1. Excitation of Vibrational Eigenstates of Coupled Microcantilevers Using Ultrasound Radiation Force ASME 2nd International Conference on Micro and Nanosystems Brooklyn, NY August 6, 2008
Thomas M. Huber, Brad Abell, Sam Barthell, Dan Mellema, Eric Ofstad
Physics Department, Gustavus Adolphus College
Arvind Raman, Matthew Spletzer
Department of Mechanical Engineering, Purdue University

2. Introduction Ultrasound Radiation Force Excitation
Excitation of microcantilevers using ultrasound radiation force
Resonance frequency and mode shapes
Higher order modes
Selective excitation by phase shift
Conclusions

3. Ultrasound Stimulated Radiation Force Excitation
Vibro-Acoustography Developed in 1998 at Mayo Clinic Ultrasound Research Lab by Fatemi & Greenleaf
Difference frequency between two ultrasound sources causes excitation of object.
Technique has been used for imaging in water and tissue, and mode excitation of objects in air
Ultrasound Stimulated Radiation Force Excitation

4. Modal Excitation Using Ultrasound Radiation Force
Originally demonstrated in 2004 for Pipe Organ Reeds
Have since used for ever smaller devices and higher frequencies
Organ Reed Hard Drive MEMS Coupled AFM
Suspension Gyroscope Microcantilevers Microcantilever
12 mm x 5 mm mm x 2 mm 3mm x 0.8mm mm x mm x 0.02 mm
100 Hz – 10 kHz Up to 30 kHz kHz Up to 80 kHz Up to 200 kHz
Organ Reed
12 mm x 5 mm
100 Hz – 10 kHz
The same ultrasound transducer has been used to excite from Hz up to 200 kHz!

5. Acoustic Radiation Force Excitation
Consider two sound waves impinging on an object
P(r,t)=P1(r) sin(2πf1t + φ1) + P2(r) sin(2πf2t + φ2)
The dynamic acoustic radiation force on an object is proportional to the square of the pressure
FAcoustic = [ P(r,t)2 / ρc2 ] dr(r) dS P.J. Westervelt, JASA, 23, 312 (1951) G. Silva et al, Phys. Rev. E, 71, (2005)
This radiation force will have component at the difference frequency Δf
FDifference = F0 sin [2π Δf t + (φ2 - φ1) ]
Δf =f2 - f1

6. Ultrasound Radiation Force Excitation
Suppressed carrier AM signal
Centered at, for example, 450 kHz

7. Radiation Force Excitation: Advantages
Non-Contact
Does not have driver resonances and does not excite fixture modes
Wide Bandwidth
Using our 500 kHz transducer, can excite structures with resonances from 100 Hz to over 200 kHz
Focused
The transducer used has focal spot of about 2 mm diameter
Capability for selective excitation using multiple transducers

8. Generation of Excitation Signal
Can also generate a chirp waveform
For example, fMod=4.5 kHz to 5.5 kHz in 0.6 seconds
Leads to excitation frequency chirp from 9 kHz to 11 kHz

9. Radiation Force Excitation: Experimental Setup

10. Radiation Force Excitation: Experimental Setup

11. Microcantilever Pair using Ultrasound Radiation Force
Gold Microcantilevers (500 micron by 100 micron, 250 micron separation)
Ultrasound 450 kHz central frequency
Modulation chirp frequency of 4950 Hz to 5150 Hz
Difference frequency of 9900 Hz to Hz
Measure motion using laser Doppler vibrometer
Comparison with scanning probe microsystem (Blue Triangles)

12. Microcantilever Pair using Ultrasound Radiation Force
Measure amplitude & phase at multiple points to determine operating deflection shapes

13. 2nd Transverse Modes of Au pair (about 60 kHz)

14. First Torsional Mode of Au Pair (about 87 kHz)

15. Excitation of AFM Cantilever
Tipless Silicon AFM Microcantilever (300 micron by 20 micron)
Ultrasound 450 kHz central frequency
Modulation chirp frequency of 4500 Hz to 6750 Hz
Difference frequency of 9000 Hz to Hz
Smallest structure excited using ultrasound radiation force in air

16. Excitation using Ultrasound Radiation Force
Silicon AFM Cantilever (300 micron by 20 micron)
Vibrometer response using Piezo base excitation (Cyan Triangles)
Nearly identical frequency response obtained using Ultrasound Excitation

17. Excitation using Ultrasound Radiation Force
Silicon AFM Cantilever (300 micron by 20 micron)
Repeat for 2nd bending mode (72 kHz)
Ultrasound data taken at single frequencies using lock-in amplifier

18. Excitation using Ultrasound Radiation Force
Repeat for 3rd bending mode (204 kHz)
Highest frequency excited using ultrasound radiation force in air
Note: Additional peaks in base excitation spectra due to fixture/piezo resonances

19. Selective Excitation using Phase-Shifted Pair of Transducers
Instead of using a single transducer, use a pair of ultrasound transducers to allow selective excitation
If radiation force from both transducers are in phase, selectively excites symmetric mode while suppressing antisymmetric mode
If radiation force is out of phase, selectively excites antisymmetric mode while suppressing symmetric mode
Previously demonstrated for selectively exciting transverse and torsional modes of cantilevers, and hard drive suspensions

20. Phase-shifted selective excitation: Detailed Description
Two 40 kHz transducers, each with dual sideband suppressed carrier AM waveform
Modulation frequency swept from Hz
Difference frequency Δf leads to excitation from 9900 Hz – kHz
Modulation phase difference of 90 degrees leads to 180 degree phase difference in radiation force

21. Photos of apparatus used for phase-shift excitation

22. Phase Shifted Selective Excitation
Adjust amplitudes of two 40 kHz transducers to give roughly equal response

23. Phase Shifted Selective Excitation
Adjust amplitudes of two 40 kHz transducers to give roughly equal response
When they are driven together in phase, strong enhancement of the symmetric peak, while some cancellation of the antisymmetric peak

24. Phase Shifted Selective Excitation
Adjust amplitudes of two 40 kHz transducers to give roughly equal response
When they are driven out of phase, strong suppression of the the symmetric peak, while some enhancement of the antisymmetric peak

25. Phase Shifted Selective Excitation
Driving in-phase excites symmetric but suppresses antisymmetric mode
Driving out-of-phase excites antisymmetric while suppressing symmetric mode
Can differentiate two overlapping modes.
This capability may be very valuable for coupled cantilevers.
High mass sensitivity requires weak coupling, but this implies that the symmetric and antisymmetric would nearly overlap
By using ultrasound excitation, the symmetric mode can be highly suppressed

26. Conclusions
Ultrasound excitation allows non-contact excitation of microcantilever
Excitation demonstrated up to 200 kHz
Selective excitation of symmetric versus antisymmetric modes
Using phase-shifted pair of transducers
Allows overlapping modes to be individually excited
May increase sensitivity of mass sensing
Future possibilities:
Other MEMS devices
New transducers should allow about 300 kHz or more of bandwidth
Excitation of microcantilevers in water
In-plane excitation

27. Mostafa Fatemi and James Greenleaf
Acknowledgements
Brad Abell, Dan Mellema,
Physics Department, Gustavus Adolphus College
Mostafa Fatemi and James Greenleaf
Ultrasound Research Laboratory, Mayo Clinic and Foundation
This material is based upon work supported by the National Science Foundation under Grant No
Thank You

28. Mass Sensing using Microcantilevers
General Goal: Detect small masses using change in vibrational state of a microcantilever
For example, a microcantilever can be coated with a chemical that will bond with the target material
Adding mass ∆m to cantilever (m0) will lower resonance frequency f0

29. Coupled Microcantilevers
Instead of a single microcantilever, pair of coupled microcantilevers
Coupling is through the overhang
As with all coupled oscillators, has symmetric and antisymmetric eigenstates
Sensitivity requires measuring amplitudes of both peaks
Use Ultrasound Radiation Force Excitation for this Device

30. Ultrasound Excitation of Nickel Cantilever Pair
Symmetric: kHz
Antisymmetric: kHz
Symmetric: kHz
Antisymmetric: kHz

31. Coupled Microcantilevers
Using coupled cantilevers may increase ability for mass detection
Recall, shift of frequencies due to mass is
Change in amplitude of eigenstates is
Weak coupling (κ<<1) implies very large change in amplitude of eigenstate
Problem is that symmetric and antisymmetric states nearly overlap
Selective excitation using ultrasound excitation may be advantageous