BOOK REVIEWS: Piezoelectricity: An Introduction to the Theory and Applications of Electro-mechanical Phenomena in Crystals

Cady, W. G.; Valasek, Joseph

doi:10.1119/1.2349067

Cited by 151 publications

(231 citation statements)

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“…where ((A-l)tm) is the average value of an element of a 3 x 3 symmetric tensor determined from the elastic constants and the direction cosines of the wave vector [A is Christoffers elasticity matrix -see, for example, Cady (1964)], and q~B is the radius of a sphere of equivalent volume to an extended* Brillouin zone. There are two methods of evaluating ((A-l)l,, ) (see Stevenson, 1983).…”

Section: Analysis and Resultsmentioning

confidence: 99%

Thermal vibrations and bonding in GaAs: an extended-face crystal study

Stevenson¹

1994

Acta Cryst Sect A

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Accurate X-ray integrated-intensity data collected from an extended-face crystal of GaAs are analysed to provide detailed information on the thermal vibrations of atomic species, including cubic anharmonicity, at room temperature. The values obtained for the thermal parameters are BGa = 0.622 (3) A 2, B s = 0.483(5)A 2 and ~GaAs'-" --0.6(1) X 10-18jX -3 (defined in the text). The inclusion of cubic anharmonic thermal vibrations is shown to be highly significant. In order to interpret the data collected for certain low-angle Bragg reflections for which m h + k + l = 4n + 2 (in particular, 200, 222 and 222), it is necessary to consider bonding effects. It is shown that there is a net transfer of electron charge from gallium to arsenic [Q --0.12 (3) e] and that the inclusion of bonding effects in the least-squares analysis is highly significant. The analysis includes allowance for the extremely severe extinction effects present for such a perfect sample (minimum extinction factor 0.286). The refined value of the mean radius of © 1994 International Union of Crystallography Printed in Great Britain -all rights reserved perfect-crystal domains is 4.6 (2)I~m. The final fit, for 153 independent Bragg reflections, is excellent, as indicated by the weighted R factor of 0.683% and the goodness-of-fit parameter of 1.083. The results of the least-squares analysis are compared for the cases of relativistic Hartree-Fock, Thomas-Fermi-Dirac and relativistic Dirac-Slater atomic scattering factors, the former being favoured.

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Section: Analysis and Resultsmentioning

confidence: 99%

Thermal vibrations and bonding in GaAs: an extended-face crystal study

Stevenson¹

1994

Acta Cryst Sect A

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“…In fact, for one-dimensional analysis of the vibrations of a partially electroded plate or ring (Fig. 3a), k t 2 can be found to be [17]:…”

Section: A One Port Resonatorsmentioning

confidence: 99%

One and two port piezoelectric higher order contour-mode MEMS resonators for mechanical signal processing

Piazza¹,

Stephanou²,

Pisano³

2007

Solid-State Electronics

121

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This paper reports on the design, fabrication and testing of novel one and two port piezoelectric higher order contour-mode MEMS resonators that can be employed in RF wireless communications as frequency reference elements or arranged in arrays to form banks of multi-frequency filters. The paper offers a comparison of one and two port resonant devices exhibiting frequencies approximately ranging from 200 to 800 MHz, quality factor of few thousands (1000-2500) and motional resistances ranging from 25 to 1000 Ω. Fundamental advantages and limitations of each solution are discussed. The reported experimental results focus on the response of a higher order one port resonator under different environmental conditions and a new class of two port contour resonators for narrow band filtering applications. Furthermore, an overview of novel frequency synthesis schemes that can be enabled by these contour-mode resonators is briefly presented. Keywords AbstractThis paper reports on the design, fabrication and testing of novel one and two port piezoelectric higher order contour-mode MEMS resonators that can be employed in RF wireless communications as frequency reference elements or arranged in arrays to form banks of multi-frequency filters. The paper offers a comparison of one and two port resonant devices exhibiting frequencies approximately ranging from 200 to 800 MHz, quality factor of few thousands (1,000-2,500) and motional resistances ranging from 25 to 1000 Ω. Fundamental advantages and limitations of each solution are discussed. The reported experimental results focus on the response of a higher order one port resonator under different environmental conditions and a new class of two port contour resonators for narrow band filtering applications. Furthermore, an overview of novel frequency synthesis schemes that can be enabled by these contour-mode resonators is briefly presented.

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“…1 Some of the most ubiquitous among these are electrical oscillators, clocks, and microbalances based on piezoelectric crystals such as quartz. 2,3 Recent development of micromachining techniques has greatly facilitated the realization of various miniaturized piezoelectric devices, including zinc-oxide ͑ZnO͒ beam-structured, 4 disk, 5 and film bulk acoustic resonators ͑FBARs͒, 6 the noteworthy Agilent's commercialized AlN FBARs, 7 AlN contour-mode resonators and filters, 8 and monolithically integrated FBAR-complementary metal oxide semiconductor ͑CMOS͒ filters. 9 All these piezoelectric microelectromechanical systems ͑MEMS͒ have relied on active layers of approximately micron scale thickness that provide strong electromechanical coupling.…”

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Piezoelectric nanoelectromechanical resonators based on aluminum nitride thin films

Karabalin

Matheny

Feng

et al. 2009

Applied Physics Letters

159

119

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We demonstrate piezoelectrically actuated, electrically tunable nanomechanical resonators based on multilayers containing a 100-nm-thin aluminum nitride ͑AlN͒ layer. Efficient piezoelectric actuation of very high frequency fundamental flexural modes up to ϳ80 MHz is demonstrated at room temperature. Thermomechanical fluctuations of AlN cantilevers measured by optical interferometry enable calibration of the transduction responsivity and displacement sensitivities of the resonators. Measurements and analyses show that the 100 nm AlN layer employed has an excellent piezoelectric coefficient, d 31 = 2.4 pm/ V. Doubly clamped AlN beams exhibit significant frequency tuning behavior with applied dc voltage.

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BOOK REVIEWS: Piezoelectricity: An Introduction to the Theory and Applications of Electro-mechanical Phenomena in Crystals

Cited by 151 publications

References 0 publications

Thermal vibrations and bonding in GaAs: an extended-face crystal study

Thermal vibrations and bonding in GaAs: an extended-face crystal study

One and two port piezoelectric higher order contour-mode MEMS resonators for mechanical signal processing

Piezoelectric nanoelectromechanical resonators based on aluminum nitride thin films

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