半导体材料宽带微波电导率和介电常数测量分析
Analysis of broadband microwave conductivity and permittivity measurements of semiconducting materials
摘要：
我们进行宽带相敏测量的反射系数从45 MHz到20 GHz采用矢量网络分析仪与2.4 mm的同轴传感器，这是终止的样品下测试。虽然材料参数（电导率和介电常数）可以很容易地从所获得的阻抗数据中提取，如果样品是金属的，没有直接的解决方案是可能的，如果被调查的材料是绝缘体。专注于杂质半导体，电导率变化很大，在这里，我们提出了一个封闭的校准和评估程序的频率高达5 GHz的，基于严格的解决方案的电磁场分布内的样品结合变分原理，基本上没有限制的假设是必要的。一个简单的静态模型的基础上的电流分布证明产生相同的频率依赖性的复杂的电导率高达1 GHz。经过严格的讨论后，我们将所发展的方法应用于温度低至1K的Si：P中的跳跃输运。
英文摘要：
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.
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