Electricity: measuring and testing – Impedance – admittance or other quantities representative of... – Distributive type parameters
Reexamination Certificate
2000-08-04
2002-04-02
Metjahic, Safet (Department: 2858)
Electricity: measuring and testing
Impedance, admittance or other quantities representative of...
Distributive type parameters
C324S653000, C324S662000
Reexamination Certificate
active
06366096
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to a technique adapted to perform accurate measurements of the metallic and dielectric properties of materials at microwave frequencies; and more particularly, to an apparatus and method for determining the absolute screening length (or penetration depth) and surface resistance of metals or superconductors, either films or bulk, absolute complex conductivity and surface impedance of metals and superconductors, as well as for determination of dielectric constants and loss tangent of gases and liquids.
The present invention further relates to a technique using a resonant structure formed of a pair of substantially identical samples under investigation which are positioned in substantially parallel relationship each with respect to the other having a dielectric spacer of variable thickness disposed between the samples. The resonant frequency and quality factor vs. the variable thickness of the dielectric spacer are measured to be inserted in predetermined mathematical formulas correlated to the type of the samples in order to extract the absolute values of penetration depths and surface resistance for the samples. Extracted values of penetration depths and surface resistance are further used for determination of absolute complex conductivity and surface impedance of metals and superconductors in both films and bulk materials.
BACKGROUND OF THE INVENTION
Investigation of the microwave surface impedance Z
S
=R
S
+iX
S
of superconductors has been given prominence. Much of such prior investigations has been based on the pioneering works of Pippard and has been invigorated by the discovery of high temperature superconductors (HTS). An additional impetus for the development has been the appearance of a new family of synthesized microwave sources and network analyzers which has enabled a number of techniques to be developed.
Most of these techniques provide accurate determinations of the absolute value of the surface resistance, R
S
, and provide sensitive measurements of changes in the surface reactance X
S
=&mgr;
0
&ohgr;&lgr; or the magnetic penetration depth &lgr;. However, there still exists the problem of experimentally determining the absolute value of &lgr; since it is small, possibly on the order of tens to hundreds of nanometers. In fact, unlike R
S
measurements, there is no well-established universal and commonly accepted technique for determining the absolute penetration depth in superconductors.
Investigation of superconducting surface impedance is important since it yields valuable information about intrinsic (charge carrier density, pairing state symmetry, quasiparticle excitation spectrum and relaxation time) and extrinsic properties (microstructure) of the specimen under study. These properties can be deduced from the surface impedance Z
S
={square root over (i&mgr;
0
+L &ohgr;/&sgr;)} (local limit) measured as a function of temperature, applied magnetic field, doping, or impurity concentration, wherein &mgr;
0
is a constant of permeability of free space, and &ohgr; is an angular frequency of the field. The complex conductivity, &sgr;=&sgr;
1
−i&sgr;
2
, is a fundamental quantity which theories of superconductivity are able to calculate. However, the inability to determine both the surface resistance and the absolute value of &lgr; for the same sample often hampers effort to construct the complex conductivity from the surface impedance data. For example, the real part of the conductivity &sgr;
1
can be extracted from R
S
only if the absolute &lgr; is available.
The appearance of low loss HTS epitaxial thin films on single crystal dielectric substrates has led to a growing field of superconducting wireless communication. In this respect, knowledge of the surface impedance is important to obtain the optimum performance of superconducting RF/microwave components and circuits. Another important issue is the establishment of a standard characterization technique for HTS thin films for microwave applications.
Existing experimental techniques suitable for measurement of absolute &lgr; in superconductive thin films and single crystals may be divided into the following four categories: absolute length scale techniques, reflection or transmission measurements of electromagnetic fields (mutual inductance, microwave/millimeter wave, infrared (IR) spectroscopy), measurement of internal magnetic field distribution (muon spin rotation [&mgr;SR], neutron scattering), and Josephson tunneling experiments. Each of these techniques will be described in the following paragraphs.
1. Absolute Length Scale Techniques
An optimum way to measure an absolute screening length in a superconducting (or normal metal) sample is to determine an absolute length scale, l, which is comparable to and directly linked to the absolute value of &lgr;. Many of the existing techniques for measuring changes in &lgr; measure a signal proportional to the value of l−&lgr;, hence the greater the &lgr;/l ratio, the higher the sensitivity to the penetration depth. However, little effort has been made to measure an absolute &lgr; via determination of an absolute length scale due to the fact that in practice, the latter cannot be measured with sufficient accuracy.
The absolute length scale techniques are generally based on the effect of electromagnetic field exclusion in the Meissner state of a superconductor. For single crystals these include DC/AC magnetometry and RF/microwave resonator perturbation techniques. In all of them l is the specimen's linear dimension and the measured signal (for example, shift in the resonant frequency between the empty and perturbed resonator) is proportional to (l−&ggr;&lgr;)×(area of the sample), where &ggr;~l depends upon the sample geometry and the field configuration. Usually, for crystals &lgr;/l~10
−3
-10
−4
and the relevant calibration does not allow measurement of an absolute &lgr;.
In the case of a resonator in which all or a substantial part of it is made up of the superconductive material, l=&Ggr;/&mgr;
0
&ohgr;, where &Ggr; is the resonator geometrical factor. The resonant frequency is f
SC
≈f
0
(l−&lgr;/2l), where f
0
is the frequency of the same perfectly conducting resonator. Cavity-like resonators, such as end-plates or dielectric resonators have l on the order of the wavelength of electromagnetic radiation and the ratio &lgr;/l≦10
−4
is generally small.
Planar resonators, such as stripline or conventional parallel plates, carry a slowed-down electromagnetic wave with a phase velocity c
SW
=c/{square root over (∈
eff
+L (1+2+L &lgr;/s))}, where c is velocity of light in vacuum, ∈
eff
is the effective dielectric constant of the transmission line, and s is the dielectric thickness. Each have a high sensitivity to the penetration depth (down to 0.1 nm), since &lgr;/l=2&lgr;/s~10
−2
-10
−4
in this case. However, neither the cavity-like nor planar resonators are suitable for direct measurement of absolute &lgr; (except possibly for the coplanar resonator), and only changes in &lgr; may be extracted from the experiment.
The most common way to evaluate an absolute &lgr;(T=0) using the above techniques involves fitting of the measured temperature dependence of the parameter relevant to the changes in &lgr; (commonly, shift in the resonant frequency) to a theoretical dependence for &lgr;(T) (a proper electrodynamic description of the experimental structure is required). Usually, this procedure works adequately for conventional superconductors where appropriate models (two fluid or BCS) for &lgr;(T) are well established. However, such models fail in the presence of extrinsic effects in the sample under study. In the case of HTS there is a lack of suitable models for &lgr;(T), and usually the absolute &lgr; values deduced from experiment are strongly dependent (up to 50%) on the form of the temperature model assumed.
The other three categories of techniques generally
Anlage Steven Mark
Talanov Vladimir V.
Metjahic Safet
Nguyen Vincent Q.
Rosenberg , Klein & Lee
University of Maryland College Park
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