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Hexagonal semiconductors such as 4H SiC have important high-frequency, high-power, and high-temperature applications. The applications require accurate knowledge of both ordinary and extraordinary relative permittivities, ε and ε||, perpendicular and parallel, respectively, to the c axis of these semiconductors. However, due to challenges for suitable test setups and precision high-frequency measurements, little reliable data exists for these semiconductors especially at millimeter-wave frequencies. Recently, we reported ε|| of 4H SiC from 110 to 170 GHz. This paper expands on the previous report to include both ε and ε|| of the same material from 55 to 330 GHz, as well as their temperature and humidity dependence enabled by improving the measurement precision to two decimal points. For example, at room temperature, real ε and ε|| are constant at 9.77 ± 0.01 and 10.20 ± 0.05, respectively. By contrast, the ordinary loss tangent increases linearly with the frequency f in the form of (4.9 ± 0.1)  10−16 f. The loss tangent, less than 1  10−4 over most millimeter-wave frequencies, is significantly lower than that of sapphire, our previous low-loss standard. Finally, both ε and ε|| have weak temperature coefficients on the order of 10−4 /°C. The knowledge reported here is especially critical to millimeter-wave applications of 4H SiC, not only for solid-state devices and circuits, but also as windows for high-power vacuum electronics. 

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 4H SiC at mmW frequencies using substrateintegrated 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 ± 0.01 exhibits little dispersion and is significantly lower than the previously reported extraordinary permittivity of 10.2 ± 0.1. This confirms that both ordinary and extraordinary permittivities are needed for accurate design and model of devices fabricated on 4H SiC. By contrast, the measured loss tangent increases linearly from 3  10−5 to 1.6  10−4 from 55 GHz to 330 GHz and can be fitted with (4.9 ± 0.1)  10−16 f, where f is the frequency in Hz. In fact, 4H SiC is the lowest-loss solid we have ever measured. The present approaches for permittivity characterization can be extended to other solids.