Ordinary and Extraordinary Permittivities of 4H SiC at Different Millimeter-Wave Frequencies, Temperatures, and Humidities

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.