Faraday Discuss., 1997, 107, 1È13
Introductory Lecture
Acoustic interactions
from FaradayÏs crispations to MEMS
Richard M. White
Department of Electrical Engineering and Computer Sciences, and the Berkeley Sensor and
Actuator Center, University of California, Berkeley, CA, USA, 94720
In an 1831 paper, Michael Faraday described observations of the interaction of a vibrating solid with a liquid supported by the solid. The motions
induced on the surface of the liquid, which he termed crispations, resulted
from the creation of capillary waves, which are still a subject of research.
The contributions to the present Faraday Discussion concern chieÑy the use
of piezoelectric crystals to study the properties of Ðlms and of liquids at
liquid/solid interfaces. In this Introductory Lecture, the characteristics of
piezoelectric acoustic devices used for sensing are reviewed and contrasted.
Recent developments in the fabrication of micromechanical structures to
make microelectromechanical systems (MEMS) are reviewed. Some applications of this technology to make ultrasonic piezoelectric devices that sense
and actuate liquids and gases are described.
1 From Faraday to the present
The topic of acoustic interactions is quite appropriately the subject of a Faraday Discussion, since Faraday himself contributed to this Ðeld.
Faraday published in 1831 a long paper on the interactions of vibrating solid surfaces with particles and liquids.1 Faraday described many ingenious experiments performed on metal, glass and wooden plates that supported piles of granular media such
as sand, or which were in contact with water or other liquids such as “ white of egg, ink
and milk Ï. The solid members were excited by rubbing, bowing or being struck. In the
articleÏs long appendix, titled “ On the Forms and States assumed by Fluids in contact
with vibrating elastic surfaces Ï, Faraday wrote that “ Crispations appear on the surface of
the water . . . The crispation presents the appearance of small concoidal elevations . . . Ï.
In other words, the surface has been “ curled Ï as a result of the acoustic interaction.
Faraday studied the relationship of the frequency of the vibrations of the liquid
surface to that of the underlying solid member. In order to be able to make these measurements, he had to lower the frequencies of the vibrations to values low enough so
that he could count them. This entailed making his apparatus larger and larger, and he
ultimately worked with a board “ eighteen feet long . . . , the layer of water being now
three fourths of an inch in depth and twenty-eight inches by twenty inches in extent Ï.
A key Ðnding was that “ Each heap [of liquid] . . . recurs or is re-formed in two
complete vibrations of the sustaining surface ; but as there are two sets of heaps, a set
occurs for each vibration. Ï In other words, the frequency of the disturbance at a point on
the liquid surface is one-half that of the supporting vibrating surface. As the support
rises, alternate peaks appear on the liquid surface ; as the support falls, the liquid
forming those peaks Ñows sideways, so that on the next upward motion of the support,
1
2
Introductory L ecture
peaks appear on the liquid surface between the original peaks. Any peak rises only once
for every two upward motions of the support.
This conclusion was the subject of discussion for the next Ðfty years, until, in 1883,
Lord Rayleigh published a paper titled, “ On the Crispations of Fluid Resting Upon a
Vibrating Support Ï that settled the matter.2 Incidentally, Rayleigh noted in his initial
paragraph that ““ Similar crispations are observed on the surface of liquid in a large
wine-glass . . . which is caused to vibrate in the usual manner by carrying the moistened
Ðnger round the circumference. ÏÏ, thus opening this experimental Ðeld to us all. By the
time Rayleigh studied these disturbances, the experimental arts had advanced substantially, so he was able to excite the vibrating members electromagnetically and measure
the frequency with a motor-driven apertured disk that rotated at a known rate and
through which he could observe the motion of the liquid surface and the underlying
support. From such observations made with liquid on a bar vibrating at 31 Hz, Rayleigh was able to determine that “ there are two complete vibrations of the support for
each complete vibration of the water, in accordance with FaradayÏs original statement. Ï
Rayleigh proceeded to analyze the vibrations and identify the role of surface tension,
which governs the velocity of wave propagation for small wavelengths where the e†ect
of gravity is negligible. Incidentally, such capillary waves are still the subject of research.
It is interesting to compare FaradayÏs 1831 paper with scientiÐc articles today. His
paper is quite long by modern standards, and it is enjoyable to read. Faraday describes
his ingenious experiments, which he illustrates with small drawings, but he uses no equations. This is probably due to FaradayÏs lack of mathematical training.3 TodayÏs journal
articles are much shorter, often less readable, and they typically employ mathematical
techniques ranging from classical analysis to numerical modelling and simulations.
Experimental observations are made using sophisticated electronic, mechanical, optical,
chemical and biochemical techniques, with instruments that are often controlled by a
computer. We now take for granted our ability to “ see Ï individual atoms and to design
molecules. These substantial changes are reÑected in the papers that follow in the
present Discussion. But for experimentalists, some problems remain from the old days,
such as how to glue one part onto another to form a room temperature bond that
survives in a humid atmosphere.
2 Acoustics
The range of frequencies involved in acoustical phenomena is today enormous, as Fig. 1
shows. Useful frequencies range from roughly 0.01 Hz for terrestrial phenomena to
several terahertz, the highest frequency at which coherent elastic waves have been generated piezoelectrically, by means of light incident upon a piezoelectric crystal. The frequencies used in the papers that follow range from a few to hundreds of MHz for the
acoustic sensors indicated in boxes in Fig. 1, and up to 1 GHz for the acoustic microscope.
The choice of materials that can be used for acoustic transduction is now large. In
the early 1900s, the only practical piezoelectric material was natural quartz that had
been cut and polished. Today, properly oriented crystalline quartz is still important, but
many other piezoelectrics are also used, such as lithium niobate and tantalate, zinc
oxide, aluminium nitride, lead-zirconate-titanate and gallium arsenide.
Some of these piezoelectrics are cut from a larger crystal, an example being the
familiar quartz crystal shear-mode crystal employed in the quartz crystal microbalance
(QCM). Films of these piezoelectrics are also important. They are produced by a variety
of means : sputtering (from the pure element in a reactive chemical gas or from a compound source), pulsed laser deposition (ablation from a compound target upon which
intense laser pulses are incident), chemical vapor deposition (CVD), spun-on polymeric
piezoelectrics, and the solÈgel technique (spin-on deposition of chemical precursors in an
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Fig. 1 Acoustic (elastic) wave spectrum. The frequencies of waves that have been excited or
detected range over roughly fourteen orders of magnitude. The chief acoustic devices used for
studying acoustic interactions are boxed.
organic binder that is later vaporized). Magnetic, electrostatic and thermal acoustic excitation means are also available.
Fig. 2 shows the conÐgurations, electrodes and particle motions of the acoustic
sensors that have been used most frequently to study acoustic interactions with thin
Ðlms and interfaces.5 In Fig. 2 the arrows indicate the particle motion in the solid, and
the heavy black regions represent the conducting electrodes used to excite the devices.
Fig. 2 Structures and properties of selected acoustic devices that may be used to study interactions with thin Ðlms and liquids. See text for details. (Reprinted with permission from ref. 4 (
1993 American Chemical Society.)
4
Introductory L ecture
Fig. 3 Pictorial representations of elastic waves in solids. Motions of groups of atoms are depicted
in these cross-sectional views of plane elastic waves propagating to the right. Vertical and horizontal displacements are exaggerated for clarity. Typical wave speeds, v , are shown below each
p
sketch.
The familiar QCM, used in the majority of the papers that follow, is identiÐed here
as the thickness-shear mode device (TSM), emphasizing the mode rather than the crystalline material or its gravimetric capability. The particle motion at the boundary of the
piezoelectric is parallel to the plane face of the crystal ; coupling into an adjacent liquid
occurs because of the zero-slip condition : the molecules of liquid must follow the motion
of the solid. (Detailed consideration of this boundary condition appears in several
papers in this Discussion.) The acoustic energy is distributed throughout the thicknessshear crystal, which is usually operated at resonance and so is an odd integral number of
half-wavelengths thick. Because of the mechanical fragility of very thin crystals, the
operating frequencies of TSM devices are typically no higher than tens of MHz. As a
result, the acoustic energy in the solid is contained in a relatively thick region (the
crystal thickness is 100 lm or more). Since the gravimetric response decreases as the
volume-to-surface ratio of a device increases, the gravimetric sensitivity, S , of the TSM
m
is low in comparison with that of the other devices illustrated.6 The gravimetric
sensitivity is deÐned as S \ (*f/f )/*m, where f is the resonant frequency of the device and *f
m frequency produced when a mass per unit area *m is added to the
is the shift of resonant
surface of the device.
In the surface acoustic wave device (SAW), the acoustic energy in the solid is concentrated within a region near the free surface whose thickness is a small fraction of a
wavelength. SAW operation at hundreds of MHz is possible and the attainable gravimetric sensitivity can be an order of magnitude greater than that of the typical TSM
device. Since the particle motion of the simple SAW has components that are both
normal and parallel to the free surface, and since the SAW phase velocity greatly
exceeds the speed of sound in most liquids, acoustic energy is radiated into an adjacent
liquid, limiting the usefulness of the SAW for studying acoustic interactions with liquids.
An alternative SAW device, the surface transverse wave device,7 employs a contoured or
coated free surface and an oriented crystalline substrate that permits generation of a
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surface-bound acoustic wave that has purely transverse particle motion, permitting its
use in studies of acoustic interactions with liquids.
The third device in Fig. 2, the Ñexural plate wave (FPW) device, is made by micromachining processes discussed below. A piezoelectric Ðlm located on one side of a thin
supporting membrane is excited by interdigitated conducting electrodes, as with SAW
excitation. Because of its location to one side of the neutral plane of the composite
membrane, the electrically induced deformation of the piezoelectric excites a propagating wave that involves Ñexure of the membrane, as shown by the cross section in the
FPW view in Fig. 2. The gravimetric sensitivity of the FPW device may be quite large.
Because the phase velocity for the FPW decreases as the ratio of membrane thickness to
wavelength decreases, the FPW typically operates in the low MHz range. In practical
devices, the FPW phase velocity may be as low as a few hundred m s~1 (see Fig. 3), a
value smaller than the speed of sound in water, and even in air at STP. Hence, even
though the FPW membrane moves both perpendicularly and parallel to its surface, as
does the surface of a SAW device, the FPW does not radiate a propagating wave into an
adjacent Ñuid. Instead, an evanescent acoustic disturbance is generated in the Ñuid.
The fourth structure shown in Fig. 2 is the acoustic plate mode (APM) device. Its
particle motions are parallel to the top surface, resulting from the orientation of that
surface relative to the crystalline axes of the single-crystal piezoelectric substrate. The
APM device is rugged mechanically, as is the SAW, but its gravimetric sensitivity is
relatively low because the acoustic energy is distributed throughout the relatively thick
crystal.
3 Microfabrication and MEMS
Starting in the 1980s, technologists have learned how to fabricate small mechanical
structures using techniques, adaptations and augmentations of the photolithographic
processes developed for making integrated circuits.8,9 Culminating in the active Ðeld
called MEMS, for microelectromechanical systems, these developments are relevant to
the present Discussion for two reasons : (1) one can use micromachining to make acoustic sources that can be used in research studies of acoustic interactions and (2) it is likely
that some of the acoustic interactions being studied may Ðnd their way into commercial
characterization systems made by the MEMS approach. Here, brieÑy, are some of the
present MEMS fabrication capabilities.
Fig. 4 shows the two chief approaches to micromachining. In bulk micromachining,
one fabricates structures via thin-Ðlm deposition and photolithography atop a singlecrystal silicon wafer. Ultimately, by etching through an aperture in a protectively coated
region on the bottom of the wafer, one removes the majority of the underlying silicon.
As an example, this process is used to make the FPW device of Fig. 2 ; etching of the
silicon leaves a membrane that must be thin in order to support low-velocity plate
waves.
The other approach is surface micromachining. Here one builds the desired structures on an easily etched sacriÐcial layer that is dissolved after patterning of the structures. This is the technique used to make movable structures such as the rotor of a
micromotor or structures that are suspended only a few microns above a substrate (Fig.
5).
Wet chemical etching used in such fabrication is classiÐed as either isotropic (etch
rate independent of crystalline plane) or anisotropic (orientation dependent). Wet
etchants whose etch rate is strongly a†ected by boron doping of crystalline silicon are
sometimes also used to produce desired features ; an example is shown later in Section 4
(Fig. 12) where this technique was used to fabricate the 45¡ reÑectors in the corners of
the diamond-shaped FPW device. Dry (plasma) etching is often preferred over wet
etching as it avoids the stiction (sticking of the structures to the underlying surface)
6
Introductory L ecture
Fig. 4 Bulk and surface micromachining processes.
associated with the removal of Ñexible microstructures from a liquid etch or rinse bath.
Techniques for dealing with stiction include supercritical carbon dioxide drying10 and
the application of special organic surface coatings.11
Many MEMS devices employ polycrystalline silicon (polysilicon) Ðlms that are only
a few lm thick and many lm long. For sti†er members, high-aspect-ratio structures
have been made by electroplating into cavities produced photolithographically in a very
thick photoresist (the LIGA process9) or by forming polysilicon structures produced by
chemical vapor deposition in deeply etched cavities made in reusable crystalline silicon
molds (the Hexsil process12).
Newer micromechanical structures of note include the following : (1) hinged structures made by surface micromachining.13 A planar structure formed on a sacriÐcial layer
is provided with a staple-like polysilicon part that forms a hinge after removal of the
sacriÐcial layer. When released, such structures can be rotated upwards and locked into
position at right angles to the supporting substrate. Members having lengths of a mm or
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Fig. 5 Scanning electron micrographs of surface micromachined polysilicon structures suspended
one to two microns above underlying silicon substrate. Top : spring. Bottom : interleaved electrodes of a torsional oscillator driven electrostatically. (Photographs courtesy of Berkeley Sensor
and Actuator Centre.)
more and a thickness of only a few lm have been made for use as mirrors and, when
properly interconnected, as structural members. (2) Electronic or mechanical parts made
on separate wafers by many di†erent processes combined to make rugged hybrid
devices. For example, one can attach Ñuid-tight caps and channels over micromechanical parts, and can locate and bond IIIÈV laser dies onto chips containing micromechanical devices such as movable mirrors. (3) Inexpensive polymeric MEMS devices
made using reusable etched silicon molds. Precise replication of structures on the lm
scale is possible.9
4 Flexural plate wave devices
The FPW devices described in Section 2 can be used for sensing and as actuators for
liquids and gases.
8
Introductory L ecture
4.1 Sensing
FPW devices have shown the ability to measure liquid or gas density, liquid viscosity,
the concentration of chemical vapors absorbed in a polymer Ðlm on the membrane, and
the deposition of proteins from solution.5 Recently, two additional gravimetric uses of
these devices have been demonstrated.
In the Ðrst, the FPW was used to follow the growth of the bacterium Pseudomonas
putida, which has been proposed for the in situ remediation of toxic organic waste
deposits in the ground. A suspension of non-adherent bacteria was made and placed in a
gas-tight chamber containing an FPW device (shown in Fig. 6), connected in a delay-line
oscillator circuit. A bolus of toluene was then injected into the chamber. After a one
hour period of adjustment (the so-called lag phase for the bacteria), the frequency of the
FPW oscillator steadily decreased as the bacteria Ñourished. This was expected, since
fractional oscillator frequency changes, *f/f, are equal to the fractional phase velocity
changes, *v/v, caused by increase of the bacterial concentration in the chamber. Changes
ceased at the time expected for exhaustion of the toluene. The advantage of using this
acoustic interaction is that one obtains real-time information about the growth without
having to remove samples for measurement in a microscope.
The second gravimetric interaction observed was the shift of phase velocity in an
FPW device due to the reaction of antibodies in an immunoassay for an antigen present
Fig. 6 Typical Ñexural wave device. Thickness of the surrounding silicon frame, nominally 500
lm, is reduced here for clarity. P, the periodicity of the interdigital transducers (IDT), which
equals the wavelength, is typically 100 lm. (Reprinted with permission from ref. 14.)
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in breast cancer patients.15 In this case, a novel mass ampliÐcation step was used to
increase the detection sensitivity, as we shall now describe.
These experiments were carried out in an enclosed Ñow cell like that shown in Fig. 7.
A sandwich immunoassay developed at the Cancer Research Fund of Contra Costa was
employed (Fig. 8). First, the membrane surface was coated with a fusion protein, NP5.
Next, a solution containing a mixture of serum with a monoclonal antibody, Mc5, was
added in an incubation step. Mc5 can bind either to the NP5 fusion protein on the
surface or to the antigen BrE-Ag in solution. After this the cell was Ñushed (wash step).
If the breast cancer antigen BrE-Ag was present in the serum, it would compete with
the NP5 for binding to the Mc5 and leave the surface less densely covered with antibody
than in the case where no antigen is present. (The wash step would carry away any Mc5
that was bound to the antigen.) The next step was to present a second antibody (goat
anti-mouse IgG) that could react with the NP5-bound Mc5 and which was conjugated
to 10 nm gold spheres. This produced mass loading of the membrane that was proportional to the amount of NP5-bound Mc5 present. The mass loading will be greater
when the antigen is not present, as there is no competition with the NP5 for binding of
Mc5.
In order to increase sensitivity, a solution was added that plated silver onto the gold
spheres to which the IgG was conjugated. The resultant silver plating increased the
sphere diameters by about 15 times and produced a clear gravimetric indication of the
presence of the antigen (Fig. 9). This test was run with the antigen at disease levels ;
detection at a level at least ten times smaller appears possible.
The advantages of using this acoustic interaction are the avoidance of the need for
radioactive techniques and certiÐcation, and the possibility of being able to detect at
even lower concentrations than are possible with the present radioactive technique.
Fig. 7 Exploded schematic view of a Ñow-cell FPW liquid sensor. (Figure courtesy of Dr. Ben
Costello, Berkeley MicroInstruments, Inc.)
10
Introductory L ecture
Fig. 8 Schematic summary of breast epithelial antigen competitive assay performed on an FPW
device. The breast cancer antigen is denoted BrE-Ag. (Illustration courtesy of Amy Wang.)
4.2 Actuation
Owing to its small volume-to-surface ratio and its generation of an evanescent disturbance in a Ñuid to which it is coupled, the FPW amplitude can be large and the wave
can produce signiÐcant non-linear acoustic e†ects in Ñuids. In particular, the phenome-
Fig. 9 Results of gravimetric detection in competitive assay for breast epithelial antigen. Top
curve : shift of FPW oscillator frequency when antigen is present at concentration 12 lg ml~1.
Middle curve : larger oscillator frequency shift observed in absence of antigen. Bottom curve : net
frequency shift (magnitude of the di†erence between the larger shift observed in the absence of
antigen and that observed when antigen is present), showing clear evidence of the presence of the
antigen. (Illustration courtesy of Amy Wang).
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non of acoustic streaming can induce steady Ñow in either a liquid or gas adjacent to the
membrane.5 Two manifestations of this streaming will be described brieÑy.
Fig. 10 shows how one may produce and observe Ñuid motion generated by acoustic
streaming. Water seeded with 2 lm diameter polystyrene marker spheres is placed on an
FPW membrane. When the FPW transducer is driven (for example, at 3 MHz with 10 V
amplitude), the spheres observed with an optical microscope move in the direction of
wave propagation. The steady velocity of the liquid motion is proportional to the square
of the wave amplitude, which is measured by laser di†raction.5 In an 18 lm high
channel closed at the ends [Fig. 10(a)], recirculation was observed (Fig. 11) in good
agreement with analysis.16 Similarly made observations on liquid behavior in a
diamond-shaped re-entrant closed chamber that had a unidirectional transducer
Fig. 10 Set-up for measuring velocity of liquid Ñow produced by acoustic streaming. (a) Crosssection view of Ñow cell having an FPW transducer on the bottom membrane and glass slide to
cover top of well. (b) Cell mounted on stage of microscope with video camera and VCR for
recording images (left), and sketch of liquid containing marker spheres (right). (Reproduced with
kind permission from ref. 16. ( 1995, IEEE.)
Fig. 11 Flow velocity vs. height above the membrane showing good agreement of measured (data
points) and calculated (solid curve) values for the Ñow cell shown in Fig. 10. Below 170 lm, the
liquid Ñows to the right in the direction of wave propagation ; above that height it Ñows left due to
recirculation in the closed cell. (Reproduced with kind permission from ref. 16. ( 1995, IEEE.)
12
Introductory L ecture
beneath the membrane showed that marker spheres that were initially randomly distributed were forced into discrete channels, evidently as a result of wave interference at the
45¡ reÑecting boundaries (Fig. 12). This channelling may be applicable to performing
Ñow cytometry on a small chip.
The agitation near the membrane caused by the FPW action may have applications
other than transport along the membrane. We noted in an earlier publication17 that the
stirring produced near the membrane of an FPW device that formed part of an electrochemical cell increased current Ñow by aiding di†usion in bringing reactants to the
electrode deposited on the membrane. In more recent work, we have found18 that a
biochemical reaction at a surface can be stimulated or suppressed by the FPW.
Fig. 13 shows frequency shifts measured in the immunoassay illustrated in Fig. 8
when the incubation of Mc5 on the membrane was performed while the FPW transducer was being excited at di†erent amplitudes. With no ultrasonic excitation, incu-
Fig. 12 Top view (right) and magniÐed corner view (left) of diamond-shaped re-entrant Ñow cell.
Unidirectional transducers beneath the diamond-shaped membrane produce steady Ñow in the
clockwise direction. Near the 45¡ reÑectors at top and bottom, the 2 lm diameter polystyrene
marker spheres are forced into discrete channels 70 lm apart ; this distance equals the wavelength/
21@2. (Reproduced with kind permission from ref. 16 ( 1995, IEEE.)
Fig. 13 FPW oscillator frequency shifts vs. wave amplitude as antibody is allowed to attach to the
membrane while liquid is stirred by the Ñexural plate wave. With an intermediate level of excitation (20 nm amplitude) more antibody binds than when agitation is absent. For 40 nm amplitude,
virtually no antibody binds. (Unpublished data provided by Amy Wang.).
R. M. W hite
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bation produced some surface coverage. With a 20 nm wave amplitude, the amount
deposited on the NP5-coated surface increased. At twice the wave amplitude, which
would result in four times as much Ñuid motion due to acoustic streaming, binding was
almost entirely suppressed. It appears possible to use this e†ect to enhance or suppress
the attachment of molecules at surfaces.
5 Concluding remarks
The study of acoustic interactions at interfaces has a long history. The papers that
follow show what a wealth of information can be gleaned from such research. One may
hope that the growth of micromachining will contribute both tools for research in this
Ðeld and to realizing devices that exploit these interactions for real-world applications.
References
1 M. Faraday, Philos. T rans. R. Soc. (L ondon), 1831, 299.
2 Lord Rayleigh, Philos. Mag., 1883, 16, 50.
3 C. C. Gillispie, Dictionary of ScientiÐc Biography, Charles ScribnerÏs Sons, New York, 1991, pp. 527È
540.
4 J. W. Grate, S. J. Martin and R. M. White, Anal. Chem. A, 1993, 65, 940
5 D. S. Ballantine, R. M. White, S. J. Martin, A. J. Rico, E. T. Zellers, G. C. Frye and H. Wohltjen,
Acoustic W ave Sensors : T heory, Design and Physico-Chemical Applications, Academic Press, New York,
1997.
6 S. W. Wenzel and R. M. White, Appl. Phys. L ett., 1989, 54, 1976.
7 R. L. Baer, B. J. Costello, S. W. Wenzel and R. M. White, Proc IEEE Ultrason. Symp., 1991, 293.
8 S. M. Sze, Semiconductor Sensors, John Wiley & Sons, New York, 1994.
9 M. Madou, Fundamentals of Microfabrication, CRC Press, Boca Raton, FL, 1997.
10 G. T. Mulhern, D. S. Soane and R. T. Howe, T echnical Digest, 7th International Conference on SolidState Sensors and Actuators, T ransducer Ï93, Yokohama, Japan, June 7È10, 1993, p. 296.
11 M. R. Houston, R. Maboudian and R. T. Howe, T echnical Digest, 1996 Solid-State Sensor and Actuator
W orkshop, Hilton Head, SC, June 1996, p. 42.
12 C. G. Keller and R. T. Howe, L ate News Digest, 1996 Solid-State Sensor and Actuator W orkshop, Hilton
Head, SC, June 1996, p. 31.
13 K. S. J. Pister, M. Judy, S. Burgett and S. Fearing, Sens. Actuators, 1992, 33(3), 249.
14 S. W. Wenzel, Doctoral dissertation, EECS, Dept. University of California, Berkeley, CA, 1993.
15 A. W. Wang, R. Kiwan, R. M. White and R. Ceriani, 9th International Conference on Solid-State Sensors
and Actuators, Chicago, IL, June 16È19, 1997, p. 191.
16 C. E. Bradley and R. M. White, Proc. IEEE Ultrason. Symp., 1994, 593 ; C. E. Bradley, J. M. Bustillo
and R. M. White, Proc. IEEE Ultrason. Symp., 1995, 505.
17 T. R. Tsao, R. M. Moroney, B. A. Martin and R. M. White, Proc. IEEE Ultrason. Symp., 1991, 181.
18 A. W. Wang, unpublished data.
Paper 7/07747E ; Received 27th October, 1997