Measurement of Dielectric Loss in Silicon Nitride at Centimeter and Millimeter Wavelengths

This work presents a suite of measurement techniques for characterizing the dielectric loss tangent across a wide frequency range from $\sim$1 GHz to 150 GHz using the same test chip. In the first method, we fit data from a microwave resonator at different temperatures to a model that captures the two-level system (TLS) response to extract and characterize both the real and imaginary components of the dielectric loss. The inverse of the internal quality factor is a second measure of the overall loss of the resonator, where TLS loss through the dielectric material is typically the dominant source. The third technique is a differential optical measurement at 150 GHz. The same antenna feeds two microstrip lines with different lengths that terminate in two microwave kinetic inductance detectors (MKIDs). The difference in the detector response is used to estimate the loss per unit length of the microstrip line. Our results suggest a larger loss for SiN$_x$ at 150 GHz of ${\mathrm{\tan \delta\sim 4\times10^{-3}}}$ compared to ${\mathrm{2.0\times10^{-3}}}$ and ${\mathrm{\gtrsim 1\times10^{-3}}}$ measured at $\sim$1 GHz using the other two methods. {These measurement techniques can be applied to other dielectrics by adjusting the microstrip lengths to provide enough optical efficiency contrast and other mm/sub-mm frequency ranges by tuning the antenna and feedhorn accordingly.