Thomas M. Huber, Brad Abell, Sam Barthell, Dan Mellema, Eric Ofstad Physics Department, Gustavus Adolphus College Arvin

1. Excitation of Vibrational Eigenstates of Coupled Microcantilevers Using Ultrasound Radiation ForceASME 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. Vibro-AcoustographyDeveloped 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, andmode 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 10 mm x 2 mm 3mm x 0.8mm 0.5 mm x 0.1 0.3 mm x 0.02 mm 100 Hz – 10 kHz Up to 30 kHz 18 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 100 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, 056617 (2005) • This radiation force will have component at the difference frequencyΔf • FDifference = F0sin [2π Δft + (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. 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 10300 Hz • Measure motion using laser Doppler vibrometer • Comparison with scanning probe microsystem (Blue Triangles)

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

12. 2nd Transverse Modes of Au pair (about 60 kHz)

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

14. 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 13500 Hz • Smallest structure excited using ultrasound radiation force in air

15. 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

16. 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

17. 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

18. 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

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

20. 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

21. 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

22. 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

23. 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

24. 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. 0509993 Thank You