Excitation of Vibrational Eigenstates of Coupled Microcantilevers Using Ultrasound Radiation

Force

ASME 2nd International Conference on Micro and Nanosystems

Brooklyn, NY August 6, 2008Thomas M. Huber, Brad Abell, Sam Barthell, Dan Mellema,

Eric OfstadPhysics Department, Gustavus Adolphus College

Arvind Raman, Matthew SpletzerDepartment of Mechanical Engineering, Purdue University

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

Ultrasound Stimulated Radiation Force Excitation 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

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

Modal Excitation Using Ultrasound Radiation Force Originally demonstrated in 2004 for Pipe Organ Reeds

Have since used for ever smaller devices and higher frequencies

The same ultrasound transducer has been used to excite from 100 Hz up to 200 kHz!

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 frequency Δf FDifference = F0 sin [2π Δf t + (φ2 - φ1) ]

Δf =f2 - f1

Ultrasound Radiation Force Excitation

Suppressed carrier AM signal

Centered at, for example, 450 kHz

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

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

Radiation Force Excitation: Experimental Setup

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)

Microcantilever Pair using Ultrasound Radiation Force Measure amplitude & phase at

multiple points to determine operating deflection shapes

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

First Torsional Mode of Au Pair (about 87 kHz)

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

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

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

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

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

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

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

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

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

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

Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No. 0509993

Thank You

Brad Abell, Dan Mellema, Physics Department, Gustavus Adolphus College

Mostafa Fatemi and James GreenleafUltrasound Research Laboratory, Mayo Clinic and Foundation