Computer-Aided Design Tools for Micro-electromechanical [MEMS] Systems

Simulation Tools for Micro-machined Device Design

Micro-machining technology has enabled the fabrication of several novel micro-sensors and micro-actuators. Because of the specialized processing involved, the cost of prototyping even simple micro-sensors, micro-valves, and micro-actuators is enormous. In order to reduce the number of prototype failures, designers of these devices need to make frequent use of simulation tools. To efficiently predict the performance of micro-electro-mechanical systems (MEMS) these simulation tools need to account for the interaction between electrical, mechanical, and fluidic forces. Simulating this coupled problem is made more difficult by the fact that most MEMS devices are innately three-dimensional and geometrically complicated. It is possible to simulate efficiently these devices using domain-specific solvers, provided the coupling between domains can be handled effectively. In this work recent development showed several new approaches and tools for efficient computer aided design and analysis of MEMS.

One of the recent efforts in this area has been in developing algorithms for coupled-domain mixed regime simulation. We developed a matrix-implicit multi-level Newton method for coupled domain simulation which has much more robust convergence properties than just iterating between domain-specific analysis programs, but still allows one to treat the domain analysis programs as black boxes. In addition, an another approach to accelerating coupled-domain simulation is by allowing physical simplifications where appropriate. This is referred to as mixed regime simulation. For example, self-consistent coupled electromechanical simulation of MEMS devices face a bottleneck in the finite element based nonlinear electrostatic solver. Replacing a stiff structural element by a rigid body approximation which has only 6 variables, all variables associated with the internal and surface nodes of the element are eliminated which is now a function of the rigid body parameters. Using this coupled domain approach has made it possible to perform coupled electromechanical analysis of an entire comb drive accelerometer in less than 15 minutes.

Analysis of the resonance behavior of micro-machined devices packaged in air or fluid requires that fluid damping be considered. Since the spatial scales are small and resonance analyzes are typically done assuming a small amplitude excitation, fluid velocities can often be analyzed by ignoring convective and inertial terms and then using the steady Stokes equation. For higher frequency applications, the convective

term may still be small, but the inertial term rises linearly with frequency. Therefore, analyzing higher frequency resonances requires the unsteady Stokes equations, though the small amplitudes involved make it possible to use frequency domain techniques. We have developed a fast Stokes solver, Fast Stokes,

based on the pre-corrected-FFT accelerated boundary-element techniques. The program can solve the steady Stokes equation or the frequency domain unsteady Stokes equation in extremely complicated geometries. For problems discretized using more than 50,000 unknowns, our accelerated solver is more than three orders of magnitude faster than direct methods.

Enhancing MEMS Design Using Statistical Process Information

Micro Electro-Mechanical Systems (MEMS) design is often done using circuit design rules for layout and complex synthesis or mechanical simulation for actual device structure. The problem with this approach is that devices that work well in simulation often have high sensitivity to process variation and therefore can have properties that differ substantially from projected values. These effects lead to both poor performances and lower yields.

Figure above shows a picture as well as a diagram of a comb-drive resonator. This device is ideal for process sensitivity analysis because its resonant frequency is a key system parameter that can be easily computed in simulation and is directly affected by the process and underlying geometries.As an example of the importance of process variation to device performance, Figure below compares a 50 K Hz resonator based on a 2 mm folded beam flexure to a 50Khz resonator using a 4 mm beam. The graph shows that for a 1 s manufacturing variation in beam width (taken from actual MEMS fabrication data), the 4 mm system experienced a 4.2 frequency variation compared to the 10 reduction in system variation (for frequency) would lead to higher yield and tighter system specifications.A methodology for enhancing MEMS designs was developed using the property shown in one of the figure. The comb-drive resonator was used as an example device. A tool for synthesizing resonators that is more robust to process variation was developed. One of the figures shows the results of synthesizing three resonators using the tool. The above figure shows a 50 K Hz resonator synthesized for area alone. Typical fabrication process variation would cause this device over 10variation, figure shows the same resonator optimized for less than 95process robustness.