MEMS Resonator Design and Simulation

Replacing conventional quartz resonators with MEMS based resonators in the 3-billion dollar timing market is a dream shared by many of today’s MEMS innovators. Unlike Quartz, MEMS resonators can be miniaturized and flattened to better address the form-factor needs for hand-held wireless devices. MEMS-based resonators can also be integrated together with their driving circuitry, offering a complete timing solution in a single package, saving valuable board space. These advantages, together with the power advantages inherent in MEMS devices, make a compelling case for MEMS based resonators.

MEMS Resonator

Design Challenge

To make MEMS-based resonators commercially viable, designers need to match the phase noise performance, temperature stability and frequency accuracy of quartz crystals while leveraging the advantages of size, cost, and power which are possible with MEMS technology.

After the initial requirements are defined (size, target frequency, and impedance), designers explore the trade-offs between power handling capacity, phase noise performance, temperature and frequency stability.

To achieve optimal performance for their specific design, finite element analysis (FEA) and tools like Spice are used. The problem is these tools are painfully slow, they introduce new uncertainties, and very often designers simply revert back to the “tried and true” approach of build-and-test. This greatly limits design exploration, significantly increases development costs and time, and leaves design margin on the table.

Coventor’s hybrid-design methodology for resonators challenges the status-quo. Our integrated platform provides extremely fast design-of-experiment (DOE) studies, highly accurate and detailed verification, and the ability to address the MEMS+IC system . We invite you to learn more.

New Hybrid-Design Methodology

  1. Rapid Design Exploration
    First, geometries are created using electromechanical library elements which can be enhanced by variables, equations and tolerances to create a parametric design. Simulations are run on this full electromechanical system in combination with statistical solvers to create optimized designs. Monte Carlo simulation can be used to improve yield. Optimization algorithms are employed to achieve the desired performance.

    mems Resonators

    Fig 1. Geometries corresponding to operating frequency – 3.37MHZ, 2.40MHZ, 2.80MHZ.

    Because these simulations are extremely fast and include critical non-linearities, they allow designers to create hundreds of potential solutions and study coupling effects and other criteria of interest up front, before committing to a specific architecture.

    mems Resonators

    Fig 2. Minimal impact of anchor is at 250um of Coupling Beam Length

    Shown here are the effects of coupling beam length on resonant frequency. Using Coventor’s interface to MATLAB from The MathWorks, simulations are run using a MATLAB script where the mode shape of interest is specified and coupling beam lengths are swept. Coventor’s approach automatically extracts the mode frequency for the mode shape of interest (even if the mode number is changed), and the total solution times was less than 3 minutes (step size of 10um and 384 Degrees of Freedom). Such rapid computation time compared to standard FEA opens the door to far more design exploration than previously possible.

  2. Add Detailed Analysis with Field Solvers
    Simulating non-linearities due to electro-mechanical spring softening, duffing, and pull in are extremely important to the overall success of the resonator design. Consequently, a MEMS designer focuses on all of theses aspects in the design exploration phase of the designprocess, shown in Section 1.  Yet, to ensure greater confidence in the numerical results, additional verification using FEA might be desired. For instance, an FEA simulation can provide conclusive validation of linearity assumption that may be desired in later coupled electro-mechanical simulations.   Relevant to Coupled Electromechanical Simulations, it must be noted that Coventor’s technology is based on a hybrid Finite Element (FEM)/Boundary Element (BEM) approach.  Using BEM to compute electrostatic forces and moments requires a mesh on only the surface of conducting bodies, avoiding the need to mesh the infinite volume surrounding the conductors as with traditional FEM electrostatics.  A BEM approach is not only more computationally efficient, but avoids the need to remesh the volume between two conductors as they move into contact bodies.  Thus it makes it practical to explore these phenomena on standard platforms.

    Fig. 4 Magnitude of displacement field in substrate showing outgoing acoustic wave

    At this stage, a designer can also explore various loss mechanisms: Gas damping, acoustic radiation through the anchors (i.e. Anchor Loss), and thermo-elastic-Damping (TED). Coventor provides specialized algorithms, tools, and expertise to assist with these tasks. Shown below are several design variations that were explored to minimize the impact of TED and their corresponding predicted Qs.

    Thermo-elastic-daming

    Fig. 5 Design Variation for minimizing Thermo-elastic damping – Q = 26550,330383 and 26800

    Furthermore, the designer can utilize Coventor’s FEA solvers for exhaustive failure analysis such as adding fillets to minimize stress.  The fully integrated platform also provides the ability to import pre-meshed or solid models of package designs, run thermo-mechnanical analysis and pass on stress/deformation results to the system-levels tools to incorporate the effects on the performance of the resonator.   Only Coventor offers the unique approach to combine the power and speed of behavioral analyses with the accuracy of FEA.

    mems stress-distribution

    Fig. 6 Exploring effect of fillet size on stress distribution.

  3. MEMS + IC System Simulation
    Integrating the 3D MEMS device with the sensor control circuit and validating performance via an accurate SOC test-bench simulation is yet another critical element to successfully bringing MEMS resonators to market. At this stage, designers choose to run Coventor’s models on best in class tools from either Cadence or The Mathworks to achieve the speed and capacity they need to solve these difficult problems. Note, this approach forgoes the time-consuming effort of extracting models and generating equivalent circuit models, leaving much more time for exploring trade-offs that can be made at the circuit level, the MEMS design, or both.

    MEMS+IC integration in Cadence

    Fig. 7 MEMS+IC integration in Cadence Virtuoso.

Coventor’s methodology uses FEA-based, fully parametric and nonlinear high order finite elements that obviate traditional methodologies such as extraction of equivalent circuits. The simulations below capture the mechanics and electrostatic nonlinearities.

mems x-displacement

mems DCBias

Fig. 8. Temperature and DC Bias effects on Output Curren

A Complete Platform for MEMS Resonator Design

Coventor has an established MEMS design platform for MEMS Resonators, providing designers solutions to a broad range of critical design challenges. These range from simulating the complex multi-domain, multi-physics of the sensing element and associated electronics to system level modeling, package analysis and manufacturing yield enhancement.

The advantages of this new hybrid approach are numerous. Because the underlying physics of the MEMS Resonator is included in the 3D Model that is referenced in system-level simulations, designers no longer need to create a reduced order or equivalent model networks from FEA data and/or analytical expressions. This saves valuable time and resources. In addition, these models are fully parametric, enabling designers to rapidly explore effects of design and process changes that were simply impractical to do via other methods.

Finally, by selecting a platform that uses best-in-class simulators like Spectre and/or Matlab/Simulink, designers obtain the best on-going combination of accuracy and capacity. As Coventor, Cadence and The Mathworks all continue to make algorithm improvements, resonator designers realize exponential increases in capacity and speed. Build and test methodologies and custom, in-house programs simply can not keep pace with the continued advancement of well organized, commercial endeavors.

[Yu-Wei Lin, Seungbae Lee, Zeying Ren, Yuan Xie, Clark Nyugen Series Resonant VHF Micromechanical Resonator Reference Oscillators IEEE Journal of Solid-State Circuits December 2004]

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