Analysis of broadband microwave conductivity and permittivity measurements of semiconducting materials

Abstract

We perform broadband phase sensitive measurements of the reflection coefficient from 45MHz up to 20GHz by employing a vector network analyzer with a 2.4mm coaxial sensor which is terminated by the sample under test. While the material parameters (conductivity and permittivity) can be easily extracted from the obtained impedance data if the sample is metallic, no direct solution is possible if the material under investigation is an insulator. Focusing on doped semiconductors with largely varying conductivity, here we present a closed calibration and evaluation procedure for frequencies up to 5GHz, based on the rigorous solution for the electromagnetic field distribution inside the sample combined with the variational principle; basically, no limiting assumptions are necessary. A simple static model based on the electric current distribution proves to yield the same frequency dependence of the complex conductivity up to 1GHz. After a critical discussion, we apply the developed method to the hopping transport in Si:P at temperature down to 1K.