Complex Permittivities of Ultra-Low-Loss 4H-SiC from 55 GHz to 330 GHz

Hexagonal semiconductors such as GaN and SiC have important power applications at radio and millimeter-wave (mmW) frequencies. They are characterized by both ordinary and extraordinary permittivities, parallel and perpendicular to the densest packed c plane, respectively. However, due to the challenges of high-frequency measurements, little reliable data exist for these permittivities especially at mmW frequencies. Recently, for the first time, we reported the extraordinary permittivity of 4 HSiC at mmW frequencies using substrate-integrated waveguides. We now report the ordinary permittivity of the same material using several Fabry-Perot resonators to cover most mmW frequencies. The resulted relative ordinary permittivity of $9.76 \pm 0.01$ exhibits little dispersion and is significantly lower than the previously reported extraordinary permittivity of $10.2 \pm 0.1$. This confirms that both ordinary and extraordinary permittivities are needed for accurate design and model of devices fabricated on $\mathbf{4 H ~ S i C}$. By contrast, the measured loss tangent increases linearly from $3 \times 10^{-5}$ to $1.6 \times 10^{-4}$ from 55 GHz to 330 GHz and can be fitted with $(4.9 \pm 0.1) \times 10^{-16} f$, where f is the frequency in Hz. In fact, 4 H SiC is the lowest-loss solid we have ever measured. The present approaches for permittivity characterization can be extended to other solids.