Christian J. Long

Despite the industrial relevance of sapphire and gallium arsenide (GaAs) for electronic applications, there are few reports on the value of complex permittivity and dielectric loss at frequencies above 110 GHz using integrated circuit topologies such as coplanar waveguides. Available materials characterization reports at microwave frequencies use methods that quantify bulk material properties and may miss the effective material properties present in the substrate structure and most relevant for integrated circuits at the frequencies of interest. Using a wafer-level method to extract the complex permittivity of sapphire and GaAs to 220 GHz, we found that the complex permittivity of intrinsic GaAs (εon−wafer≈13) and the convoluted in-plane and out-of-plane complex permittivity of c-plane sapphire (εon−wafer≈10.5) did not show dispersion up to 100 GHz. This result shows the importance of wafer-level tests for sapphire, where on-wafer permittivity diverges from nominal single-axis values. Above about 100 GHz, different data analysis approaches yielded increasingly different permittivities. This result provides useful data to electronics designers, materials scientists, and physicists while also providing insight into mechanisms that could produce unexpected frequency dependence.

Multiline thru-reflect-line (mTRL) is a calibration algorithm for vector network analyzers (VNAs) that uses S-parameter measurements of transmission lines with different lengths. While the conventional thru-reflect-line algorithm chooses the line lengths based on phase relationships, choosing the line lengths in mTRL is not as straightforward because the thru is not always the common line. This work tested a simple algorithm to iteratively compute all line lengths with a recursive fraction, only assuming that the longest and the shortest line lengths are known. A cursory theoretical analysis showed that certain recursive fractions should outperform others in terms of calibration error, S-parameter uncertainty, kit compactness, and resilience to the removal of any two lines from the kit. To test this analysis, we fabricated and measured 51 different mTRL calibration kits and benchmarked them against a kit whose normalized uncertainty was optimized by brute force Monte Carlo simulations with a supercomputer. After analyzing the kits, we performed a comparative analysis to determine which recursive fraction kits most closely matched the behavior of the optimized kit. We then developed a figure of merit to capture the strengths and weaknesses of each kit, revealing that the user should choose a recursive fraction within the range of 53/128 ( $\approx 0.41$ )–37/64 ( $\approx 0.58$ ) to design line lengths for mTRL. The proposed algorithm offers a simple and practical solution for designing high-performance mTRL line kits, enhancing measurement accuracy and robustness for high-frequency measurement applications.

Electromagnetic simulations are a ubiquitous tool for microwave engineers. We benchmark simulations by their agreement with experimental results. Transmission lines are an excellent test case because they have well-established measurement methodologies and are straightforward to simulate. However, when disagreements between simulation and experiment arise, finding the root cause can be quite difficult due to the number of design parameters. Here, we investigated a fabrication-motivated model that reduces this complexity by leveraging correlations between transmission line design parameters. We validated our model by comparing its prediction of cross-sectional geometry to scanning electron microscopy (SEM) measurements. Our procedure provides a simple path for microwave engineers to improve simulations on a broad range of on-wafer devices.

We characterize a radio-frequency micro-electro-mechanical-systems single-pole-six-throw switch designed for cryogenic operation to 10 GHz from room temperature to millikelvin temperatures. The switch contains an internal electronic calibration capability suitable for performing multiport vector and large-signal network analysis at room temperature and cryogenic temperatures. We demonstrate two calibration types, the first designed for measuring the scattering parameters of microwave devices connectorized with 3.5 mm coaxial connectors and the second for measuring the scattering parameters of microwave devices connectorized with Sub-Miniature version A (SMA) connectors.

Modern microchips utilize multilayer stack-ups with many interstitial layers of dielectrics. Optimizing device performance and maximizing yield requires precise measurements of the out-of-plane permittivity of these dielectric layers. At the same time, high-performance microchips are pushing operating frequencies into the millimeter-wave range, requiring precise materials property knowledge at these frequencies to perform as intended. With this context, one outstanding challenge is to accurately measure the out-of-plane permittivity of thin films. Unfortunately, the conventional method to extract this property, the metal-insulator-metal (MIM) capacitor technique, produces inconsistent and therefore unreliable material data for frequencies above a few gigahertz. To address these inconsistencies, we designed an experiment with on-wafer devices of varying topology and varying geometry. We chose to study silicon nitride for this experiment because it is a ubiquitous dielectric in microchips, widely accepted as approximately dispersionless, and available with established processes in our cleanroom. Our experiment resulted in an out-of-plane permittivity of thin film silicon nitride of ${\varepsilon }_{r} = 7.0~\pm ~0.1$ and a loss tangent of $\tan \delta \lt 0.03$ up to 90 GHz. Our key findings about improving on-wafer calibrations and modeling of the MIM devices will help material scientists and microchip designers obtain reliable permittivity data on thin films at millimeter wave frequencies.

We evaluate the accuracy of small-signal on-wafer device characterization in the sub-THz frequency range when employing conventional and advanced calibration methods with state-of-the-art design of on-chip standards. We report that major discrepancies resulting from an interlaboratory comparison experiment are mainly attributed to the influence of microwave probes. When performing conventional multiline thru-reflect-line (mTRL) calibrations with six different models of probe from 140 to 325 GHz, we observe significant variations in the measured scattering-parameters (S-parameters) and show that probes made by various manufacturers induce disparate crosstalk responses that vary between -70 and -15 dB on open–open standards. After applying a crosstalk correction approach as a second-tier calibration, we obtain significantly better agreement between the RF performance of the same heterojunction bipolar transistor (HBT) measured with two different probe models. While the difference between the maximum stable gain (MSG) reaches 1.8 dB at 210 GHz after applying a conventional mTRL calibration, we reduce the error to ~0.5 dB after crosstalk correction. This study shows that crosstalk correction methods must be implemented in the sub-THz frequency range to accurately estimate the RF performance of active devices and circuits.

We developed an interconnect characterization procedure that first embeds the interconnect into the error boxes of a multiline thru-reflect-line (mTRL) calibration and subsequently de-embeds the interconnect with a multitiered calibration. We experimentally validated our method to 325 GHz with distributed contactless interconnects in the form of broadside coupled coplanar waveguides (CPWs) as a test case. We find excellent agreement between experimental, full-wave simulations, and a distributed model of contactless interconnects. This work provides a general method to accurately characterize interconnects and to translate measurement reference planes beyond interconnect boundaries when one or more interconnect ports are not directly accessible.

We demonstrate a glass microwave microfluidic device for determining the permittivity of a wide range of liquid chemicals from 100 MHz to 30 GHz with associated uncertainties. Conventional microwave microfluidic devices use polymer-based microfluidic layers for fluid delivery, but these polymers swell in organic solvents and are not suitable for many applications. Our device incorporates glass microfluidic channels with platinum coplanar waveguides (CPWs) to provide a solvent-resistant architecture for broadband dielectric spectroscopy. We utilize broadband scattering parameter measurements with a vector network analyzer (VNA) on a wafer probing station and multiline thru-reflect–line (mTRL) calibrations to extract the distributed circuit parameters of transmission lines and solve for fluid permittivity. In this work, we demonstrate the utility of the device by measuring the permittivity of four organic solvents difficult to measure otherwise: hexane, heptane, decane, and toluene.

We demonstrate three different broadside-coupled coplanar waveguides (CPWs) to 325 GHz that do not require bump bonds, wire bonds, or direct metal-to-metal bonding. Our design approach used a multimoded distributed theory rather than the conventional $\lambda/4 $ approximation. The different interconnects had insertion losses better than 0.7 dB at 63, 93, and 120 GHz.