A theoretical model for the dc bias dependence of induced acoustic resonances in paraelectric materials is presented. The field dependent piezoelectric constitutive equations were derived from the Landau free energy expansion with respect to the ferroelectric part of the polarization P. To derive the field dependent coefficients correctly, we demonstrate that it is important to take both linear and nonlinear electrostriction as well as the background permittivity into account. Two different resonator geometries, corresponding to the thickness excitation (TE) and the lateral field excitation (LFE) modes, are discussed and compared. In the TE mode the resonance frequency is expected to be much stronger dc bias dependent than the antiresonance frequency. In the LFE mode, both resonance and antiresonance frequencies may exhibit comparable dc bias dependences. In this case the antiresonance frequency shows a stronger tuning with increasing dc bias than the resonance frequency. We model the behavior of the field dependent acoustic resonances in BaxSr1−xTiO3 thin films addressing different compositions and orientations of the films. Our theoretical model corroborates the experimental results available in the literature.

Direct current ͑dc͒ bias-induced acoustic resonance phenomena have been observed in micromachined tunable thin-film capacitors based on paraelectric Ba 0.3 Sr 0.7 TiO 3 thin films. Both resonance and antiresonance frequencies are dc bias dependent. The antiresonance frequency is only weakly dc bias dependent and shifts slightly down with increasing dc bias. The resonance frequency shows a much stronger dependence on the applied dc bias than the antiresonance frequency, and also shifts down to lower frequencies with increasing bias. The resonance frequency shifted by 2.0% for a frequency of about 3 GHz and an applied field of 730 KV/cm. At the same time the effective electromechanical coupling constant k t,eff 2 increased up to 3.6%. The tuning of the resonance frequency depends on the tunability of the film permittivity and on the mechanical load on the piezoactive layer. The constitutive equations controlling the tuning of the resonance and antiresonance frequency were derived from the Landau theory using the P-expansion of its free energies. The theoretical predictions show that, in the considered system, the frequency of the first-order resonance ͑ / 2 resonance͒ will always shift down with increasing bias, whereas the antiresonance frequency might shift up or down with increasing bias. The sense of the shift of the antiresonance frequency depends on the sign and the magnitude of the corresponding coefficients of the tensors of linear and nonlinear electrostriction. The theoretical predictions corroborate the experimental observations very well.

A tunable membrane-type thin film bulk acoustic wave resonator (TFBAR) based on a Ba(0.3)Sr(0.7)TiO(3)(BST) thin film has been fabricated. The resonance and antiresonance frequencies of the device can be altered by applying a dc bias: both shift down with increasing dc electric field. The resonance and antiresonance frequencies showed a tuning of -2.4% and -0.6%, respectively, at a maximum dc electric field of 615 kV/cm. The electromechanical coupling factor of the device increased up to 4.4%. We demonstrate that the tuning of the TFBAR is nonhysteretic. The Q-factor of the device showed some variation with dc bias and is about 200. The tuning of the TFBAR is caused by the dc bias dependence of the sound velocity and the intrinsic electromechanical coupling factor of the BST layer. We apply our recently developed theory on the electrical tuning of dc bias induced acoustic resonances in paraelectric thin films to successfully model the tuning behavior of the TFBAR. The modeling enabled us to de-embed the intrinsic electromechanical properties of the BST thin film. We show that the mechanical load of our device does not significantly degrade the tuning performance of the BST layer. The performance of the TFBAR is compared with the available data on varactor tuned TFBARs.

Capacitors are essential building blocks of electrical radiofrequency (rf) circuits. Reconfigurable circuits whose electrical characteristics can be altered dynamically are of interest for space and weight economy, especially in future multifunctional, multiband hand-held electronic devices. Electrically tunable capacitors, that is, varactors, are therefore in demand. Two emerging solutions compete over this market: rf-microelectromechanical systems (rf-MEMS) tunable capacitor technology and ferroelectric thin-film capacitor technology. The former has the advantages of very low loss and relatively low voltage operation, but suffers inherently from low speed and reliability problems due to the moving parts at the microsystem level.[1] The latter involves the use of a ferroelectric material as a tunable element, and is attractive for being a fast-response, low-noise, competitive-loss level, [2] robust, all-solid technology, but is limited by circuit considerations due to the high permittivity of ferroelectrics. [3,4] This communication introduces a new, rather unexpected and yet simple way to overcome the limitation of ferroelectric materials by a self-assembled oriented nanocolumnar composite approach, which lowers the permittivity of the material and simultaneously amplifies its tunable response to electric field. A ferroelectric perovskite BaTiO 3 in the form of oblique nanofibers with lateral dimensions as fine as 2-8 nm embedded in dielectric fluorite CeO 2 matrix results in an appreciable tunability with a very low relative permittivity of 50. As a result, the coefficient of dielectric nonlinearity increases up to 25 times that of conventional BaTiO 3 -based ferroelectrics. The system is attractive also in manifesting low dielectric losses and excellent temperature stability of the dielectric properties. Beyond the interest in this approach for the field of reconfigurable microelectronics, the perovskite-fluorite nanocomposite approach shown here may be of interest to other fields, such as oxide fuel microcells with fluorite electrolytes and perovskite cathodes.The high permittivity of ferroelectrics is of a structural origin. It can be tuned by an external electric field. The tunability of the ferroelectric n, under dc field E, is strongly correlated with its initial permittivity e(0), as expressed by n ¼ "ð0Þ="ðEÞ % 1 þ 3 " 0 "ð0Þ ½ 3 bE 2 , for n % 1, and 3" 0 "ð0Þb 1=3 E 2=3 , for n ) 1, where b is the coefficient of the dielectric nonlinearity and e 0 is the permittivity of vacuum. [3] Therefore, a large permittivity is necessary in order to have a large tunability. However, the circuit consideration (impedance matching) imposes the use of low permittivity materials, especially with the increase of operational frequency, and with the drive toward miniaturization, which requires the use of the material in a thin-film, parallel-plate configuration. Consequently, two conflicting demands, namely low permittivity and high tunability, are required, which hinder the use of ferroelectric materials in reconfigura...

No abstract