Grazing incidence reflectivity of high-Tc superconductors: mm wave technique of conductivity measurements
Non-resonant nondestructive technique has been described for investigation of high-temperature superconductive and relative materials through the measurement of the microwave reflection at grazing incidence. As authors discussed earlier, a reflection coefficient of the electromagnetic wave at grazin...
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irk-123456789-1058032016-09-23T23:05:31Z Grazing incidence reflectivity of high-Tc superconductors: mm wave technique of conductivity measurements Gubin, A.I Cherpak, N.T. Lavrinovich, A.A. Радиофизика твердого тела и плазмы Non-resonant nondestructive technique has been described for investigation of high-temperature superconductive and relative materials through the measurement of the microwave reflection at grazing incidence. As authors discussed earlier, a reflection coefficient of the electromagnetic wave at grazing incidence can be used to determine an absolute complex conductivity over a wide temperature and frequency range. As of now the experimental measurement setup was realized in millimeter wave range using waveguide phase bridge based approach. The conductivity of YBa₂Cu₃O₇₋δ film was measured at temperatures higher than critical. Описан метод неразрушающего микроволнового исследования высокотемпературных сверхпроводников и родственных материалов посредством измерения их коэффициента отражения при скользящих углах падения. Измерения коэффициента отражения при скользящих углах падения электромагнитной волны могут быть использованы для получения абсолютных значений комплексной проводимости образца в широком температурном и частотном диапазонах. Разработана и реализована экспериментальная установка на основе фазового моста в миллиметровом диапазоне длин волн. Измерена проводимость YBa₂Cu₃O₇₋δ-пленок при температурах выше критической. Описано метод неруйнівного мікрохвильового дослідження високотемпературних надпровідників та споріднених матеріалів за допомогою вимірювання їх коефіцієнта відбиття при ковзних кутах падіння. Вимірювання коефіцієнта відбиття при ковзних кутах падіння електромагнітної хвилі можуть застосовуватись для отримання абсолютних значень комплексної провідності зразка в широкому температурному та частотному діапазонах. Розроблено та реалізовано експериментальну установку на базі фазового мосту в міліметровому діапазоні довжин хвиль. Виміряно провідність YBa₂Cu₃O₇₋δ-плівок при температурах вищих за критичну. 2010 Article Grazing incidence reflectivity of high-Tc superconductors: mm wave technique of conductivity measurements / A.I. Gubin, N.T. Cherpak, A.A. Lavrinovich // Радіофізика та електроніка. — 2010. — Т. 15, № 2. — С. 87-91. — Бібліогр.: 27 назв. — англ. 1028-821X http://dspace.nbuv.gov.ua/handle/123456789/105803 537.312.62 en Радіофізика та електроніка Інститут радіофізики і електроніки ім. А.Я. Усикова НАН України |
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Радиофизика твердого тела и плазмы Радиофизика твердого тела и плазмы |
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Радиофизика твердого тела и плазмы Радиофизика твердого тела и плазмы Gubin, A.I Cherpak, N.T. Lavrinovich, A.A. Grazing incidence reflectivity of high-Tc superconductors: mm wave technique of conductivity measurements Радіофізика та електроніка |
| description |
Non-resonant nondestructive technique has been described for investigation of high-temperature superconductive and relative materials through the measurement of the microwave reflection at grazing incidence. As authors discussed earlier, a reflection coefficient of the electromagnetic wave at grazing incidence can be used to determine an absolute complex conductivity over a wide temperature and frequency range. As of now the experimental measurement setup was realized in millimeter wave range using waveguide phase bridge based approach. The conductivity of YBa₂Cu₃O₇₋δ film was measured at temperatures higher than critical. |
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Article |
| author |
Gubin, A.I Cherpak, N.T. Lavrinovich, A.A. |
| author_facet |
Gubin, A.I Cherpak, N.T. Lavrinovich, A.A. |
| author_sort |
Gubin, A.I |
| title |
Grazing incidence reflectivity of high-Tc superconductors: mm wave technique of conductivity measurements |
| title_short |
Grazing incidence reflectivity of high-Tc superconductors: mm wave technique of conductivity measurements |
| title_full |
Grazing incidence reflectivity of high-Tc superconductors: mm wave technique of conductivity measurements |
| title_fullStr |
Grazing incidence reflectivity of high-Tc superconductors: mm wave technique of conductivity measurements |
| title_full_unstemmed |
Grazing incidence reflectivity of high-Tc superconductors: mm wave technique of conductivity measurements |
| title_sort |
grazing incidence reflectivity of high-tc superconductors: mm wave technique of conductivity measurements |
| publisher |
Інститут радіофізики і електроніки ім. А.Я. Усикова НАН України |
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2010 |
| topic_facet |
Радиофизика твердого тела и плазмы |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/105803 |
| citation_txt |
Grazing incidence reflectivity of high-Tc superconductors: mm wave technique of conductivity measurements / A.I. Gubin, N.T. Cherpak, A.A. Lavrinovich // Радіофізика та електроніка. — 2010. — Т. 15, № 2. — С. 87-91. — Бібліогр.: 27 назв. — англ. |
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Радіофізика та електроніка |
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2025-07-07T17:24:34Z |
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__________
ISSN 1028–821X Радиофизика и электроника, 2010, том 15, № 2, с. 87–91 © ИРЭ НАН Украины, 2010
УДК 537.312.62
GRAZING INCIDENCE REFLECTIVITY OF HIGH-Tc SUPERCONDUCTORS:
MM WAVE TECHNIQUE OF CONDUCTIVITY MEASUREMENTS
A. I. Gubin, N. T. Cherpak, A. A. Lavrinovich
A. Usikov Institute of Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12, Ac. Proskura Str., Kharkov, 61085, Ukraine
E-mail: gubin@ire.kharkov.ua
Non-resonant nondestructive technique has been described for investigation of high-temperature superconductive and relative ma-
terials through the measurement of the microwave reflection at grazing incidence. As authors discussed earlier, a reflection coefficient of the
electromagnetic wave at grazing incidence can be used to determine an absolute complex conductivity over a wide temperature and frequen-
cy range. As of now the experimental measurement setup was realized in millimeter wave range using waveguide phase bridge based ap-
proach. The conductivity of YBa2Cu3O7- film was measured at temperatures higher than critical. Fig. 5. Ref.: 27 titles.
Key words: grazing incidence reflectivity, microwave conductivity, superconducting films.
Microwave impedance properties study of
various materials including high-temperature super-
conductors (HTS) plays important role in fundamen-
tal physics and engineering. Different techniques are
used for the mentioned above investigation. A num-
ber of the techniques make use of different resonant
structures [1]. The other ones are based on measure-
ment of microwave power transmitted through or
reflected from HTS sample [1]. The first investiga-
tion of conductivity by measurements of signal
transmitted through the thin superconducting film in
cylindrical waveguide was performed using certain
assumptions to obtain complex value by measured
real part of the transmission coefficient [2]. The fur-
ther investigations was performed without any ap-
proximations by measuring of the real parts of trans-
mission and reflection coefficients [3, 4]; by measu-
ring complex value of the transmission coefficient
[5–7] and by measuring of the complex reflected
signal [8]. As a form of the non-resonant method, the
technique based on short circuit termination in a co-
axial cable was also used [9, 10]. The investigation of
complex conductivity by non-resonant method is
possible over a wide frequency range and allows ob-
taining absolute values of imaginary part of complex
conductivity (penetration depth) while by the reso-
nant methods it is necessary to use fitting proce-
dure [11]. Moreover another advantage of the method
is the possibility of the investigations in the tempera-
ture region close to and higher the superconductor
critical temperature, where the resonant methods has
pure accuracy [12]. This fact makes the method very
useful for investigations of fluctuation conductivity
(which is mainly studied in DC and there is only few
works in microwave region [13–17]) and pseudogap
effects (which is one of challenges in physics of un-
conventional superconductivity) [18]. Unfortunately
the investigations of the transmitted signal are appli-
cable only for thin films of thickness less than a field
penetration depth. Although the reflection coefficient
for a thick conducting plate (which is normal to a
longitudinal axis of the waveguide) is close to unity.
It has small changes under large variation of the
sample conductivity [2, 3, 8]. It is evident from a
simple relation for absolute value R of the reflection
coefficient:
,
4
1
0Z
R
R s
where Rs is surface resistance of the sample under
test and Z0 is characteristic impedance of free space.
The relation Rs << Z0 is true for all conductors inclu-
ding superconductors.
However situation could be improved by us-
ing grazing incident p-polarized wave. This fact was
recently discovered in the infrared [19] and millime-
ter [20] wavebands under free-space and rectangular
waveguide conditions accordingly. In this case sensi-
tivity of the reflection coefficient to conductivity
changes can be increased by order of values and
higher [21]. As it is shown by authors, this fact is
connected to decreasing of the p-polarized wave re-
flection coefficient by the approaching to Brewster
angle. The Brewster angle is close to 90 degrees for
conducting plate, but it is different for the samples
with various conductivity, e. g. for superconductor in
normal and superconducting states. As a result, the
reflection coefficient sensitivity to conductivity
changes rises under grazing incidence angles condi-
tions [22].
The report gives a description of experi-
mental setup, where the idea of grazing incidence re-
flecti-vity technique of conductivity measurement is
realized in millimeter wavelength range using wave-
guide phase bridge-based approach. The first results of
the method application to investigation of HTS materi-
als are presented. YBa2Cu3O7- film (Tc 92 K) of
300 nm thickness deposited on 0,3 mm sapphire sub-
strate with CeO2 buffer layer was studied.
1. The experimental setup. To realize the
grazing incidence of the p-polarized wave on a sam-
ple in Ka-band, the special rectangular waveguide
section with fundamental mode H10 (fig. 1) was de-
mailto:gubin@ire.kharkov.ua
A. I. Gubin et al. / Grazing incidence reflectivity…
_________________________________________________________________________________________________________________
88
veloped. The section has been realized by oblique
short-circuit termination by the measured sample.
The temperature sensor is placed on a top of the
sample. An angle of incidence was chosen equal to
80 degrees on the basis of the theoretical study
[21, 22].
Temperature
sensor
Spring
Sample
Flange Screw
Waveguide
Pin
Fig. 1. Waveguide section
The computer-controlled experimental setup
(fig. 2) for investigation of temperature dependence
of complex reflection coefficient was developed in
Ka-band based on phase bridge method [23].
Fig. 2. Schematic diagram of the experimental setup for measure-
ment of complex reflection coefficient
A magic-Tee 1 splits the signal of micro-
wave oscillator in two branches. The first branch,
which is a reference, consists of attenuator 1 and
phase shifter. The latter devices have been improved
to achieve digital control and to obtain data by PC.
The second branch, which is a measuring one, in-
cludes attenuator 2 and circulator. Attenuator 2 is
intended for isolation and a circulator allows decou-
pling incident and reflected waves in the waveguide
section. Sample under test with a waveguide section
is placed in the cryostat which allows to perform
measurements in a wide temperature range, namely
from liquid nitrogen temperature up to room one.
Microwave signal from both branches as a result of
combining by magic-Tee 2 is converted in DC volt-
age by detector. Thereafter the signal is amplified
and converted to digital by the designed interface and
passes into PC for further processing. The tempera-
ture at the sample surface was determined by a sensor
placed in the copper plate (fig. 1) which is on a top of
the sample. The changes of the phase shift and losses
were recorded by PC simultaneously with the tem-
perature changes using interface.
The special code was written to control the
measurement process. It allows one to detect temper-
ature changes of the sample, change positions of both
attenuator1 and a phase shifter in a reference branch
of the phase bridge in order to achieve compensation
of the bridge output signal throughout minimum of
the detected signal. At the same time the code allows
determining positions of the attenuator and phase
shifter in a reference branch and represents tempera-
ture dependencies in real time. The minimum detect-
able phase shift and attenuation in measuring system
were 0.1 degree and 0.03 dB, respectively.
2. Calibration. To obtain absolute values of
the complex reflection coefficient the calibration of
the setup is needed. It was performed by measuring
of samples with known characteristics. The relation
of the measured Rm and actual Ra reflection
coefficients is determined by [9]:
,
1 Sa
Ra
Dm
ER
ER
ER
where ,RE SE and DE are coefficients specified by
imperfections such as losses and reflection in the
microwave waveguide transmission line. RE is the
reflection tracking which is connected to the losses
and phase shift in the transmission line and SE is
referred to as the source match. The error coefficient
DE is the directivity, which arises from the imperfect
nature of the circulator and reflections due to wave-
guide connections. Three calibration measurement
cycles were performed to obtain temperature depend-
ence of the three calibration coefficients by solving
system of equations for each temperature point. Bulk
copper, titanium and absorber were used as calibra-
tion samples. The samples were chosen with different
enough but known values of conductivity. Absorber
reflection coefficient is close to zero in a whole tem-
perature region, which was proven by low standing
wave ratio (SWR) of the waveguide section with
such sample (less than 1.1). This means that the ab-
sorber measured reflection coefficient is equal to
calibration coefficient .DE The actual reflection coef-
ficient could be obtained by equation:
.
DmSR
Dm
a
EREE
ER
R
Temperature dependence of microwave losses
mRL log20 in measurement branch of the phase
A. I. Gubin et al. / Grazing incidence reflectivity…
_________________________________________________________________________________________________________________
89
bridge for three calibration samples (▲ – absorber,
■ – titanium, ● – copper) and superconducting
YBa2Cu3O7- film (♦) at frequency 39.6 GHz is
shown in fig. 3, a. Changes of the losses at S-N tran-
sition are equal to about 1.5 dB, which is well meas-
urable value (in comparison with normal incidence
case [20]).
80 85 90 95 100
5
10
L
,
d
B
T, K
a)
80 85 90 95 100
0,90
0,95
R
T, K
b)
Fig. 3. Losses of YBa2Cu3O7- superconducting film and three
calibration samples dependence on temperature at frequency
39.6 GHz (a) and temperature dependence of the film reflection
coefficient (b)
Knowing the loss of the copper, absorber
and titan samples depending on temperature, it is
possible to obtain absolute reflection coefficient of
the superconducting film – dielectric substrate struc-
ture depending on temperature (fig. 3, b) by solving
the abovementioned equations.
3. Results and discussion. Complex con-
ductivity (or complex surface impedance) could be
obtained by plane wave approach. Full reflection
coefficient r from multilayer structure could be cal-
culated by using Fresnel equations, Snell’s law and
dielectric function by [21, 22]:
,
1 2
2020
2
202002
02 i
i
er
er
r
where 02 is the total transmission coefficient through
the first (i. e. superconducting) layer taking all the
reflections into account; t02 and r02 are the Fresnel
transmission and reflection coefficients for the se-
cond interface; 02 reflection coefficient from the
first layer which takes into account the interference
which occurs within the film due to the reflection at
the last interface; 20 and 02 are introduced analo-
gously to 02 and 20; kd2 p, k 2 /, where is
the wavelength, d2 is the substrate thickness and
Sp are the refractive index of the substrate.
Reflection coefficient
2
rR could be recalculated
from film permittivity f knowing film thickness,
substrate thickness and permittivity (which was taken
from [24]), and also angle and frequency of incident
wave.
Eigen waves in the waveguide including a
basic H10-wave are not plane ones but they can be
represented as a superposition of the plane waves, so
our approximation is hold true at a certain orientation
of microwave electric field with regard to plane of
the sample under test, i. e. microwave electric field
E
must lie in incident plane of guide wave (see
fig. 1). The plane wave approach is more useful than
electromagnetic analysis in the waveguide due to its
simplicity. The exact electromagnetic analysis is
complex at angles, higher than 78 degrees due to a
large length of the measurement sample at a wave-
guide shear comparable to wavelength. Besides the
data obtained by plane wave approach and using ex-
act electromagnetic analysis are agreed for thin su-
perconducting films and bulk samples in both normal
and superconducting states up to 78 degrees of inci-
dence angles.
To obtain complex conductivity from
measured sample reflection coefficient it is neces-
sary to find relation of complex conductivity and
reflection coefficient. It is impossible to solve this
problem analytically therefore iteration procedure
was used.
To check reliability of the measurement ap-
proach and calibration procedure the investigation of
conductivity of silicon, YBaCuO ceramics at room
temperature (which was used only as a test material
and does not has as good quality as superconducting
film, mentioned above, but is thick) and duralumin
samples was performed by two methods. The first
one is a given method and the second, i. e. reference,
one is a method based on whispering gallery mode
sapphire disk resonator with the sample as conduc-
ting endplate [25]. The data obtained by both meth-
ods conform to each other well within the measure-
ment errors (fig. 4).
A. I. Gubin et al. / Grazing incidence reflectivity…
_________________________________________________________________________________________________________________
90
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
Cu
Ti
Si
YBaCuO
,
S
m
/m
(
g
iv
en
m
et
h
o
d
)
, Sm/m (QDR Method)
Duralumin
Fig. 4. Conductivity of the bulk test samples (silicon, ceramics,
duralumin) and calibration samples (titanium and copper) obtained
by given method and method based on whispering gallery mode
resonator. All of the samples were at room temperature
The measured dependence of the real part of
YBa2Cu3O7- film complex conductivity is shown in
fig. 5. The calculated dependence of the conductivity
on temperature is shown by solid line.
100 120 140 160 180
1,0
1,5
2,0
2,5
1
m
1
·1
0
6
T, K
Fig. 5. Experimental temperature dependence of YBa2Cu3O7-
superconducting film conductivity (points) and calculated results
on the basis of linear dependence of the sample resistance in nor-
mal state (line)
Here linear dependence of the normal state
film resistance on temperature and assumption that
normal state conductivity at T Tc is equal to
1.35·10
6
Sm/m were taken into account. There is a
good coincidence of the theoretical and experimental
results in temperature region higher than 120 K. Ex-
perimental and theoretical conductivities at tempera-
tures 92…120 K differ and experimental values are
higher than theoretical ones. This distinction is obvi-
ously connected with fluctuation conductivity phe-
nomenon of the superconducting YBCO film
[16, 26].
Conclusion. Thus, the possibility to study
superconductor impedance properties by measure-
ments of reflection coefficient at grazing incidence
angles in rectangular waveguide with a sample in-
clined at the large angle (more than 80°) in a plane of
microwave electric field is shown. The method al-
lows performing study of the superconductors and
other materials, e. g. CMR substances [27], conduc-
tivity of which changes under different external con-
ditions such as temperature, magnetic field, etc. The
technique to obtain such HTS characteristics as com-
plex conductivity or surface impedance at tempera-
ture above Tc using measured complex reflection
coefficient, calibrated by absolute values of reflection
coefficient of the known materials, has been shown.
The applicability of the method to studying the mi-
crowave properties of YBa2Cu3O7- superconducting
film in normal state and near Tc was demonstrated.
Although only the real part of conductivity is mea-
sured in the present work, the measurement of the
imaginary part is possible as well. It is worthy to note
also, that although a given work was performed in
single frequency mode, the grazing incidence reflec-
tivity technique is frequency broadband one in prin-
ciple. For realization of such a broadband approach,
the sweep oscillator or frequency synthesizer is nec-
essary.
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МЕТОД ИССЛЕДОВАНИЯ ПРОВОДИМОСТИ
ВЫСОКОТЕМПЕРАТУРНЫХ
СВЕРХПРОВОДНИКОВ ПРИ ПОМОЩИ
ИЗМЕРЕНИЯ КОЭФФИЦИЕНТА ОТРАЖЕНИЯ
ВОЛНЫ ПРИ СКОЛЬЗЯЩИХ УГЛАХ
ПАДЕНИЯ В МИЛЛИМЕТРОВОМ
ДИАПАЗОНЕ
А. И. Губин, Н. Т. Черпак, A. A. Лавринович
Описан метод неразрушающего микроволнового
исследования высокотемпературных сверхпроводников и
родственных материалов посредством измерения их коэффи-
циента отражения при скользящих углах падения. Измерения
коэффициента отражения при скользящих углах падения
электромагнитной волны могут быть использованы для полу-
чения абсолютных значений комплексной проводимости об-
разца в широком температурном и частотном диапазонах.
Разработана и реализована экспериментальная установка на
основе фазового моста в миллиметровом диапазоне длин
волн. Измерена проводимость YBa2Cu3O7--пленок при темпе-
ратурах выше критической.
Ключевые слова: коэффициент отражения при
скользящих углах падения, микроволновая проводимость,
сверхпроводящие пленки.
МЕТОД ДОСЛІДЖЕННЯ ПРОВІДНОСТІ
ВИСОКОТЕМПЕРАТУРНИХ
НАДПРОВІДНИКІВ ЗА ДОПОМОГОЮ
ВИМІРЮВАННЯ КОЕФІЦІЄНТА ВІДБИТТЯ
ХВИЛІ ПРИ КОВЗНИХ КУТАХ ПАДІННЯ
У МІЛІМЕТРОВОМУ ДІАПАЗОНІ
О. І. Губін, М. T. Черпак, О. A. Лавринович
Описано метод неруйнівного мікрохвильового до-
слідження високотемпературних надпровідників та спорідне-
них матеріалів за допомогою вимірювання їх коефіцієнта
відбиття при ковзних кутах падіння. Вимірювання коефіцієнта
відбиття при ковзних кутах падіння електромагнітної хвилі
можуть застосовуватись для отримання абсолютних значень
комплексної провідності зразка в широкому температурному
та частотному діапазонах. Розроблено та реалізовано експе-
риментальну установку на базі фазового мосту в міліметрово-
му діапазоні довжин хвиль. Виміряно провідність YBa2Cu3O7--
плівок при температурах вищих за критичну.
Ключові слова: коефіцієнт відбиття при ковзних
кутах падіння, мікрохвильова провідність, надпровідні плівки.
Рукопись поступила 14 января 2010 г.
Печатается в авторской редакции.
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