Nathan D. Orloff

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.

Quantitative Permittivity Measurements of Nanoliter Liquid Volumes in Microfluidic Channels to 40 GHz

We describe the design, fabrication, and evaluation of a new on-wafer measurement platform for the rapid and quantitative determination of the complex permittivity of nanoliter fluid volumes over the continuous frequency range from 45 MHz to 40 GHz. Our measurement platform integrates micrometer-scale poly(dimethylsiloxane) (PDMS)-based microfluidic channels with high-frequency coplanar waveguide (CPW) transmission lines to accurately place small fluid volumes at well-defined locations within planar measurement structures. We applied new on-wafer calibration techniques to accurately determine the scattering parameters of our integrated devices, and we developed a transmission-line model to extract the distributed circuit parameters of the fluid-loaded transmission line segment from the response of the overall test structure. All the necessary model parameters were experimentally determined directly from a single set of measurements without requiring a reference fluid of known permittivity. We extracted the complex permittivity of the fluid under test from the distributed capacitance and conductance per unit length of the fluid-loaded transmission line segment using finite-element analysis of the transmission line cross section. Our measurements show excellent agreement with bulk fluid permittivity determinations for methanol at room temperature and yield consistent results for the extracted fluid permittivity for the same microfluidic channel embedded in multiple CPW transmission lines of different dimensions.

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.

Broadband Permittivity of Liquids Extracted from Transmission Line Measurements of Microfluidic Channels

We present a semi-analytical procedure to extract the permittivity of fluids from measurements in our microfluidic-microelectronic platform. This platform consists of broadband coplanar waveguide transmission lines with integrated microfluidic channels for characterizing the dielectric properties of submicroliter fluid samples. On-wafer calibration techniques are used to obtain the S-parameters of the composite structure (transmission line and microfluid channel) up to 40 GHz. Using microwave network analysis theory, we isolated the response of the microfluidic channel. We modeled the microfluidic channel as a distributed transmission line segment and as a single RLCG elemental segment. Both approaches analytically yield the circuit capacitance CF and conductance GF per unit length of the segment incorporating the microfluidic channel. A finite element electromagnetic simulator is then used to obtain the permittivity of the fluid as a continuous function of frequency. We applied this technique to extract the permittivity of submicroliter liquid volumes. Here we present results on polystyrene latex beads suspended in an aqueous solution over the frequency range from 100 MHz to 40 GHz.

Dielectric Characterization by Microwave Cavity Perturbation Corrected for Nonuniform Fields

Nonuniform fields decrease the accuracy of dielectric characterization by microwave cavity perturbation. These fields are due to the slot in the cavity through which the sample is inserted and the boundary between the sample and the metallic walls inside of the cavity. To address this problem, we measured the natural frequency and damping ratio of a resonant cavity as a sample is inserted into the rectangular cavity. We found that for a range of cavity filling fractions, a linear regression on the natural frequency and damping ratio versus the effective volume fraction of the sample in the cavity could be used to extract the complex permittivity of the sample. We verified our technique by measuring a known quartz substrate and comparing the results to finite-element simulations. When compared to the conventional technique, we found a significant improvement in the accuracy for our samples and measurement setup. We confirmed our technique on two lossy samples: a neat stoichiometric mixture bisphenol A epoxy resin and one containing a mass fraction of 3.5% multi-walled carbon nanotubes (MWCNTs). At the TE103 mode (7.31 GHz), the permittivity and loss tangent of the epoxy were measured to be εr=2.93±0.11 and tanδ = 0.028±0.002, respectively. The epoxy with a mass fraction of 3.5% MWCNTs had a permittivity of εr=8.01±0.48 and loss tangent of tanδ = 0.137±0.010.

Broadband dielectric spectroscopy of Ruddlesden–Popper Srn+1TinO3n+1 (n=1,2,3) thin films

We explore the frequency-dependent relative permittivity of Ruddlesden–Popper series Srn+1TinO3n+1 (n=1,2,3) thin films as a function of temperature and dc electric field. Interdigitated capacitors and coplanar waveguides were used to extract the frequency response from 500 Hz to 40 GHz. At room temperature, the in-plane relative permittivities (ϵ11) obtained for Srn+1TinO3n+1 (n=1,2,3) were 42±3, 54±3, and 77±2, respectively, and were independent of frequency. At low temperatures, ϵ11 increases and electric field tunability develops in Sr4Ti3O10.

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.

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.

Temperature-dependent dielectric relaxation in bismuth zinc niobate thin films

We apply broadband measurement techniques to determine the dielectric permittivity of Bi1.5Zn1.0Nb1.5O7 (BZN) thin films over the frequency range 1 kHz to 40 GHz. At room temperature, the permittivity function shows relaxation at high frequencies (∼1 GHz), and as the temperature is reduced, the onset of relaxation rapidly moves to lower frequencies, reaching ∼1 kHz at 100 K. The observed frequency-dependent dielectric response of BZN thin films is quantitatively similar to the response of bulk ceramics, which suggests that the intrinsic disorder in the BZN material system can be conveniently explored via measurements on thin films.