Techniques for the Measurement of Complex Microwave Conductivity and the Associated Errors
TL;DR: In this paper, an attempt has been made to improve the reflection results from an analysis of the parameters of a circle diagram for reflection coefficient obtained on using a variable reactive termination after the semiconductor-filled waveguide section.
Abstract: Complex microwave conductivity of 9 /spl Omega/ /spl dot/ cm p-type silicon samples has been measured using conventional reflection and transmission bridges to examine their relative advantages and disadvantages. An attempt has been made to improve the reflection results from an analysis of the parameters of a circle diagram for reflection coefficient obtained on using a variable reactive termination after the semiconductor-filled waveguide section. In conformity with the calculated accuracy attainable from different types of measurement under the actual experimental condition, using commercial standards, the dielectric constant for the sample was found to be scattered over a region of /spl plusmn/0.4. It has been concluded that because of lack of accuracy in commercial standards for attenuation and phase shift, the potential accuracy of the conventional microwave methods falls too short of its mark to make any detinite conclusion about the effective mass of carriers in semiconductors at room temperatures.
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TL;DR: An overview of transmission/reflection-based methods for the electromagnetic characterisation of materials is presented in this article, which is applicable to conventional transmission reflection devices such as coaxial cables or waveguides.
Abstract: An overview of transmission/reflection-based methods for the electromagnetic characterisation of materials is presented. The paper initially describes the most popular approaches for the characterisation of bulk materials in terms of dielectric permittivity and magnetic permeability. Subsequently, the limitations and the methods aimed at removing the ambiguities deriving from the application of the classical Nicolson–Ross–Weir direct inversion are discussed. The second part of the paper is focused on the characterisation of partially conductive thin sheets in terms of surface impedance via waveguide setups. All the presented measurement techniques are applicable to conventional transmission reflection devices such as coaxial cables or waveguides.
92 citations
TL;DR: In this article, the use of the network analyzer to measure the dielectric properties of materials over a broad frequency range is described, with simple procedures for obtaining initial estimates and unambiguous solutions for the parameters.
Abstract: This paper outlines the use of the network analyzer to measure the dielectric properties of materials over a broad frequency range. The method described here is based on transmission techniques with simple procedures for obtaining initial estimates and unambiguous solutions for the dielectric parameters. A further feature is that this measurement technique provides a degree of self-checking for inconsistent results.
43 citations
TL;DR: A simple yet powerful method is proposed for removing the multiple solutions problem in the complex permittivity, ϵ, determination from measured transmission scattering parameter measurements of lossy materials by derived a one-variable objective function for fast evaluation.
Abstract: A simple yet powerful method is proposed for removing the multiple solutions problem in the complex permittivity, ϵ, determination from measured transmission scattering (S-) parameter measurements of lossy materials. The method uses amplitude-only measurements at two slightly separated frequencies to estimate an accurate initial guess. For this purpose, we derive a one-variable objective function for fast evaluation, which lends itself to measurement automation. The method provides an estimation for real and imaginary parts of the ϵ, which can be utilized as a measure for checking the correctness of initial ϵ estimate. The method is very useful for band-limited measurements. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 337–341, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24048
39 citations
TL;DR: In this paper, the cavity coupling factor in the absence of perturbation, together with the change in the reflected power and the cavity resonance frequency shift, are used for the determination of the material properties.
Abstract: Cavity perturbation techniques offer a very sensitive highly versatile means for studying the complex microwave conductivity of a bulk material. A knowledge of the cavity coupling factor in the absence of perturbation, together with the change in the reflected power and the cavity resonance frequency shift, are adequate for the determination of the material properties. This eliminates the need to determine the Q-factor change with perturbation which may lead to appreciable error, especially in the presence of mismatch loss. The measurement accuracy can also be improved by a proper choice of the cavity coupling factor prior to the perturbation.
22 citations
07 Oct 2003
TL;DR: In this paper, the free-space reflection and transmission coefficients of a silicon wafer sandwiched between two teflon plates which are quarter-wavelength at midband were measured in the frequency range of 11-12.5 GHz.
Abstract: A non-destructive, non-contact technique has been developed to characterize p-type and n-type silicon semiconductor wafers at microwave frequencies. The measurement system consists of a pair of spot-focusing horn lens antennas, mode transitions, coaxial cables and a vector network analyser (VNA). In this paper, the free-space reflection and transmission coefficients, S/sub 11/ and S/sub 21/, for a normally incident plane wave, are measured for a silicon wafer sandwiched between two teflon plates which are quarter-wavelength at midband. The actual reflection and transmission coefficient, S/sub 11/ and S/sub 21/, of the silicon wafers are calculated from the measured S/sub 11/ and S/sub 21/ of the teflon plate-silicon wafer-teflon plate assembly in which the complex permittivity and thickness of the teflon plates are known. From the complex permittivity, the resistivity and conductivity can be obtained. Results are reported in the frequency range of 11-12.5 GHz. The values of the dielectric constant obtained were close to published values for silicon wafers.
9 citations
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62 citations
01 Jun 1964
TL;DR: In this article, an accurate reflection bridge technique for measuring microwave conductivity and permittivity is described, and measurements of n-type silicon and p-type germanium at 24 Gc and at temperatures between 77° and 300° Kelvin are presented and compared with theory.
Abstract: The conduction process in semiconductors exhibits effects associated with inertia of the carriers when the observation frequency is comparable to the reciprocal of the relaxation time for randomization of momenta. These effects can cause significant changes in the conductivity and permittivity of germanium and silicon measured at ordinary microwave frequencies and should become increasingly important as semiconductor devices are developed for ultra-microwave applications. The present paper derives equivalent circuits which illustrate inertial effects and discusses their temperature dependence. A highly accurate reflection bridge technique for measuring microwave conductivity and permittivity is then described. Finally, measurements of conductivity and permittivity of n-type silicon and p-type germanium at 24 Gc and at temperatures between 77° and 300° Kelvin are presented and compared with theory. At 77°, the inertial effects are found to be largest for the p-type germanium and cause the microwave conductivity to be less than the dc conductivity by a factor of one-half.
59 citations
TL;DR: In this article, the complex microwave conductivity of lightly-doped n and p-type silicon and genmanium was measured by observing the reflectivity of the circular T E01 mode at 48 GHz and were thus free of errors caused by the impedance of the waveguide.
Abstract: This paper presents measurements of the complex microwave conductivity of lightly‐doped n‐ and p‐type silicon and genmanium as functions of impurity concentration and of temperature between 77° and 300°K. The measurements were obtained by observing the reflectivity of the circular T E01 mode at 48 GHz and are thus free of errors caused by the impedance of the waveguide‐sample contact. Analysis utilized currently accepted scattering models including ionized impurity scattering, intravalley acoustic and optical mode scattering, and intervalley scattering. The results are used to investigate the temperature and doping dependence of the average relaxation time and the conductivity ``effective'' mass.
47 citations
TL;DR: In this paper, the authors used the TE01° mode of circular waveguide in a ''reflection coefficient bridge'' to eliminate the source of error caused by the impedance of the contact between the sample and the broad waveguide wall.
Abstract: Microwave conductivity of semiconductors determined from transmission or reflection of the dominant mode of rectangular waveguide may contain a significant error caused by the impedance of the contact between the sample and the broad waveguide wall. This error increases with increasing bulk conductivity. The present paper describes a technique which eliminates this source of error by utilizing the TE01° mode of circular waveguide in a ``reflection coefficient bridge.'' Measurements of intrinsic germanium at 48 GHz show no contact influence over the conductivity range between 2 and 2×103 mho/m. In contrast, the conductivity measured with a conventional rectangular waveguide transmission bridge saturates at about 50 mho/m.
34 citations