Eduard Rocas

Exploiting dimensionality and defect mitigation to create tunable microwave dielectrics

The miniaturization and integration of frequency-agile microwave circuits—relevant to electronically tunable filters, antennas, resonators and phase shifters—with microelectronics offers tantalizing device possibilities, yet requires thin films whose dielectric constant at gigahertz frequencies can be tuned by applying a quasi-static electric field. Appropriate systems such as BaxSr1−xTiO3 have a paraelectric–ferroelectric transition just below ambient temperature, providing high tunability. Unfortunately, such films suffer significant losses arising from defects. Recognizing that progress is stymied by dielectric loss, we start with a system with exceptionally low loss—Srn+1TinO3n+1 phases—in which (SrO)2 crystallographic shear planes provide an alternative to the formation of point defects for accommodating non-stoichiometry. Here we report the experimental realization of a highly tunable ground state arising from the emergence of a local ferroelectric instability in biaxially strained Srn+1TinO3n+1 phases with n ≥ 3 at frequencies up to 125 GHz. In contrast to traditional methods of modifying ferroelectrics—doping or strain—in this unique system an increase in the separation between the (SrO)2 planes, which can be achieved by changing n, bolsters the local ferroelectric instability. This new control parameter, n, can be exploited to achieve a figure of merit at room temperature that rivals all known tunable microwave dielectrics.

Manipulating particle trajectories with phase-control in surface acoustic wave microfluidics

We present a 91 MHz surface acoustic wave resonator with integrated microfluidics that includes a flow focus, an expansion region, and a binning region in order to manipulate particle trajectories. We demonstrate the ability to change the position of the acoustic nodes by varying the electronic phase of one of the transducers relative to the other in a pseudo-static manner. The measurements were performed at room temperature with 3 μm diameter latex beads dispersed in a water-based solution. We demonstrate the dependence of nodal position on pseudo-static phase and show simultaneous control of 9 bead streams with spatial control of -0.058 μm/deg ± 0.001 μm/deg. As a consequence of changing the position of bead streams perpendicular to their flow direction, we also show that the integrated acoustic-microfluidic device can be used to change the trajectory of a bead stream towards a selected bin with an angular control of 0.008 deg/deg ± 0.000(2) deg/deg.

Nonlinear Distributed Model for Bulk Acoustic Wave Resonators

This work expands the model proposed by Krimtholz, Leedom, and Matthaei (KLM) model to account for the nonlinear effects occurring in acoustic devices due to the nonlinear stiffened elasticity. We show that a nonlinear distributed capacitance in the acoustic transmission line of the KLM model can account for the distributed nature of the nonlinear effects. Specifically, we use the nonlinear telegraphers equation to find closed-form equations for intermodulation distortion and harmonic generation. We confirm the validity of these equations by comparing their results with those provided by a KLM equivalent circuit in which the nonlinear transmission line is implemented by cascading many L-C cells having a voltage-dependent capacitance. To further confirm the model, we show measured nonlinear effects in a thin film bulk acoustic resonator in close agreement with the equivalent circuit simulations.

Electro-thermo-mechanical model for bulk acoustic wave resonators

We present the electro-thermo-mechanical constitutive relations, expanded up to the third order, for a BAW resonator. The relations obtained are implemented into a circuit model, which is validated with extensive linear and nonlinear measurements. The mathematical analysis, along with the modeling, allows us to identify the dominant terms, which are the material temperature derivatives and two intrinsic nonlinear terms, and explain, for the first time, all observable effects in a BAW resonator by use of a unified physical description. Moreover, the terms that are responsible for the second-harmonic generation and the frequency shift with dc voltage are shown to be the same.

Passive Intermodulation Due to Self-Heating in Printed Transmission Lines

This paper proposes a mechanism by which third-order intermodulation distortion, due to self-heating, is generated in transmission lines. This work shows how transmission lines made of several materials, whose properties are independent of the electric and magnetic fields, can generate important levels of intermodulation distortion. A circuit model supported by finite-element simulations is presented to account for the temperature generation and also for its impact on the nonlinear performance. Closed-form expressions are used to calculate the generated intermodulation products and are derived from the circuit model and compared with simulations. Finally, measurements and simulations of different transmission lines are presented, showing very good agreement.

Unified model for Bulk Acoustic Wave resonators' nonlinear effects

We present a nonlinear model for Bulk Acoustic Wave resonators that combines different sources of nonlinearity by use of device-independent material-specific parameters to predict intermodulation and harmonic generation. The model accounts for intrinsic nonlinearities due to the stiffened elasticity and thermal effects that arise from temperature changes in a sample driven by an amplitude-modulated signal. Nonlinear parameters of the aluminum nitride piezoelectric layer have been extracted that are in agreement with previously published results.

Nonlinear distributed model for IMD prediction in BAW resonators

This work presents a distributed nonlinear equivalent circuit to asses the intermodulation distortion (IMD) occurring in a BAW resonator. Closed-form expressions for intermodulation distortion at 2f1-f2 are obtained. Comparisons between analytical and simulated results are in good agreement. Extension of this analysis could be used to predict the nonlinear performance of more complex systems using BAW resonators, such as filters. Finally, measurements are presented and explained using the proposed approach.

A Compact Variable-Temperature Broadband Series-Resistor Calibration

We present a broadband on-wafer calibration from 45 MHz to 40 GHz for variable temperature measurements, which requires three standards: a thru, reflect, and series resistor. At room temperature, the maximum error of this technique, compared to a benchmark nine-standard multiline thru-reflect-line (TRL) method, is comparable to the repeatability of the benchmark calibration. The series-resistor standard is modeled as a lumped-element -network, which is described by four frequency-independent parameters. We show that the model is stable over three weeks, and compare the calibration to the multiline TRL method as a function of time. The approach is then demonstrated at variable temperature, where the model parameters are extracted at 300 K and at variable temperatures down to 20 K, in order to determine their temperature dependence. The resulting technique, valid over the temperature range from 300 to 20 K, reduced the total footprint of the calibration standards by a factor of 17 and the measurement time by a factor of 3.

First-Order Elastic Nonlinearities of Bulk Acoustic Wave Resonators

We propose a procedure to characterize the intrinsic nonlinearities of bulk acoustic wave resonators by performing one-port measurements of the second harmonic and second-order intermodulation spurious signals. Closed-form expressions have been derived that relate the nonlinear stiffened elasticity with experimental observables. These formulas are valid in a wide range of frequencies around the resonance and have been verified with nonlinear circuit simulations. The measurement setup and its effects are also discussed in our approach. Measurements of a set of aluminum nitride-based devices from several manufacturers yield consistent model parameters and allow us to obtain a coefficient of the nonlinear stiffened elasticity intrinsic to this piezoelectric material.

Third order intermodulation distortion in Film Bulk Acoustic Resonators at resonance and antiresonance

This paper presents recent measurements and modeling of the third order intermodulation products of a Film Bulk Acoustic Resonator (FBAR), for a various values of frequency spacing between driving tones. The frequency dependence of voltage and current in the acoustic branch rules out a voltage-dependent nonlinearity. The results show different slopes at resonance and antiresonance, which are correctly adjusted by the model with a current dependent inductor and/or capacitor. The intermodulation distortion is found to be dependent on the frequency spacing between driving tones, indicating memory effects.