Thin-film Bulk Acoustic Wave Resonator Research Articles

Correspondence - Analysis of thickness vibrations of c-axis inclined zig-zag two-layered zinc oxide thin-film resonators

The free vibrations of a two-layered C-axis inclined zig-zag ZnO thin-film bulk acoustic wave resonator (FBAR) connected to external impedance are analyzed. The frequency equation and mode shape for this resonator are derived based on the linear piezoelectric theory. The impedance characteristics of the FBAR are derived and compared with previous experimental results.

Two-dimensional analysis of FBAR by using FDTD method

The film bulk acoustic resonator (FBAR) devices are lighter, smaller, cheaper and capable of dealing with larger power than SAW devices. Therefore, the FBAR technology is more competitive in satisfying the commands of modern mobile phone systems. In this paper, the finite-difference time-domain method is applied to analyze the two-dimensional thin-film bulk acoustic wave resonators. The piezoelectric governing equations and Newton's equation of motion are discretized to centered finite-differences in spatial and temporal domain. An electrostatic field simulator named ANSOFT Maxwell 2D is used to calculate the electric field intensity. The frequency domain electrical impedance characteristics of FBAR with different electrode thicknesses are calculated by using the Prony's method. From the simulation results, the optimal electrode thickness is suggested.

Measurement of evanescent wave properties of a bulk acoustic wave resonator [Letters

Acoustic wave fields in a thin-film bulk acoustic wave resonator are studied using a heterodyne laser interferometer. The measurement area is extended outside the active electrode region of the resonator, so that wave fields in both the active and surrounding regions can be characterized. At frequencies at which the region surrounding the resonator does not support laterally propagating acoustic waves, the analysis of the measurement data shows exponentially decaying amplitude fields outside the active resonator area, as suggested by theory. The magnitude of the imaginary wave vectors is determined by fitting an exponential function to the measured amplitude data, and thereby the experimentally determined dispersion diagram is extended into the region of imaginary wave numbers.

Unconditional Stable FDTD Method for Modeling Thin-Film Bulk Acoustic Wave Resonators

SUMMARY The unconditional stable finite-difference time-domain(US-FDTD) method based on Laguerre polynomial expansion andGalerkintemporaltestingisusedtomodelthin-filmbulkacousticwaveres-onators (TFBAR). Numerical results show the efficiency of the US-FDTDalgorithm. key words: US-FDTD,thin-film bulk acoustic wave resonators (TFBAR) 1. IntroductionBulkacousticwaveresonatorshavereceivedlotsofresearchinterest due to their potentials in achieving compact deviceswith low insertion loss and high Q for wireless communica-tion systems [1]. Numerical methods have been used in themodeling and simulation of BAW devices [2]–[4], amongwhich the finite-difference time domain (FDTD) method [4]is to be preferred because of its simplicity and easy imple-mentation. However, using the conventional FDTD methodtomodelthin-filmBAWdevicesisinefficientbecauseaverysmall spatial grid size is necessary to resolve the thin struc-ture which leads to a very small time step by the Courant-Friedrich-Levy (CFL) condition. In the end, a large numberof time steps are needed. The alternating-direction-implicit(ADI) FDTD method [5],[6], developed to remove the CFLconstraints on the time step, yields an unconditionally sta-ble (US) algorithm. Though the ADI-FDTD method hasbeen successfully used in the modeling of thin-film BAWresonators [7], it suffers from large dispersion error whenlargetimestepisused. Recently,anotherUS-FDTDschemebased on the Laguerre polynomial expansion and Galerkintemporaltestingwasproposedtoovercomethisproblem[8].As compared to the ADI-FDTD method, the time step isused only to calculate the Laguerre coefficients due to theexcitationatthestartofthecomputations. Thereforeasmalltime step value can be used to increase the accuracy with-out increasing computing time. In this letter, the US-FDTDmethod is employed to model the thin-film bulk acousticwave resonator (TFBAR). Numerical results are presentedto validate the algorithm.2. US-FDTD for TFBAR modelingThe governing equations of the TFBAR are given by [4],

3.4 GHz composite thin film bulk acoustic wave resonator for miniaturized atomic clocks

Triple layer SiO2/AlN/SiO2 composite thin film bulk acoustic wave resonators (TFBARs) were studied for applications in atomic clocks. The TFBAR’s were tuned to 3.4 GHz, corresponding to half the hyperfine splitting of the ground state of rubidium 87Rb atoms. The quality factor (Q) was equal to 2300 and the temperature coefficient of the resonance frequency fr amounted to 1.5 ppm/K. A figure of merit Qfr of ∼ 0.8 × 1013 Hz and a thickness mode coupling factor of 1% were reached. Such figures are ideal for frequency sources in an oscillator circuit that tracks the optical signal in atomic clocks.

Numerical modeling of thin‐film bulk acoustic wave resonators using a Crank‐Nicolson finite‐difference time‐domain method

AbstractIn this study, an unconditionally stable finite‐difference time‐domain (FDTD) method implemented with Crank‐Nicolson scheme is presented for the analysis of thin‐film bulk acoustic wave resonators (TFBARs).The proposed approach is unconditionally stable and therefore, the algorithm can significantly reduce the computer processing unit (CPU) time compared to that of the conventional FDTD algorithm. The accuracy and efficiency of the proposed method for calculating resonator frequencies of TFBARs are verified by simulation results. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26135

Chemically Sensitized Thin-Film Bulk Acoustic Wave Resonators as Humidity Sensors

A humidity sensor based on a thin-film bulk acoustic wave resonators (FBARs) operating at sub gigahertz frequencies has been developed in this work. The FBAR was microfabricated, electrically characterized, and then coated with the hygroscopic polymer poly[vinylpyrrolidone] (PVP). The FBAR was electrically connected to transmission lines and sealed within a temperature stabilized environmental isolation chamber. Changes in the moisture content of a nitrogen stream were measured with FBAR and verified with external hygroscopes. Response time, sensitivity, and hysteresis of the prototype sensor were examined. In some experiments, the thickness of the PVP polymer film exceeded the total thickness of the FBAR, yet the device still continued to resonate with sufficient quality Q factor to allow for continuous tracking of frequency changes in response to humidity change.

Tunable thin film bulk acoustic wave resonators with improved Q-factor

The tunable solidly mounted Ba0.25Sr0.75TiO3 (BSTO) thin film bulk acoustic wave resonators (TFBARs) with improved Q-factor are fabricated and characterized. The BSTO films are grown by magnetron sputtering at temperature 600 °C and extremely low sputter gas pressure 2 mTorr using on-axis configuration. The measured TFBARs Q-factor is more than 250 and mechanical Q-factor is more than 350 at 5 GHz resonance frequency. The improvement in the Q-factor is associated with reduction in the BSTO film grain misorientation. The latter is responsible for generation of shear waves leaking through the Bragg reflector and corresponding acoustic loss.

Tunable thin film bulk acoustic wave resonator based on BaxSr1-xTiO3 thin film

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.

Power deduction from surface fields in multilayer waveguides

This paper proposes a method to estimate power carried by a propagating Lamb mode in an arbitrary multilayer waveguide from calculated or measured surface displacements. To this end, we calculate the so-called mode power coefficient relating the surface amplitude of the mode to the total power flow toward the lateral direction. The coefficient is given by the gradient of the effective acoustic admittance with respect to the lateral wavenumber, and can be readily calculated by slightly modifying software codes developed for calculating the dispersion relation of Lamb waves. This calculation procedure is simpler and more efficient than the conventional technique based on the estimation of total power flow passing through the waveguide cross section. We apply this technique to the quantitative evaluation of acoustic losses in a thin-film bulk acoustic wave resonator (FBAR), and the effectiveness of this technique is demonstrated.

Spurious Resonance Suppression in Gigahertz-Range ZnO Thin-Film Bulk Acoustic Wave Resonators by the Boundary Frame Method: Modeling and Experiment

Zinc-oxide-based thin-film bulk acoustic wave (BAW) resonators operating at 932 MHz are investigated with respect to variation of dimensions of a boundary frame spurious mode suppression structure. A plate wave dispersion-based semi-2-D model and a 2-D finite element method are used to predict the eigenmode spectrum of the resonators to explain the detailed behavior. The models show how the boundary frame method changes the eigenmodes and their coupling to the driving electrical field via the modification of the mechanical boundary condition and leads to emergence of a flat-amplitude piston mode and suppression of spurious modes. Narrow band suppression of a single mode with a nonoptimal boundary frame is observed. Reduction of the effective electromechanical coupling coefficient k2eff as a function of the boundary width is observed and predicted by both models. The simple semi-2-D plate model is shown to predict the device behavior very well, and the 2-D finite element method results are shown to coincide with them with some additional effects. Breaking the resonator behavior down to eigenmodes, which are not directly observable in measurements, by the models, yields insight into the physics of the device operation.

Analytical and Finite-Element Modeling of Localized-Mass Sensitivity of Thin-Film Bulk Acoustic-Wave Resonators (FBAR)

Analytical and finite-element models of a localized-mass sensor fabricated with thin-film bulk acoustic wave resonator (FBAR) are reported. While our group demonstrated FBAR-based localized-mass sensors, no previous modeling of these sensors is found in the literature. The finite-element model (FEM) defines the boundary conditions and performs parametric analysis of the sensor's mass loading, whereas the analytical approach takes advantage on a modified Mason's model to describe the transmission-line circuit of the sensor. The sensitivity of the resonance frequency to location and size of mass deposition has been studied. Both the experimental and modeled responsivities exhibit a nonlinear dependence on the location and size of the localized-mass.

Prototype Design of a Thin-Film Bulk Acoustic-Wave Resonator by the Finite Element Method

A thin film bulk acoustic wave resonator (FBAR) used in the RF frequency region of a few gigahertz is considered and its impedance is evaluated by using a harmonic analysis with the three-dimensional finite element method. In particular, the spurious characteristics caused by variations in the electrode area, as well as all the resonant modes and the mode shapes are analyzed. A design procedure is presented by using a prediction software tool. An experimental prototype is built and the measured results are compared to the numerical ones.

Piezoelectric materials parameters for piezoelectric thin films in GHz applications

Piezoelectric thin films have existing and promising new applications in microwave filter technologies. The final performance depends on many parameters, and very specifically on the materials properties of each involved material. In this article, materials and properties for thin-film bulk acoustic wave resonators are discussed on some selected issues: the piezoelectric coefficients and acoustic losses of AlN, the relation of the first one with microstructural parameters, the inclusion of parasitic elements, and the merits of and problems with ferroelectric materials.

Real-time imaging of acoustic waves on a bulk acoustic resonator

Time resolved images of acoustic waves in the 100 MHz–2.2 GHz range are obtained for an electrically excited thin-film bulk acoustic wave resonator by means of an ultrafast optical technique. Electrical pulses, synchronized to ultrashort laser pulses, piezoelectrically excite the device, and synchronous near-infrared laser pulses interferometrically detect surface motion. The frequency dispersion is extracted using spatiotemporal Fourier transforms, revealing both longitudinal and surface acoustic modes.

High-frequency sensor technologies for inertial force detection based on thin-film bulk acoustic wave resonators (FBAR)

High-frequency technologies and fabrication processes intended for inertial force detection have been developed. The sensing devices are based on longitudinal-mode thin-film bulk acoustic wave resonators (FBAR) monolithically integrated with silicon (Si) technologies. Thus, compatibility with both technologies has been achieved in order to design and fabricate FBAR-based inertial force sensors. Characterization of the FBAR was carried out and the operating principle of the inertial force detectors studied. Additionally, characterization of a resonant accelerometer with embedded-FBAR was performed with the aim of concept’s demonstration. So far, future developments of the technology and the application are discussed.

Thin-Film Bulk Acoustic Wave Resonator Floating Above CMOS Substrate

A thin-film bulk acoustic wave resonator (FBAR) having a floating, 3-D structure above a CMOS substrate is presented. The integration of the FBAR to the CMOS substrate is performed with independence of FBAR or CMOS fabrication technologies. Wafer-level transfer is carried out to obtain a suspended FBAR above CMOS substrates of different technologies, whose resonant frequency is found in the 2.4 GHz band. The electrical interconnection between the FBAR and CMOS is provided by at least two conducting posts, which at the same time offer mechanical support to the resonator's structure. Experimental characterization results and Q-factor comparison with conventional FBAR technologies are discussed.

Focused-ion-beam-assisted tuning of thin-film bulk acoustic wave resonators (FBARs)

A focused-ion-beam-assisted procedure with the aim of frequency tuning thin-film bulk acoustic resonators (FBARs) is presented. The procedures of focused-ion-beam-based deposition and milling on the FBAR are described, detailing calibration and alignment issues. A C/Pt/Ga composite was locally deposited on the top electrode of the FBAR by means of ion-assisted deposition. Selected areas of the electrode were chosen to deposit the localized composite, having micrometer dimensions and nanometer thicknesses. Based on the mass-loading principle, a down-shifting in the resonance frequency was observed. The achieved responsivity of 7.4 × 10−19 g Hz−1 was demonstrated to be at least one order of magnitude better than for the thin-film deposition case. Different localized-mass-loading configurations were tested and the possible effects of the ion beam on the physical properties of the resonator analyzed. It was found that responsivity is dependent on the size of the tuning mass and that the Q factor does not suffer significant variation due to the i-beam operation.

Localized-mass detection based on thin-film bulk acoustic wave resonators (FBAR): Area and mass location aspects

Localized-mass sensors using thin-film bulk acoustic resonators (FBAR) have been implemented for the study of sensitivity and possible configurations in biological applications. In a first experiment, a group of resonators are loaded with the same amount of mass but different contact areas, achieving responsivities as high as 10 −19 g/Hz, and potential sensitivities in the order of 10 −14 g. These numbers are at least one order of magnitude higher than those obtained for uniform thin-film loadings, although it is clear that sensitivity decreases with the area of the localized-mass. The current phase-noise levels and the quality factor of resonators would allow measuring frequency changes of 30 kHz – the minimum measured frequency shifting has been 500 kHz so far – due to a mass deposition of 9.0 × 10 −15 g. In a second experiment, localized-loadings with the same mass are located in different positions of the top electrodes of the corresponding FBARs. It was found out that a location change of the mass in the electrode causes different magnitudes of frequency shifting. A discussion on these topics is opened, in order to define future applications and research lines concerning localized-mass sensing in FBARs.

Characteristics of ZnO thin film for film bulk acoustic-wave resonators

Highly c-axis-oriented zinc oxide (ZnO) thin films were deposited on Au electrodes by reactive radio frequency (RF) magnetron sputtering and their sputtering pressure on thin film bulk acoustic-wave resonator (FBAR) characteristics are presented. The evolution of the preferred orientation and the surface morphologies of the deposited ZnO films are investigated using X-ray diffraction, scanning electron microscopy, and atomic force microscopy measurement techniques. The result obtained in this study show that the ZnO films prepared using a lower sputtering pressure of 2 × 10−3 Torr have a strong c-axis orientation, promote smoother surface and higher resonance frequency. The experimental results demonstrate that the fabricated two-port FBAR using the optimum process parameters yields an effective electromechanical coupling constant (\( k^{2}_{{{\text{eff}}}} \)) of 2.8%, series quality factor (Qs) of 436, and a parallel quality factor (Qp) of 600.