Complex Permittivity Measurement of Dielectric Substrate in Sub-THz Range

Abstract

In this article, three frequency independent optical paths are designed and analyzed. A two-parabolic-mirror system and a four-parabolic-mirror system are studied and developed over 140–220 GHz to achieve precision complex permittivity measurements of a dielectric substrate. To achieve a wide plane wave zone for the center of the four-parabolic-mirror system, two 80-mm-length corrugated horns are designed and fabricated for the measurement systems. The Gaussicity of the corrugated horn is larger than 97.4%. For the multiple reflection model and direct wave model, two closed-form expressions of loss tangent are derived from the transmission parameters (insertion losses) of the measurement systems. Meanwhile, the resolution and uncertainty of loss tangent can be calculated according to the working frequency, the thickness of the wafer, the real part of the relative permittivity, and the $| {{S_{21}}} |$ measurement uncertainty. The complex permittivity of the Rogers/Duroid series PCB substrates, which are commonly used at microwave frequencies, and silicon wafers are measured in G -band.