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Simulating RF MEMS David Bindel UC Berkeley, CS Division Simulating RF MEMS – p.1/21

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Page 1: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Simulating RF MEMSDavid Bindel

UC Berkeley, CS Division

Simulating RF MEMS – p.1/21

Page 2: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Collaborators

Faculty Grad students

A. Agogino (ME) D. Bindel (CS)

Z. Bai (Math/CS) J.V. Clark (AS&T)

J. Demmel (Math/CS) D. Garmire (CS)

S. Govindjee (CEE) T. Koyama (CEE)

R. Howe (EE) R. Kamalian (ME)

J. Nie (Math)

S. Bhave (EE)

Simulating RF MEMS – p.2/21

Page 3: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

MEMS Basics

Micro-electro-mechanical systemsChemical, fluid, thermal, optical (MECFTOMS?)

Applications:Sensors (inertial, chemical, pressure)Ink jet printers, biolab chipsRF devices

Use IC fabrication technology

Large surface area / volume ratio

Still mostly classical (vs. nanosystems)

Simulating RF MEMS – p.3/21

Page 4: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

SUGAR

Goal: “Be SPICE to the MEMS world”

Fast enough for early design stages

Simple enough to attract users

Support design, analysis, optimization, synthesis

Verify models by comparison to measurement

System assembly

Models

Solvers

Matlab Web Library

Sensitivity analysis

Static analysis

Steady−state analysis

Transient analysis

Results

Netlist

Interfaces

Simulating RF MEMS – p.4/21

Page 5: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

SUGAR: Analysis of a micromirror

(Mirror design by M. Last)

Simulating RF MEMS – p.5/21

Page 6: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

SUGAR: Design synthesis

Simulating RF MEMS – p.6/21

Page 7: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

SUGAR: Comparison to measurement

Simulating RF MEMS – p.7/21

Page 8: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Why RF resonators?

Microguitars from Cornell University (1997 and 2003)

Frequency references

Sensing elements

Filter elements

Neural networks

Really high-pitch guitars

Simulating RF MEMS – p.8/21

Page 9: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Micromechanical filters

Mechanical filter

Capacitive senseCapacitive drive

Radio signal

Filtered signal

Mechanical high-frequency (high MHz-GHz) filter

Saves power and cost over electronic filters

Advantage over piezo-actuated quartz SAW filtersIntegrated into chipLow power

Simulating RF MEMS – p.9/21

Page 10: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Governing equations

Time domain:

Mu′′ + Cu′ + Ku = Pφ

y = V T u

Frequency domain:

H(ω) = V T (−ω2M + iωC + K)−1P

y = Hφ

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.510

−4

10−2

100

102

104

106

108

Simulating RF MEMS – p.10/21

Page 11: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

First proposed design: Checkerboard

� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �

� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �

����

����

� �� �� �� ����

� � � �� �

�����

� �� � � �� �� �� �� ����

�� �� �� �� �

D+

D−

D+

D−

S+ S+

S−

S−

Array of loosely coupled resonators

Anchored at outside corners

Excited at northwest corner

Sensed at southeast corner

Surfaces move only a few nanometers

Simulating RF MEMS – p.11/21

Page 12: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Design questions

−8 −6 −4 −2 0 2 4 6 8

x 10−5

−8

−6

−4

−2

0

2

4

6

8x 10−5

−8 −6 −4 −2 0 2 4 6 8

x 10−5

−8

−6

−4

−2

0

2

4

6

8x 10−5

Where should drive and sense be placed?

How should the individual resonators be connected?

How should the system be anchored?

How many components? What topology?

Simulating RF MEMS – p.12/21

Page 14: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Checkerboard response

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

x 108

−550

−500

−450

−400

−350

−300

−250

Hz

dB

Corner−connected response

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

x 108

−550

−500

−450

−400

−350

−300

Hz

dB

Beam−connected response

Corner-connected details Beam-connected details

Simulating RF MEMS – p.14/21

Page 15: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Current questions

How do we model damping?

How do we compute frequency response quickly?

How do we track dependence on geometry?

How do we optimize designs?

Simulating RF MEMS – p.15/21

Page 16: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Energy loss and Q

Goal: strong output signal and high Q

Challenge: Model details of energy lossAnchor lossThermoelastic dampingAkheiser dampingAir damping

How are losses affected by fabrication errors (e.g.anchor misalignment)?

Simulating RF MEMS – p.16/21

Page 17: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Model reduction

Sun Ultra 10Sec n

ROM: 28 4834Full: 1474 50

Project onto an unusual Krylov subspace

Preserve second order system structure

Plan to use substructuring

Simulating RF MEMS – p.17/21

Page 18: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Mode tracking: Shear ring resonator

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9hw = 5.000000e−05

Value = 2.66E+07 Hz.

Ring is driven in a shearing motion

Can couple ring to other resonators

How do we track the desired mode?

Simulating RF MEMS – p.18/21

Page 19: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Mode tracking: Results

2 2.5 3 3.5 4 4.5 5 5.5 6

x 10−5

2.5

3

3.5

4

4.5

5

5.5x 107

Half width of annulus

Fre

quen

cy (

Hz)

Finite elementAnalytic result

Predictor-corrector iteration

Convergence criteria, step control based on|q(sk)

T q(sk+1)|

Simulating RF MEMS – p.19/21

Page 20: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Transfer function optimization

Choose geometry to make a good bandpass filter

What is a “good bandpass filter?”|H(ω)| is big on [ωl, ωr]

|H(ω)| is tiny outside this interval

How do we optimize?Overton’s gradient sampling methodUse Byers-Boyd-Balikrishnan algorithm for distanceto instability to minimize |H(ω)| on [ωl, ωr]

Small Hamiltonian eigenproblem (with ROM)

Simulating RF MEMS – p.20/21

Page 21: Simulating RF MEMS - Cornell Universitybindel/present/2004-03-bascd.pdf · Ink jet printers, biolab chips RF devices Use IC fabrication technology ... Radio signal Filtered signal

Conclusions

RF MEMS are an interesting source of problemsUnderstanding the physicsApplying numerical tools

http://bsac.berkeley.edu/cadtools/sugar/sugar/

http://www.cs.berkeley.edu/∼dbindel/feapmex.html

Simulating RF MEMS – p.21/21