linear harmonic analysis and noise analysis. The model can also be directly simulated in Mathworks MATLAB® to rapidly explore the design space through the use of scripted DOE simulations and optimization algorithms. In this example, the comb element is configured to include both electrostatics and squeeze film damping [1]. This enables the bandwidth variation with pressure to be simulated and plotted, shown here using the MATLAB interface to MEMS+.

Contour plot showing comb-gap pressure variation for the lateral Y-sense mode at 10000 Pa cavity pressure. The left hand inset plot shows 10 harmonic sweeps over a pressure range of 1000 Pa to 100000 Pa, simulated via the MATLAB interface in 30s. The vertical lines mark the 3 dB points from which the variation of bandwidth is plotted with pressure (right hand inset plot).

Contour plot showing comb-gap pressure variation for the lateral Y-sense mode at 10000 Pa cavity pressure. The left hand inset plot shows 10 harmonic sweeps over a pressure range of 1000 Pa to 100000 Pa, simulated via the MATLAB interface in 30s. The vertical lines mark the 3 dB points from which the variation of bandwidth is plotted with pressure (right hand inset plot).

Co-Simulation with Circuit and System Simulators

Using Coventor’s unique methodology, the accelerometer can be co-simulated together with the control system and/or motion sensing electronics. The control system can be modeled using the Mathworks Simulink® environment, leveraging standard Simulink toolboxes to optimize system performance. Equally, the sensing electronics can be modeled by loading the MEMS+ model directly into Cadence Virtuoso® , or automatically exporting the model from MEMS+ to a VerilogA model that can be used in a compatible simulator.

Simulink schematic containing <em>MEMS</em>+ model of the Accelerometer, including mechnical-contact and non-linear <em>squeeze</em> film damping. The model is connected to a simple second order sigma-delta controller, comprised of an ideal comparator and a D-type latch. Two anti-phase feedback signals are generated from the output bit-stream using ideal switches and fed back to the control combs on the Accelerometer. The inserted scope plot shows the input acceleration (upper) and feedback control voltage (lower).

Simulink schematic containing MEMS+ model of the accelerometer, including mechnical-contact and non-linear squeeze film damping. The model is connected to a simple second order sigma-delta controller, comprised of an ideal comparator and a D-type latch. Two anti-phase feedback signals are generated from the output bit-stream using ideal switches and fed back to the control combs on the accelerometer. The inserted scope plot shows the input acceleration (upper) and feedback control voltage (lower).

Coventor’s unique design platform couples best-in-class MEMS finite element and solver support.  It can be used by MEMS accelerometer designers to rapidly and accurately explore today’s critical design challenges. The platform offers the ability to simulate the complex multi-domain, multi-physics behavior of the sensing elements and their associated electronics, and to accurately predict sensitivity, bandwidth, noise, control-loop stability and more.

References:

  1.  “A Novel Squeezed-Film Damping Model for MEMS Comb Structures”, Alexandre Sinding1, Arnaud Parent1, Ilker E. Ocak2, Wajih U. Syed3, Aveek N. Chatterjee4, Christopher Welham1, Shuangqin Liu5, Jun Yan5, Stephen Breit5, Hyun-Kee Chang2, Ibrahim (Abe) M. Elfadel3, and Zouhair Sbiaa4                 1Coventor SARL, Villebon-sur-Yvette, FRANCE 2Institute of Microelectronics, A*STAR (Agency for Science, Technology and Research), SINGAPORE 3Masdar Institute of Science and Technology, Abu Dhabi, UAE 4GLOBALFOUNDRIES, SINGAPORE and 5Coventor, Inc., Waltham, MA, USA