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We perform broadband phase sensitive measurements of the reflectioncoefficient from 45 MHz up to 20 GHz employing a vector network analyzer with a2.4 mm coaxial sensor which is terminated by the sample under test. While thematerial parameters (conductivity and permittivity) can be easily extractedfrom the obtained impedance data if the sample is metallic, no direct solutionis possible if the material under investigation is an insulator. Focusing ondoped semiconductors with largely varying conductivity, here we present aclosed calibration and evaluation procedure for frequencies up to 5 GHz, basedon the rigorous solution for the electromagnetic field distribution inside thesample combined with the variational principle; basically no limitingassumptions are necessary. A simple static model based on the electric currentdistribution proves to yield the same frequency dependence of the complexconductivity up to 1 GHz. After a critical discussion we apply the developedmethod to the hopping transport in Si:P at temperature down to 1 K.

Analysis of broadband microwave conductivity and permittivity measurements of semiconducting materials