Anna Osella

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.

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.

DyScO3 (DSO) is an attractive substrate on which to grow epitaxial thin films with extraordinary materials physics. However, its highly anisotropic permittivity makes some measurements exceedingly difficult: For instance, its permittivity tensor has not yet been fully characterized at millimeter-wave frequencies. While there are methods to characterize anisotropic permittivity at millimeter-wave frequencies, there are very few methods those are suitable for the small lateral dimensions that DyScO3 can be grown in. To overcome this lack in the material characterization, we tested an on-wafer method based on coplanar waveguides to measure the full anisotropic permittivity tensor from 0.1 to 110 GHz. We characterized two orthogonal sets of coplanar waveguides fabricated on each of two substrates with (001) and (110) crystallographic orientations to resolve the full permittivity tensor. To validate our measurements, we compared our results to data from dc parallel plate capacitors and THz time-domain spectroscopy. Our measurements fill the need for measurements of the permittivity of DyScO3, while the methodology, more generally, enables quantitative characterization of anisotropic dielectrics.