Tuomas Pensala

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 keff 2 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.

Piezoelectrically transduced single-crystal-silicon plate resonators

We report on the design, fabrication and characterization of piezoelectrically actuated single-crystal silicon plate resonators vibrating mainly in their bulk acoustic wave modes. Two resonator types are presented: one operates in the square extensional mode at 26 MHz with Q~18000 and motional resistance Rm~0.240 kOmega, while the other resonator features a resonance at 22 MHz with Q~51000 and Rm~1.5 kOmega. The resonators are characterized electrically and by scanning laser interferometry. Measured vibration fields are compared to simulated eigenmodes.

Determination of doping and temperature-dependent elastic constants of degenerately doped silicon from MEMS resonators

Elastic constants c₁₁, c₁₂, and c₄₄ of degenerately doped silicon are studied experimentally as a function of the doping level and temperature. First-and second-order temperature coefficients of the elastic constants are extracted from measured resonance frequencies of a set of MEMS resonators fabricated on seven different wafers doped with phosphorus (carrier concentrations 4.1, 4.7, and 7.5 × 10¹⁹ cm^-3), arsenic (1.7 and 2.5 × 10¹⁹ cm^-3), or boron (0.6 and 3 × 10¹⁹ cm^-3). Measurements cover a temperature range from -40°C to +85°C. It is found that the linear temperature coefficient of the shear elastic parameter c₁₁ - c₁₂ is zero at n-type doping level of n ~ 2 × 10¹⁹ cm^-3, and that it increases to more than 40 ppm/K with increasing doping. This observation implies that the frequency of many types of resonance modes, including extensional bulk modes and flexural modes, can be temperature compensated to first order. The second-order temperature coefficient of c₁₁ - c₁₂ is found to decrease by 40% in magnitude when n-type doping is increased from 4.1 to 7.5 × 10¹⁹ cm^-3. Results of this study enable calculation of the frequency drift of an arbitrary silicon resonator design with an accuracy of ±25 ppm between the calculated and real(ized) values over T = -40°C to +85°C at the doping levels covered in this work. Absolute frequency can be estimated with an accuracy of ±1000 ppm.

Temperature compensated resonance modes of degenerately n-doped silicon MEMS resonators

We model the temperature coefficients of resonance modes of degenerately n-type doped silicon resonators. By combining results from FEM-based sensitivity analysis and modelling of elastic constants of silicon with free carrier theory we are able to identify classes of resonance modes that can be temperature compensated via n-type doping. These include bulk modes such as the width/length extensional modes of a beam, Lamé/square extensional modes of a plate resonator, as well as flexural and torsional resonance modes. Our results show that virtually all resonance modes of practical importance can reach zero TCF when the resonator is aligned to a correct crystallographic orientation and when the n-dopant concentration is suitably selected.

Parametric study of laterally acoustically coupled bulk acoustic wave filters

Acoustically coupled thin-film bulk acoustic wave resonator filters, in which the coupling takes place mechanically in the lateral direction between closely-spaced narrow resonators, are a promising approach to passband filtering at gigahertz frequencies. In this paper, filters with interdigital electrode structures are studied. Electrode number, electrode width, and coupling gap width are varied. The resonators are solidly mounted, having an acoustic mirror isolating the resonator from a Si substrate and providing the means to engineer the acoustic dispersion properties of the resonators. The center frequency of the filters is around 2 GHz. Electrical frequency responses of the filters are measured and the strength of the lateral acoustic coupling is calculated from the measurements. The effects of device parameters on the acoustic coupling and the obtainable filter bandwidth are analyzed in detail. A bandpass filter with 4.9% bandwidth, minimum insertion loss of 2 dB and sharp transition from passband to suppression band, is presented.

Laterally coupled solidly mounted BAW resonators at 1.9 GHz

Laterally coupled bulk acoustic wave resonators fabricated onto an acoustic mirror are studied. The acoustic mirror comprises two W-SiO2 pairs. Thin-film AlN is used as the piezoelectric material with a Mo bottom electrode and an Al top electrode. Structures consist of laterally acoustically coupled electrodes 2.5 µm wide and 300 µm long, with gaps of 4 µm in-between. Acoustical coupling between the electrodes results in two resonances forming an electrical bandpass response at 1.9 GHz. A device with two coupled electrodes features a 1.5% relative to center frequency bandwidth, 10 dB insertion loss in 50-Ω environment and 3.9 dB insertion loss after matching. Electrical frequency responses are presented and compared to simulations. Mechanical vibration fields in the devices are studied with a laser interferometer.

Extraction of lateral eigenmode properties in thin film bulk acoustic wave resonator from interferometric measurements

A heterodyne laser interferometer is used to study acoustic wave fields excited in a 1.8 GHz AlN thin film bulk acoustic wave resonator. The electrical response of the resonator exhibits a strong thickness resonance onto which spurious modes, caused by lateral standing plate waves, are superposed. Optical interferometer measurements are used to extract dispersion curves of the laterally propagating waves responsible for the spurious responses. A discrete eigenmode spectrum due to the finite lateral dimensions of the resonator is observed. An equivalent circuit model for a multimode resonator is fitted to the mechanical resonator response extracted along a single curve in the dispersion diagram, and is used to determine properties, such as Q-values, of the individual lateral eigenmodes. Measured wave field images, extracted dispersion curves, and the eigenmode spectrum with the model fitting results are presented.

Experimental investigation of acoustic substrate losses in 1850-MHz thin film BAW resonators

After optimizing for electromechanical coupling coefficient K2, the main performance improvement in the thin film bulk acoustic wave resonators and filters can be achieved by improving the Q value, i.e., minimizing the losses. In Bragg-reflector-based solidly mounted resonator technology, a significant improvement of Q has been achieved by optimizing the reflector not only for longitudinal wave, the intended operation mode, but also for shear waves. We have investigated the remaining acoustic radiation losses to the substrate in so-optimized 1850-MHz AlN resonators by removing the substrate underneath the resonators and comparing the devices with and without substrate by electrical characterization before and after the substrate removal. Several methods to extract Q-values of the resonators are compared. Changes caused by substrate removal are observed in resonator behavior, but no significant improvement in Q-values can be confirmed. Loss mechanisms other than substrate leakage are concluded to dominate the resonator Q-value. Difficulties of detecting small changes in the Q-values of the resonators are also discussed.

2-D modeling of laterally acoustically coupled thin film bulk acoustic wave resonator filters

A 2-D model is developed for calculating lateral acoustical coupling between adjacent thin film BAW resonators forming an electrical N-port. The model is based on solution and superposition of lateral eigenmodes and eigenfrequencies in a structure consisting of adjacent regions with known plate wave dispersion properties. Mechanical and electrical response of the device are calculated as a superposition of eigenmodes according to voltage drive at one electrical port at a time while extracting current induced in the other ports, leading to a full Y-parameter description of the device. Exemplary cases are simulated to show the usefulness of the model in the study of the basic design rules of laterally coupled thin film BAW resonator filters. Model predictions are compared to an experimental 1.9-GHz band-pass filter based on aluminum nitride thin film technology and lateral acoustical coupling. Good agreement is obtained in prediction of passband behavior. The eigenmode-based model forms a useful tool for fast simulation of laterally coupled acoustic devices. It allows one to gain insight into basic device physics in a very intuitive fashion compared with more detailed but heavier finite element method. Shortcomings of this model and possible improvements are discussed.

Characterization of energy trapping in a bulk acoustic wave resonator

Acoustic wave fields both within the active electrode area of a solidly mounted 1.8 GHz bulk acoustic wave resonator, and around it in the surrounding region, are measured using a heterodyne laser interferometer. Plate-wave dispersion diagrams for both regions are extracted from the measurement data. The experimental dispersion data reveal the cutoff frequencies of the acoustic vibration modes in the region surrounding the resonator, and, therefore, the energy trapping range of the resonator can readily be determined. The measured dispersion properties of the surrounding region, together with the abruptly diminishing amplitude of the dispersion curves in the resonator, signal the onset of acoustic leakage from the resonator. This information is important for verifying and further developing the simulation tools used for the design of the resonators. Experimental wave field images, dispersion diagrams for both regions, and the threshold for energy leakage are discussed.