Abstract:A model for tunable thin film bulk acoustic resonators (TFBARs) based on ferroelectric films is proposed. The model is based on electromechanical equations taking into account piezoelectric effect and electrostriction effect induced by the dc electric field. The dc field induced shift of the resonant frequency is explained by the high-order nonlinear effects in the ferroelectric material. The main contribution to the tunability of the resonant frequency under dc electric field can be attributed to electrostric… Show more
“…So, both terms in (14) are important and one should not neglect the electrostrictive term as that was previously done in Ref. 17 where the electromechanical properties of tunable FBARs were treated based on the "D-expansion" of free energy. In Fig.…”
Section: Resultsmentioning
confidence: 98%
“…We include in our treatment a nonlinear electrostrictive coefficient m which was previously considered as a higherorder correction and customarily neglected, 18 but which actually plays an important role in the antiresonance frequency tuning of tunable FBARs. [15][16][17] Let us consider a tunable FBAR operating in the TE mode based on a [001]-oriented BST thin ferroelectric film in the paraelectric phase. DC field induced tuneabilities of paraelectric phase BST films are demonstrated experimentally for x 0:5; 19 therefore, we limit our consideration to these BST compositions.…”
Section: Description Of Tunable Fbars Tuningmentioning
confidence: 99%
“…A simple theory of tunable FBARs based on the DCbias-induced piezoelectric effect was developed recently by Noeth et al 15,16 and by Vendik et al 17 where it was shown that, for antiresonance frequency tuning, it is important to take into account the high-order electrostrictive coefficient m 111 . In these papers as m 111 values were unknown for BST, they were taken from order-of-magnitude estimations.…”
Being important for the antiresonance frequency tuning of tunable thin Film Bulk Acoustic wave Resonators (FBARs), the non-linear electrostrictive coefficient was for the first time calculated for BaTiO3 and SrTiO3 using ab initio methods. Further, taking into account the small difference of obtained values for BaTiO3 and SrTiO3 these results were linearly interpolated to the BaxSr1−xTiO3 (BST) compositions. The obtained values are consistent with previously made order-of-magnitude estimates. Using parameters obtained with first principles calculations, we simulated the resonance parameters of BST based tunable FBARs. Resulting antiresonance tuning was smaller than expected due to the compensation of two competing terms conditioned by linear and non-linear electrostrictions. Our calculations confirm that, for tunable FBAR modeling, it is important to use a polarization-based Landau free energy expansion taking into account both non-linear electrostriction and background permittivity.
“…So, both terms in (14) are important and one should not neglect the electrostrictive term as that was previously done in Ref. 17 where the electromechanical properties of tunable FBARs were treated based on the "D-expansion" of free energy. In Fig.…”
Section: Resultsmentioning
confidence: 98%
“…We include in our treatment a nonlinear electrostrictive coefficient m which was previously considered as a higherorder correction and customarily neglected, 18 but which actually plays an important role in the antiresonance frequency tuning of tunable FBARs. [15][16][17] Let us consider a tunable FBAR operating in the TE mode based on a [001]-oriented BST thin ferroelectric film in the paraelectric phase. DC field induced tuneabilities of paraelectric phase BST films are demonstrated experimentally for x 0:5; 19 therefore, we limit our consideration to these BST compositions.…”
Section: Description Of Tunable Fbars Tuningmentioning
confidence: 99%
“…A simple theory of tunable FBARs based on the DCbias-induced piezoelectric effect was developed recently by Noeth et al 15,16 and by Vendik et al 17 where it was shown that, for antiresonance frequency tuning, it is important to take into account the high-order electrostrictive coefficient m 111 . In these papers as m 111 values were unknown for BST, they were taken from order-of-magnitude estimations.…”
Being important for the antiresonance frequency tuning of tunable thin Film Bulk Acoustic wave Resonators (FBARs), the non-linear electrostrictive coefficient was for the first time calculated for BaTiO3 and SrTiO3 using ab initio methods. Further, taking into account the small difference of obtained values for BaTiO3 and SrTiO3 these results were linearly interpolated to the BaxSr1−xTiO3 (BST) compositions. The obtained values are consistent with previously made order-of-magnitude estimates. Using parameters obtained with first principles calculations, we simulated the resonance parameters of BST based tunable FBARs. Resulting antiresonance tuning was smaller than expected due to the compensation of two competing terms conditioned by linear and non-linear electrostrictions. Our calculations confirm that, for tunable FBAR modeling, it is important to use a polarization-based Landau free energy expansion taking into account both non-linear electrostriction and background permittivity.
“…TiO -based resonators exhibit bias voltage-dependent resonance frequencies due to dc electric field-dependent permittivity and polarization as well as nonlinear electrostrictive effects [30], [31]. Fig.…”
This paper presents the design and measurement results of intrinsically switchable interdigitated contour mode resonators based on barium titanate (BTO) thin films. The resonators have lithographically defined interdigitated electrodes that determine their resonance frequencies. The BTO thin film exhibits electrostriction, which allows the resonances to be switched on and off. The highest frequency device exhibits series and parallel resonance frequencies of 1.67 and 1.68 GHz and quality factors of 178 and 152, respectively, with the application of a 10-V dc bias. Resonances are turned off by removing the dc bias. This is the first demonstration of an intrinsically switchable interdigitated ferroelectric contour mode resonator.
Index Terms-Ferroelectric devices, interdigital transducers, microelectromechanical systems (MEMS).
“…However, in practical applications, tuning the resonant frequency by 5% is problematic due to the significant variation of the input impedance of the FBAR that inevitably leads to a mismatch of the microwave circuit. However, for a set of applications the use of this phenomena for small (up to (1–2)%) frequency tuning is desirable 9 .Figure 2Schematic of film bulk acoustic wave resonator with one BSTO layer, and displacement profile (η( x )) for first normal acoustic mode ( a ). Frequency dependence of the impedance of the BSTO FBAR at different bias field voltages 7 ( b ), (reproduced from I.…”
Design principles of a new class of microwave thin film bulk acoustic resonators with multiband resonance frequency switching ability are presented. The theory of the excitation of acoustic eigenmodes in multilayer ferroelectric structures is considered, and the principle of selectivity for resonator with an arbitrary number of ferroelectric layers is formulated. A so called “criterion function” is suggested that allows to determine the conditions for effective excitation at one selected resonance mode with suppression of other modes. The proposed theoretical approach is verifiedusing thepreexisting experimental data published elsewhere. Finally, the possible application of the two ferroelectric layers structures for switchable microwave overtone resonators, binary and quadrature phase-shift keying modulators are discussed. These devices could play a pivotal role in the miniaturization of microwave front-end antenna circuits.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
