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РАДИОФИЗИКА, ЭЛЕКТРОНИКА, АКУСТИКА
Известия Саратовского университета. Новая серия. Серия: Физика. 2022. Т. 22, вып. 2. С. 123-130
Izvestiya of Saratov University. Physics, 2022, vol. 22, iss. 2, pp. 123-130
https://fizika.sgu.ru https://doi.org/10.18500/1817-3020-2022-22-2-123-130
Article
Tamm resonances control in one-dimensional microwave photonic crystal for measuring parameters of heavily doped semiconductor layers
A. V. Skripal0, D. V. Ponomarev, A. A. Komarov, V. E. Sharonov
Saratov State University, 83 Astrakhanskaya St., Saratov 410012, Russia
Alexander V. Skripal, [email protected], https://orcid.org/0000-0001-7448-4560 Denis V. Ponomarev, [email protected], https://orcid.org/0000-0002-7822-937X Andrey A. Komarov, [email protected], https://orcid.org/0000-0002-9869-7920 Vasily E. Sharonov, [email protected], https://orcid.org/0000-0001-6035-7747
Abstract. The possibility has been explored to control the photonic Tamm resonances (TRs) in the one-dimensional microwave photonic crystal (MPC) with the dielectric filling by changing the thickness of the MPC's outer layer adjacent to the heavily doped layer of the semiconductor GaAs structure. The controlled photonic TRs have been used to measure the conductivity of the heavily doped semiconductor layer. It has been shown that depending on the conductivity of the layer the specific tuning of the TR frequency is necessary in order to achieve a high sensitivity of the TR to the change of the conductivity. The possibility of observing the plasma resonance in the infrared range has additionally allowed to determine the concentration and mobility of free charge carriers in the heavily doped layer of the GaAs structure.
Keywords: conductivity measurement, heavily doped semiconductor, microwave photonic crystals, plasma resonance, Tamm resonances, X-band
Acknowledgements: This work was supported by the Ministry of Science and Higher Education of the Russian Federation in the framework of the State task (project No. FSRR-2020-0005).
For citation: Skripal A. V., Ponomarev D. V., Komarov A. A., Sharonov V. E. Tamm resonances control in one-dimensional microwave photonic crystal for measuring parameters of heavily doped semiconductor layers. Izvestiya of Saratov University. Physics, 2022, vol. 22, iss. 2, pp. 123-130. https://doi.org/10.18500/1817-3020-2022-22-2-123-130
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC0-BY 4.0)
Научная статья УДК 621.372.2
Управление таммовскими резонансами в одномерных СВЧ фотонных кристаллах для измерения параметров сильнолегированных полупроводниковых слоев
А. В. Скрипаль0, Д. В. Пономарев, А. А. Комаров, В. Е. Шаронов
Саратовский национальный исследовательский государственный университет имени Н. Г. Чернышевского, Россия, 410012, г. Саратов, ул. Астраханская, д. 83
Скрипаль Александр Владимирович, доктор физико-математических наук, профессор, заведующий кафедрой физики твердого тела, [email protected], https://orcid.org/0000-0001-7448-4560
НАУЧНЫЙ ОТДЕЛ
Пономарев Денис Викторович, кандидат физико-математических наук, доцент кафедры физики твердого тела, [email protected], https://orcid.org/0000-0002-7822-937X
Комаров Андрей Александрович, аспирант кафедры физики твердого тела, [email protected], https://orcid.org/0000-0002-9869-7920
Шаронов Василий Евгеньевич, магистрант кафедры физики твердого тела, [email protected], https://orcid.org/0000-0001-6035-7747
Аннотация. Исследована возможность управления фотонными таммовскими резонансами в одномерном СВЧ фотонном кристалле с диэлектрическим заполнением с помощью изменения толщины слоя фотонного кристалла, граничащего с сильнолегированным слоем полупроводниковой GaAs структуры. Управляемые фотонные таммовские резонансы в микроволновом диапазоне частот использованы для измерения удельной электропроводности сильнолегированных полупроводниковых слоёв. Показано, что для достижения высокой чувствительности таммовского резонанса к изменению удельной электропроводности сильнолегированного слоя, необходима определенная перестройка частоты таммовского резонанса, величина которой определяется величиной удельной электропроводности сильнолегированного слоя. Возможность наблюдения плазменного резонанса в инфракрасном диапазоне позволило определить концентрацию и подвижность свободных носителей заряда в сильнолегированном слое полупроводниковой GaAs структуры. Ключевые слова: измерение проводимости, сильно легированный полупроводник, СВЧ фотонные кристаллы, плазменный резонанс, таммовские резонансы, Х-диапазон
Благодарности: Работа поддержана Минобрнауки России в рамках государственного задания (проект № FSRR-2020-0005). Для цитирования: СкрипальА. В., Пономарев Д. В., Комаров А. А., Шаронов В. Е. Управление таммовскими резонансами в одномерных СВЧ фотонных кристаллах для измерения параметров сильнолегированных полупроводниковых слоев // Известия Саратовского университета. Новая серия. Серия: Физика. 2022. Т. 22, вып. 2. С. 123-130. https://doi.org/10.18500/1817-3020-2022-22-2-123-130 Статья опубликована на условиях лицензии Creative Commons Attribution 4.0 International (CC-BY4.0)
Introduction
One of the directions in the development of microwave technology is the creation of microwave components based on periodic structures called Bragg microwave structures or microwave photonic crystals (MPC) [1-5]. The appearance of resonances (defect modes) in MPC due to the introduction of elements that disturb the periodicity of the MPC makes it possible to create measurement techniques of the material parameters and structures in the microwave range.
The materials and samples under test, such as dielectrics, polar liquids, composites, and structures with semiconductor layers, are generally inserted inside the MPC, most commonly in its central layer [1, 6-9].
However, this method has a number of limitations associated with the almost complete disappearance of the defect mode in the MPC's band gap when the samples characterized by high losses are introduced into the MPC. The disappearance of the defect mode is observed, for example, at the measurement of the samples containing thin highly conducting nanolayers.
Thin highly conducting layers are used in a wide range of microwave technology applications. Microwave matched loads, bolometric power meters of the millimeter and sub-terahertz ranges, electromagnetic shields, and elements of integrated microwave circuits are created on their basis [10-16]. Highly conducting films, created using various conducting ink printing technologies, are essential elements of
flexible electronics and photonics with large areas [17-26].
The studies of thin conducting layers using transmission line methods [27-30], as a rule, are based on the transmission/reflection coefficient measurement. The range of measured thicknesses and conductivities is determined by the dynamical range of the measured transmission/reflection coefficients of the used measuring system. For implementing resonator measurement methods [27, 31, 32], which provide a wider range of measured thicknesses and conductivities, it becomes necessary to create a precision high-Q resonator and carry out its preliminary calibration without a sample.
One of the approaches providing measurements of highly conducting layers in the microwave range is the use of surface states in MPCs. The approach was successfully applied to measure the conductivity of metal nanolayers [33]. However, the measurement ranges of the thickness and conductivity are limited due to the fact that the pronounced Tamm resonance (TR) is observed only at specific values of the thickness and conductivity of the metal nanolayer.
In this work, we have developed an approach aimed at solving the problem of diagnostics of conducting layers with high and extremely high conductivity, which are used in various fields of microwave technology. This is especially important for diagnostics of conducting graphene structures with thicknesses of several nanometers as well as heavily doped semiconductor layers with thicknesses from tens of nanometers to several micrometers.
о
-10
PQ
"О OJ
о
с
3
I -20
To achieve this goal, it is proposed to tune the Tamm resonance's frequency in the MPC depending on the thickness and conductivity of the conducting layers under test.
The possibility to tune the frequency and amplitude of the TR in the optical range was demonstrated in a number of works [34-39].
Note, that in contrast to the optical range, in which the tuning of the TR can be carried out both by a change of the conductivity and thickness of the conducting layer, and by a change of the parameters of the photonic crystal, in the MPC, a change of the conductivity and thickness of the conducting layer does not change the frequency of the TR, but only its amplitude.
In this regard, in order to observe a pronounced TR at different values of the conductivity and thickness of the conducting layer, we have implemented a frequency control procedure of the TR in the MPC by changing the thickness of the outer layer of the MPC adjacent to the conducting layer.
1. Computer simulation of controlling the TR characteristics
The MPC assembled from Al2O3 ceramic (the odd positions, e = 9.6, the thickness - 0.5 mm) and teflon (the even positions, e = 2.0, the thickness -18 mm) layers has been tested in the range 7-13 GHz. The MPC consisted of 11 layers; the thickness of the one of the outer layers is varied.
The semiconductor structure under test consisted of three gallium arsenide GaAs layers. The semiconductor structure was placed behind the MPC in such a way that the highly doped epitaxial n+-layer was directly adjacent to its outer dielectric layer. In this case, two configurations were considered: the thickness of the MPC's outer layer adjacent to the n+-layer of the GaAs structure dL was 0.5 mm (configuration 1 in Fig. 1), the thickness of the MPC's outer layer adjacent to the n+-layer of the GaAs structure dL was 1.0 mm (configuration 2 in Fig. 1).
To find out the possibility to solve the problem of measuring thin conducting layers with high and extremely high conductivity using frequency-controlled TRs, the transmission (S21) and reflection (511) coefficients of the MPC containing a semiconductor structure with a conductivity of the n+ -layer 0.8 • 105 ^-1m-1 and 1.6 • 105 ^-1m-1 were calculated (Fig.2).
Fig. 1. Design of the one-dimensional waveguide MPC with the semiconductor n+-n-/-structure: 1 - ceramic layer, 2 -teflon layer, 3 - n+-n-/-structure, 4, 5, 6 - n+, n and /-layers, 7 - outer layer (ceramic) of the photonic crystal with the changed thickness, adjacent to the n+-layer
-a
с
cd
u о
с
3 о
и q=
u Pi
PQ -a
<0 о я
-О
s
U
0
1
а
с
OJ
Pi
-30
-40
-50
\i lp\j
It / '] \ \ /
ft Ю
7
9 10 11
Frequency, GHz
12 13
9 10 11 Frequency, GHz
b
12 13
Fig. 2. Calculated Sn (curves 1), S21 (curves 2) of the MPC adjacent to the n+-layer of the semiconductor structure with the conductivity equal to 0.8 • 105 Q-1m-1 (solid curves) and 1.6 • 105 Q-1m-1 (dashed curves) for two thicknesses di of the MPC's outer layer: a - 0.5 mm, b - 1 mm. S21 of the MPC without the semiconductor structure is curve 3
The coefficients S11 and S21 were calculated by the transfer matrix method with allowance for only the fundamental H10 wave type propagation in the waveguide [33, 40, 41].
а
The frequency of the TR was controlled by varying the thickness of the MPC's outer Al2O3 ceramic layer adjacent to the n+ -layer.
As follows from the calculation results, for the thickness dL of the MPC's outer layer adjacent to the n+ -layer of the GaAs structure equal to 0.5 mm (this is the thickness of all odd layers of the MPC), two resonances appear at frequencies /Tamm1 = 7.476 GHz and /Tamm2 = 12.4 GHz. When the conductivity of the n+-layer changes in the range from 0.8x x 105 ^m"1 to 1.6 • 105 Q^m"1, the change of Su and $21 at the TR frequency /Tamm1 is 2.4 dB and 5.0 dB, and at /Tamm2 it is 4.1 dB and 4.5 dB, respectively. It should be noted that for the chosen parameters of the GaAs structure's layers, S21 and 511 are mainly determined by the parameters of the n+ -layer.
With a thickness dL = 1.0 mm, the frequencies are /Tamm1 = 7.432 GHz and /ramm2 = 12.262 GHz. At the frequency /Tamm2 = 12.262 GHz with an increase in the conductivity of the n+ -layer in the range from 0.8 • 105 to 1.6 • 105 Q_1m~\the
change of Su exceeds 20.0 dB, while the change of S21 remains at the level of 3.5 dB.
Thus, the results of computer simulation demonstrate that the frequency tuning of the TR in the MPC can be implemented by choosing the thickness of the outer Al2O3 ceramics layer of the MPC adjacent to the n+ -layer. In this case, the tuning of the TR frequency, which provides a high sensitivity of the TR to the change of the conductivity of the heavily doped layer, is determined by the conductivity value of this layer.
2. Use of controlled TRs in the 1D MPC for measuring the parameters of the heavily doped semiconductor layer
The experimental MPC created according to the described above model was tested for the frequency range 7-13 GHz.
For the experimental observation of the TRs, the epitaxial semiconductor structure made of gallium arsenide (GaAs) was used. It consisted of three layers: n+, n and /-layers with the thicknesses of 1.8 |im, 11.4 |im, and 473.8 |im. The tested semiconductor structure was placed behind the MPC. The highly doped epitaxial layer was directly adjacent to its outer dielectric layer (Fig. 3).
To experimentally confirm the possibility of tuning the TR frequency, which provides a high sensitivity of the TR to the change of the conductivity of the heavily doped layer, two configurations were considered: dL = 0.494 mm (configuration 1 in Fig. 1), dL = 0.973 mm (configuration 2 in Fig. 1).
Fig. 3. The experimental waveguide section with the MPC and the tested layered GaAs sample
The experimentally obtained coefficients Sn and S21 of the MPC with the epitaxial semiconductor structure for two configurations, performed by the network analyzer Agilent PNA-X N5242A, are presented in Fig. 4.
7 8 9 10 11 12 13
Frequency, GHz
Fig. 4. Experimental 511 (curves 1) and S12 (curves 2) of MPCs with the three-layer GaAs structure for two different configurations: solid curves - dl = 0.494 mm; dotted curves -dL = 0.973 mm. S21 of the MPC without the semiconductor structure is curve 3
As follows from the experiment at the thickness dL = 0.973 mm of the MPC's outer layer, the resonances are characterized by a low value of the Sn at frequencies /ramm1 = 7.472 GHz and /ramm2 = = 12.396 GHz. In this case, the depth and frequency of TRs are controlled by the thickness of the MPC's outer layer adjacent to the n+ -layer of the GaAs structure. This is in good agreement with the presented above calculation results and demonstrates the possibility to tune the frequency of the photonic TR to achieve a high sensitivity of the TR to changes of the conductivity of the heavily doped layer. In this case, the required value of the frequency tuning is determined by the conductivity value of this heavily doped layer.
The implementation of the highly sensitive TR makes it possible to use the method based on the measurement of S21 and S11 of the MPC containing the structure under test to determine the conductivity of the highly doped epitaxial semiconductor n+-layer [33].
The sought value of the conductivity o„+ of the
is obtained from the well-known relation:
1
p • d '
(3)
The measured by the Jandel RMS-EL-Z probe station value of the surface resistance p was 7H per square, which corresponds to the value of the con-
-layer is defined numerically by the least squares ductivity equal to 0794 • 1°
with the n+
method from solving the equation:
as(0+) _
d<5„
Here
s (On
i=1
S21 On+, fexpi) I IS21 expi | J + On+, fexpi) 1 |S11 expi 1 j
(1)
, (2)
where S21 exp, S
21 exp> "11 exp
are the experimental and S21 (o„+, /), S11(o„+, /) calculated transmission and reflection coefficients.
Using the results of measuring S21 and S11 in the vicinity of the TR frequency /Tamm? = 12.396 GHz at the thickness dL = 0.973 mm of the MPC' outer layer, the value of the conductivity an+ of the highly doped epitaxial GaAs layer with the thickness 1.8 |im has been determined as 0.843 • 105 H"1m"1 by solving the inverse problem.
The measured S21, S11 and calculated ones by using the obtained value on+ = 0.843 • 105 H"1m"1 of the highly doped epitaxial GaAs layer agree well as shown in Fig. 5.
Fig. 5. Measured (points) and calculated (curves) S11 (curve 1) and S21 (curve 2) by using the obtained value of the conductivity 0.843 • 105 Q-1m-1 of the MPC with the tested GaAs structure
To evaluate the correctness of the results, obtained by the method using the photonic TRs, the conductivity measurements were carried out by an independent method. A four-probe method based on the measurement of the surface resistance p was used as an alternative independent method for measuring the conductivity an+ of the GaAs n+-layer. The conductivity, at known thickness d of the GaAs n+ -layer,
layer thickness d = 1.8 |im.
Thus, the difference between the results of measuring the conductivity of the highly doped GaAs n+ -layer using the microwave TRs and the surface resistance is no more than 6.2%. It should be noted that the relative error in measuring the surface resistance of highly conducting layers in the selected range of resistance values by the four-probe method can reach 14%.
For the heavily doped semiconductor structures with high electron mobility it is possible to observe a pronounced plasma resonance in the infrared range. This provides the possibility of obtaining the concentration n+ of free charge carriers from measurements of the plasma resonance frequency using the relation [42]:
M*EoEL (юр)2
(4)
where m* is the effective mass of free charge carriers, depending on their concentration at a high doping level [43], eL is the permittivity of the crystal lattice in the infrared range [43].
In the infrared range from 350 to 7800 cm-1, the reflection coefficient of the tested GaAs structure was measured using the Shimadzu IRAffinity-lS spectrophotometer (Fig. 6).
Fig. 6. Reflection coefficient of the tested layered GaAs sample in the infrared range
As follows from the measurement results, the plasma frequency, defined as = 2nc/Xp is equal to 1.192 • 1014 rad/s. Here X = Xmin [(eL - 1) /eL]1/2,
Q.-1m-1
+
n
+
+1—
+
n
2
e
where is the wavelength in the minimum of the reflection coefficient in the infrared range.
Using the obtained value of the plasma frequency ©p = 1.192 • 1014 rad/s and the expression (4), the concentration has been determined as n+ = = 3.9 • 1024 m-3. The permittivity of the GaAs crystal lattice in the infrared range was chosen equal to 10.89, the effective mass of charge carriers in GaAs at this doping level was 0.078 • me, where me is the mass of a free electron.
To determine the free charge carriers mobility |i in the tested GaAs n+ -layer the well-known relation | = on+ /(en+), where n+ is the concentration of free charge carriers, was used. The calculated value of the mobility 0.134 m2/(V s) correlates well with the values known from the literature for heavily doped GaAs layers [43, 44].
To evaluate the correctness of the results of the mobility measurement using the photonic TRs and plasma resonance, the mobility was measured independently by the well-known method of microwave magnetoresistance [45, 46].
In this method, the mobility is obtained from the measured attenuation am and a of the microwave signal in the waveguide section containing the GaAs structure with and without external magnetic field B, respectively:
1 a - am BV am '
(5)
The value of the mobility of charge carriers measured using this method was 0.129 m2/(V s).
The difference between the results of measuring | using the conductivity obtained by the method of microwave TRs and by the methods of plasma resonance and magnetoresistance is no more than 4.0%.
Thus, the use of controlled TRs in the one-dimensional MPCs and the additional observation of the plasma resonance in the infrared range in the tested semiconductor structure makes it possible to implement along with the conductivity measurement technique the method for determining the concentration of charge carriers and their mobility.
Conclusion
Thus, the approach aimed at solving the problem of measuring thin highly conducting layers with high and extremely high conductivity, which are used in various fields of microwave technology as absorbers of electromagnetic radiation, bolometric power meters in the millimeter and subterahertz
ranges, electromagnetic shields, elements of electronics and photonics with large areas, has been developed in this work.
To achieve this goal, it is proposed to tune the TR's frequency in the MPC depending on the thickness and conductivity of the conducting layers under test. The control of the TR in the MPC is provided by the change of the thickness of the outer layer of the MPC adjacent to the conducting layer. In this case, the required frequency tuning value is determined by the value of the conductivity of the conducting layer. The applicability of the developed approach has been confirmed by the example of measuring heavily doped semiconductor layers.
The developed method can also find application for diagnostics of microwave microfluidic circuits, flexible and stretchable antennas for biointegrated electronics [47-49].
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Поступила в редакцию 18.02.2022; одобрена после рецензирования 06.03.2022; принята к публикации 10.03.2022 The article was submitted 18.02.2022; approved after reviewing 06.03.2022; accepted for publication 10.03.2022
