MEMS Resonator Design and Simulation

MEMS innovators are rapidly replacing conventional quartz resonators with MEMS-based resonators in the $4.5 billion dollar timing market. Unlike quartz, MEMS resonators can be miniaturized and flattened to better address the form-factor needed for hand-held wireless devices and automotive applications. MEMS-based resonators can also be integrated with their driving circuitry, offering a complete timing solution in a single package that saves valuable board space. These advantages, together with lower power requirements, reliability advantages, and the improved temperature stability inherent in MEMS devices, provide a compelling case for MEMS based resonators.

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 conventionally used. 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 entire MEMS+IC system design. 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 desired performance.

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.

A study of the effects of coupling beam length on resonant frequency is shown in Figure 2. 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 modified).  The total solution time was less than 3 minutes (step size of 10um and 384 Degrees of Freedom). This rapid analysis time (compared to standard FEA) opens the door to far more design exploration than was ever 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 design process (Section 1, above).  Yet, to ensure greater confidence in the numerical results, additional verification using FEA might be desired. For instance, an FEA simulation using coupled electro-mechanical simulations can provide conclusive validation of desired linearity assumptions.

Coventor’s approach to coupled electromechanical simulations is based upon a hybrid Finite Element (FEM)/Boundary Element (BEM) method.  To compute electrostatic forces and moments using BEM only requires a mesh on the surface of any conducting bodies.   This technique avoids the need to mesh the infinite volume surrounding the conductors, which is required when traditional FEM electrostatic modeling is used.  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.  This technique makes it practical to explore complex electromechanical phenomena on standard computational platforms.

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. Figure 4 (below) highlights several design variations that were explored to minimize the impact of TED and their corresponding predicted Qs.

Furthermore, a designer can utilize Coventor’s FEA solvers for exhaustive failure analysis, such as adding fillets to minimize stress (see Figure 5).  The CoventorMP design platform is fully integrated, and provides the ability to import pre-meshed or solid models of package designs and perform thermo-mechnanical analysis.   Resonator performance can be evaulated at the system level by delivering device-level stress/deformation results to system-level modeling tools.   Only CoventorMP offers this unique approach to MEMS design, combining the power and speed of behavioral analyses with the accuracy of FEA.

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 a complex but critical task on the road to MEMS resonator commercialization. To solve this problem, designers can use Coventor’s models with “best in class” system and circuit design tools from Cadence^® or The Mathworks^®. CoventorMP automatically extracts MEMS models and generates equivalent circuit models, avoiding the time-consuming effort of developing and extracting hand-crafted models.   This provides the designer with more time for exploring trade-offs at the circuit level, within the MEMS design, or both.

Coventor’s methodology uses FEA-based, fully parametric and nonlinear higher order finite elements.  These elements can be combined, like building blocks, into a model of the MEMS device.   This methodology avoids the difficulties experienced using traditional methodologies, such as the need to extract equivalent circuits.  Using CoventorMP, we can quickly include the MEMS design in circuit and system simulations, and identify mechanical and electrostatic nonlinearities in the design (see Figure 7).

A Complete Platform for MEMS Resonator Design

Coventor has an established design platform for MEMS resonators, providing designers with solutions to a broad range of critical challenges. These challenges range from simulating complex multi-domain, multi-physics properties 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 are included in the MEMS+ reduced order model, designers no longer need to create a reduced order or equivalent model 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 using other methodologies.

The CoventorMP platform uses best-in-class simulators like Spectre^® and/or Matlab/Simulink^®, so that designers obtain the best on-going combination of accuracy and capacity. As Coventor, Cadence and The Mathworks all continue to make algorithm improvements to their tool platforms, 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.

Reference:

[Yu-Wei Lin, Seungbae Lee, Zeying Ren, Yuan Xie, Clark Nyugen, “Series Resonant VHF Micromechanical Resonator Reference Oscillators”,  IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 39, NO. 12, DECEMBER 2004]