Speed, Accuracy and Automation in MEMS Simulation and Development C. J. Welham, Coventor, Paris

MEMS Design & Simulation Challenges

• Overview

• Simulation Challenges and Approaches

• Validation

• Case Studies

• Conclusion

• MEMS have evolved from DLP, inkjet and

airbag applications to high volume Consumer

Electronic devices >20% CAGR

• Democratization of MEMS causing a shift

in business growth from traditional MEMS

companies to semi-foundries and fabless

design houses.

• Consumer Electronic applications require

shorter product development cycles.

• Pressure to reduce size of MEMS

components whilst increasing performance

and integration.

Market data from Yole Development

Demand for MEMS is Changing

MEMS-based products are becoming smaller and more integrated

Decreasing size and greater integration pressures require more sophisticated models and simulations

• More sensitive spurious coupling between components

• More important to consider non-linearities

• More sensitive to parasitic effects

• More chance of design errors in interconnect

1-axis accel. 2-axis accel. 3-axis accel. IMU: 3-axis accel. + 3-axis gyro

Simulations must include more coupled

physics, non-linearity, parasitic effects

and the connected circuit/system

Simulation Challenges

Two Approaches

3D Design Entry

in Graphical UI

High Order FEA

- Designed for MEMS

High-order, coupled physics elements

Scripting in

MATLAB

or Python or

Meshed Model

Small 10 to 1000 DOF

Conventional Low Order FEA

- General Elements

Library of

generic, low-order

finite elements

Brick, tet, shell, and beam elements

Mesh

Generator

Meshed Model

Large 10k to 10M DOF

3D Geometry

High Order Benefits

Compatibility

Speed and Accuracy

Parameterization

3D Design Entry

in Graphical UI

High-order, coupled physics elements

Scripting in

MATLAB

or Python or

Meshed Model

Small 10 to 1000 DOF

High Order FEA

- Designed for MEMS

Compatibility

Internal Simulator

MATLAB

Simulink

Virtuoso

Simulate and Analyze Enter Design in 3D Visualize Results in 3D

Models with a small number of DOF

can run directly in MATLAB, Simulink and Cadence

High Order Finite Element Library:

MEMS coupled-physics specific, 3D, high-order, parametric

VerilogA

Models that run directly in other simulators allow MEMS and IC

Designers to collaborate easily

Design Capture

High Order FEA

Algorithmic Level

(Simulink)

Behavioral Level

(Virtuoso)

Transistor Level

(Virtuoso)

Physical Level

(Virtuoso)

High Order Elements allow

the automatic transfer of

models for use by IC or

System Designers

IC Designers MEMS Designers

Compatibility

Model Export

• High Order Models can be inherently parametric

– Explore design envelope

– Manufacturing/Sensitivity Analysis

Sidewall

Angle

CD loss

Mass

thickness

Parameterization

Mode Y

Variation of Frequency Y - 1000 Samples

Mode Z

Variation of Frequency Z - 1000 Samples

• Results from Monte Carlo Analysis

– Random input variables defined from mean and std. deviation

• Modal Analysis, 1000 samples

• 7s per sample

Parameterization

Variation of Frequency X - 1000 Samples

Mode X

*Self-aligned Vertical Electrostatic Comb drives for Micromirror Actuation”, Krishnamoorthy, U., Lee, D., Solgaard, O., JMEMS2003

• Electrostatic MEMS element 100s of times faster

Speed and Accuracy

Comb Finger - Element Level Validation

High Order Model

Low Order BEM Model

*Experimental Validation of Aluminum Nitride Energy Harvester Model with Power Transfer Circuit

S. Matova, D. Hohlfeld, R. van Schaijk, C. J. Welham, S. Rouvillois

Eurosensors XXIII conference 2009

• Compare both approaches and measurement

Validation – Device Level

Energy Harvester - Coupled-Physics, Multi-Domain

• Virtual fabrication MEMS device

– Voxel modelling for robust model build

• Silicon accurate 3D geometry

• Test design is correct before tape-out

• Communication with Foundry

– Process development

Validation - Process

Voxel Model

Release

Oxide

Bulk Silicon Thermal

Oxide

Polysilicon

Electrode

Epitaxial

Polysilicon

Hard Mask

Release Oxide

Deposition Via to Electrode Epi-poly growth and

Planarization DRIE Release Etch

Based on Chipworks teardown

Case Study - Gyroscope Benefits of MEMS specific element approach

• “The power of high order element models allows very rapid design studies

and optimize the design”

• “A 3D parametric study in low order conventional FEA can take significant

time, even though point simulations (modal) only take minutes. With high

order element models simulations take seconds: total simulation time is

therefore much lower”

• “Geometry variation is more difficult in conventional FEA ”.

Key challenges solved by Model Export

• “Writing a (VerilogA) model takes weeks and requires significant expertise.

Enhancements (e.g. spurious modes, parasitic Cs) and design variations

takes time, which is not always available.”

• “Simple hand written analytical models miss non-linearities and other

second order effects.”

• Upgrading and maintaining hand written models for ASIC design partners

is painful

Case Study - Microphone

Perform noise analysis

• Model supports noise analysis in Cadence Spectre

and accurately predict thermo-mechanical noise

• Model supports all relevant noise sources in your MEMS+IC system,

enabling you to evaluate noise cancelling strategies

Model includes mechanics,

electrostatics and fluidic

effects

Cadence Virtuoso schematic Noise analysis

in Cadence Spectre

Microphone

Case Study - Switch Switch Dynamic Response

Time (s)

Tip

position

(m)

High order elements are

very fast and can easily

combine mechanical,

electrical and fluidic effects

in a transient simulation

RF switch tip position, closing and opening

Simulated gas pressure on

electrodes as RF switch closes

Other Examples

DLP mirror, 11 DoF

RF Switch

119 DoF

Gyroscope, 96 DoF Accelerometer, 67 DoF

The High Order approach is general: it has been used to create

compact, accurate models of many real-world designs

Ring Gyro, 345 DoF

Ring Resonator, 727 DoF

Conventional FEA

Is there a place for conventional FEA models

– YES!

– Some problems are better modelled with conventional FEA

• Stress, packaging, multi-conductor, parasitic and damping problems

– TED, Gas, Anchor

– Some geometries are not suited to high order elements

Simulate stress Simulate package

Simulate FBAR

In Conclusion • Use High Order FEA for Speed, Accuracy and Automation

– MEMS-specific geometries and coupled physics

• Benefits over traditional FEA

– Much faster simulations due to reduced degrees of freedom

– Parameterization enables rapid design exploration and optimization

– Compatible with MATLAB, Simulink and Cadence simulators

– Simulate the full dynamic response of sensors and actuators

– Simulate closed-loop operation of sensors

– Deliver models of MEMS devices to system and IC designers

– Perform noise analysis of sensors

• Conventional FEA still useful for certain design tasks

• Leverage Process Modeling

– Validate design with process prior to tape out