Page 354 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

334 SURFACE ACOUSTIC WAVES IN SOLIDS

acoustic velocity 4 of 2850 m/s (Auld 1973a). Gizeli and coworkers (1995) utilised PMMA
layers of thickness up to 5.6 |im spun onto Y-cut quartz with IDTs of periodicity of
45 um at the quartz-PMMA interface. A network analyser was used to monitor the
phase of the wave. The maximum thickness reported by Gizeli and coworkers (1995)
(~1.6 um) is considerably less than the estimated optimum thickness of approximately
3 urn of PMMA (Shiokawa and Moriizumi 1988). Kovacs and co-workers (1993) have
utilised sputtered silicon dioxide on ST-cut quartz. Acoustic losses in SiO 2 are low when
compared with polymers such as PMMA. SiO 2 is more resistant to most chemicals and,
when sputtered under optimal conditions, has excellent wear resistance. Because of tech-
nical reasons, it was reported that the maximum thickness of SiO 2 that was utilised was
5.46 urn - considerably less than the optimum value of approximately 6 um (for devices
of wavelength 40 um).
Another criterion for the choice of a suitable waveguiding material would be the
absorption coefficient. It essentially depends on the material structure, which can be poly-
crystalline, crystalline, or amorphous. In polycrystalline materials, when the wavelength
becomes comparable to the grain size because of the phenomenon of Rayleigh scattering
(Rayleigh 1924), the energy absorption increases proportionally to frequency to the fourth
power (Tournois and Lardat 1969). At higher frequencies, it is obvious that the materials
employed will have to be without loss-inducing grain boundaries, that is, either single-
crystalline or amorphous. Amorphous bodies, such as certain glasses and fused silica, will
allow propagation with a limited absorption at frequencies much higher than 100 MHz.

10.6 CONCLUDING REMARKS

In this chapter, the basic equations that describe the propagation of different types of
waves in an elastic solid have been presented and expressions for the displacement of
particles therein 5 have also been obtained. The emphasis has been directed toward the
fundamental differences between the Rayleigh and SH modes and SH of vibration. The SH
and Love wave modes have been examined from the point of view of waveguide structure,
that is, the nature of the overlayer and the substrate. This mathematical discourse should
help readers to understand the nature and application of SAW microsensors and MEMS
devices in other chapters.

REFERENCES

Auld, B. A. (1973a). Acoustic Fields and Waves in Solids /, John Wiley and Sons, New York.
Auld, B. A. (1973b). Acoustic Fields and Waves in Solids //, John Wiley and Sons, New York.
Du, J. et al. (1996). "A study of Love wave acoustic sensors," Sensors and Actuators A, 56,
211-219.
Ewing, W. M., Jardetsky, W. S., and Press, F. (1957). Elastic Waves in Layered Media, McGraw-
Hill, New York.
Gangadharan, S. (1999). Design, development and fabrication of a conformal love wave ice sensor,
MS thesis, Pennsylvania State University, USA.

4
This value is sensitive to the deposition conditions.
5
Some of the material presented here may also be found in Gangadharan (1999).