Analysis of broadband microwave conductivity and permittivity measurements of semiconducting materials

TL;DR

This paper introduces a comprehensive calibration and evaluation method for broadband microwave measurements of semiconducting materials, enabling accurate extraction of conductivity and permittivity across a wide frequency range, especially for insulators.

Contribution

It presents a novel, assumption-free calibration and evaluation procedure for broadband microwave measurements of semiconductors, including insulators, using a rigorous electromagnetic model.

Findings

The method accurately characterizes doped semiconductors up to 5 GHz.

Static current distribution model agrees with the frequency-dependent conductivity up to 1 GHz.

Application to Si:P at 1 K reveals insights into hopping transport phenomena.

Abstract

We perform broadband phase sensitive measurements of the reflection coefficient from 45 MHz up to 20 GHz employing a vector network analyzer with a 2.4 mm 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 5 GHz, 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 1 GHz. After a critical discussion we apply the developed method to the hopping transport in Si:P at temperature down to 1 K.