rus
Issue #1/2022
A. V. Yakuhina, V. V. Svetukhin, A. S. Kadochkin
Comparison of the Influence of Factors on the Q-factor of Mesa Structures of Optical Resonators Manufactured Using Silicon Technology
Comparison of the Influence of Factors on the Q-factor of Mesa Structures of Optical Resonators Manufactured Using Silicon Technology
DOI: 10.22184/1993-7296.FRos.2022.16.1.10.20
The results of a study of the influence of the surface roughness of the fiber layer on the Q-factor of the mesa structures of optical resonators operating in the whispering gallery mode, manufactured using silicon technology are presented. Two variants were studied as the material of the fiber layer: SiO2 and Si. The study of the influence of the value of the roughness of the lateral surface of the light-guide layer on the value of the figure of merit for each variant of the structure has been carried out. The roughness of the lateral surface of the light guide layer was investigated using AFM and SEM. For mesa structures of optical resonators with a fiber layer made of both silicon and silicon oxide, as a result of optimization of the basic technological processes, it was possible to achieve a decrease in the roughness value from 30–40 nm to 1–3 nm. The evaluation carried out by numerical simulation showed that the Q-factor of optical resonators with a light-guide layer of SiO2 can be achieved 109, by reducing the roughness of the side surface of the light-guide layer.
The results of a study of the influence of the surface roughness of the fiber layer on the Q-factor of the mesa structures of optical resonators operating in the whispering gallery mode, manufactured using silicon technology are presented. Two variants were studied as the material of the fiber layer: SiO2 and Si. The study of the influence of the value of the roughness of the lateral surface of the light-guide layer on the value of the figure of merit for each variant of the structure has been carried out. The roughness of the lateral surface of the light guide layer was investigated using AFM and SEM. For mesa structures of optical resonators with a fiber layer made of both silicon and silicon oxide, as a result of optimization of the basic technological processes, it was possible to achieve a decrease in the roughness value from 30–40 nm to 1–3 nm. The evaluation carried out by numerical simulation showed that the Q-factor of optical resonators with a light-guide layer of SiO2 can be achieved 109, by reducing the roughness of the side surface of the light-guide layer.
Теги: integrated optics optical loss photonics quality factor roughness si silicon technology sio2 whispering gallery modes добротность интегральная оптика кремниевая технология моды шепчущей галереи оптические потери фотоника шероховатость
Comparison of the Influence of Factors on the Q-factor of Mesa Structures of Optical Resonators Manufactured Using Silicon Technology
A. V. Yakuhina, V. V. Svetukhin, A. S. Kadochkin
Scientific-Manufacturing Complex “Technological Centre”, Zelenograd, Moscow, Russia
The results of a study of the influence of the surface roughness of the fiber layer on the Q-factor of the mesa structures of optical resonators operating in the whispering gallery mode, manufactured using silicon technology are presented. Two variants were studied as the material of the fiber layer: SiO2 and Si. The study of the influence of the value of the roughness of the lateral surface of the light-guide layer on the value of the figure of merit for each variant of the structure has been carried out. The roughness of the lateral surface of the light guide layer was investigated using AFM and SEM. For mesa structures of optical resonators with a fiber layer made of both silicon and silicon oxide, as a result of optimization of the basic technological processes, it was possible to achieve a decrease in the roughness value from 30–40 nm to 1–3 nm. The evaluation carried out by numerical simulation showed that the Q-factor of optical resonators with a light-guide layer of SiO2 can be achieved 109, by reducing the roughness of the side surface of the light-guide layer.
Key words: integrated optics, whispering gallery modes, photonics, SiO2, Si, silicon technology, optical loss, quality factor, roughness
Received on: 17.12.2021
Accepted on: 27.12.2021
Introduction
Silicon photonics is the main platform for creating optoelectronic integrated circuits (OEIC). Due to the extremely large bandwidth and high speed of optical communication, integrated optical waveguides are used in optical interconnects to transmit data at the crystal level [1]. The practical deployment of silicon optoelectronic devices and integrated photonic circuits in computing and telecommunication systems has become possible thanks to the introduction of a number of innovative ideas [2]. The commercialization of silicon photonics is occasioned by the mass application in the field of telecommunications, as well as the prospects for consumption by the computer industry. Examples of this can be new technologies developed in the USA by Intel and Luxtera for a series of photonic transceiver systems [3].
The development of research in the field of silicon photonics has allowed CMOS manufacturing enterprises to launch the production of integrated nanophotonic components for a wide range of applications, including high-speed communication [4]. This made it possible to proceed to the creation of a number of prototypes of powerful highly integrated optical transmitters and receivers [5–7], monolithically integrated with processors and memory [8, 9]. Recent studies have shown that silicon photonic channels provide a bandwidth of the order of Tbit / s while maintaining an overall energy efficiency of less than 2 pJ / bit [10–12].
Silicon photonics is actively used for microwave photonics applications focusing on the use of photonic methods and technologies for generation, processing and analysis / characterization of microwave signals [12–15]. Considerable efforts are directed to the development of integrated photonic technologies for the implementation of the functions of processing microwave photonic signals [16–18].
To date, silicon-containing materials, including silicon-on-insulator (SOI) structures, as well as InP, LiNbO3 and chalcogenide glasses are considered as the main integrated platforms [20]. Very complex systems based on InP [20], Si3N4 [21] and SOI [19] have been implemented. In addition, nonlinear integrated microwave photonic circuits in chalcogenide for the implementation of highly selective filters have been demonstrated [18].
Among the various microphotonic components actively used in silicon photonics, microdisc and micro-ring resonators are distinguished [22–26] due to the long photon lifetime (high Q-factor) and a significant increase in the electric field inside. Optical microresonators [27] are universal micro photonic structures characterized by compact size, selectivity, and amplification [28]. Over the past two decades, the research of devices based on microresonators has found application as the main building blocks for integrated photonic applications in optical communication, on-chip optical interconnects, and biosensorics [29].
A special role is given to research in the field of creating ultra-high-frequency resonators that operate in the whispering gallery mode. In such resonators, it is possible to achieve the maximum photon lifetime, in other words, large Q-factor values, which is one of the most significant parameters of their operation, with small volumes of modes [30].
Optical resonators operating in the whispering-gallery-mode (WGM) regime can be used to create various biosensors [30, 31], phonon lasers [33], lasers with an ultra-low generation threshold [34]. At the same time, such resonators are widely used in the field of nonlinear optics [35–37].
This paper presents a comparative analysis of the effect of the surface roughness of the mesa structure of the light guide layer made on the basis of silicon-containing materials on the Q-factor of optical resonators operating in the whispering-gallery-mode regime (WGM).
Methods for Investigating the Effect of Roughness on Q
To conduct a comparative analysis, waveguide structures were made from a light-conducting layer of SiO2 and Si at the domestic production site of the Scientific-Manufacturing Complex “Technological Center”. Figure 1 shows the cross-sections and appearance of the studied mesa structures of optical resonators with a light guide layer of Si (Fig. 1a, c) and SiO2 [32, 38].
The main contribution to the decrease in Q-factor and the increase in optical losses in integral structures is made by scattering at the interface [39]. As the main technological parameter at this stage of research, the value of the surface roughness of the light-conducting layers of waveguide structures is chosen.
In practice, achieving a minimum surface roughness of the structure of both silicon oxide and silicon is associated with a number of technological difficulties. This has to do with the fact that when creating most silicon microelectronics devices, roughness requirements are either not imposed, or are limited to values of the order of tens of nanometers. Therefore, the standard technological processes of silicon technology preclude ensuring the minimum roughness of the formed structures. However, in the manufacture of optical devices, this technological factor is extremely significant, due to the fact that the formed surface of the light guide layer is the interface of optical media.
Achieving optimal optical properties of the mesa structures under consideration is possible in the case of minimal losses at the interface of optical media. The formula given in [40] makes it possible to estimate the Q-factor of optical resonators through insertion loss:
Qint–1 = Qmat–1 + Qsurf–1 + Qscatt–1 + Qbend–1, (1)
where Qmat is the proper absorption in the material (attenuation of waves in the material); Qsurf is the loss due to absorption on the surface; Qscatt – scattering losses, mainly due to defects such as roughness; Qbend – losses due to bending.
It is obvious that the losses caused by the imperfection of the surface make a significant contribution (about 50%) to the total loss of the optical structure and, accordingly, to its optical properties, in a particular case, the Q-factor.
Therefore, in order to form structures with a minimum amount of roughness (on the order of units of nanometers), it is necessary to resort to non-standard methods of processing structures. In the case of silicon oxide, some manufacturers use a CO2 laser to melt dielectric structures.
Indeed, in this case, a toroidal fused structure is obtained, which makes it possible to effectively use devices made on its basis in optical applications. However, this method has a number of disadvantages associated with the performance of expensive equipment, as well as the impossibility of creating an array of such resonators on a chip, since this method is designed for piece processing.
To date, in the case of silicon optical structures the smallest amount of surface roughness has been demonstrated only on single-crystal, free-standing structures [41].
Technological approaches have been developed at the Scientific-Manufacturing Complex “Technological Center”, which make it possible to reliably form arrays of optical whispering-gallery-mode resonators with a light-guide layer of silicon or silicon oxide with minimal roughness (1–3 nm), using a special complex of technological processes.
As a rule, it is customary to estimate the amount of roughness by examining samples using atomic force microscopy. However, each of the structures under consideration has a number of specific design and technological features. Due to the fact that it is necessary to investigate non-standard inclined surfaces made of silicon oxide and silicon, in order to obtain the most reliable information about roughness, the surface analysis was carried out using a combined technique. This technique includes research using a Helios 650 scanning electron microscope (SEM) and a Bruker atomic force microscope (AFM).
The basis of this roughness analysis technique using the Helios 650 SEM is the research of Japanese authors [42; 43], as well as previously presented own developments [44]. The essence of the method is to analyze the horizontal edge of the metal-test material interface in the etched area. The presentation of the stages of the methodology for analyzing the roughness of the inclined surface of mesa structures is shown in Fig. 2.
At the first stage, a contrast layer was formed in the area of the inclined plane of the mesa structure by successive spraying of thin metal layers Cr and Pt directly in the Helios 650 SEM chamber (Fig. 2a, 1). It is worth noting the special significance of this approach in the quantitative analysis of the surface roughness of dielectric structures. This is due to the fact that when studying such structures in a scanning electron microscope, charge accumulates in the dielectric layers, which causes the frame to flare and prevents analysis [44].
With the help of an ion beam, a part of the structure at the edge of the inclined plane was removed (Fig. 2a, 2) [38], and then the metal – Si interface was analyzed. Figure 2b shows the area where the points are highlighted and the graph is plotted (Fig. 2c). To quantify the amount of roughness, the average value of the spread of values along the Y axis is taken.
During the control analysis of the mesa structure surface using the Bruker atomic force microscope (AFM), the main difficulty was in positioning the cantilever and interpreting the results obtained (Fig. 3). The samples were scanned with a ScanAsyst Air probe equipped with a V-shaped cantilever.
For each of the structures under consideration, the optimization of the manufacturing process was carried out, aimed at reducing the surface roughness of the light-guide layer of the masa structures. For comparison, Fig. 4 shows SEM photographs of mesa structures from SiO2 before and after optimizing the technological process of their formation.
Table 1 provides the results of quantitative analysis of the roughness values for Si and SiO2 structures obtained using the combined technique described above.
Based on the data on the surface roughness of mesa structures and the method of finite time differences, the Q-factor of the studied mesa structures was calculated. The Q-factor calculation is based on the method of determining the attenuation of a short pulse introduced into the study subject [42]. Such a pulse contains a certain frequency spectrum, the width of which directly depends on its length (the shorter the pulse is, the wider the frequency spectrum is). This makes it possible not to pay special attention to the diameter of the structure and the frequency of the input wave at the design stage of the resonator design parameters, since in the case of a wide spectrum, several resonant frequencies can be excited [42].
Considering that the method of calculating the Q-factor of resonators from SiO2 is similar to the method used in our earlier article for resonators from Si [38], explanations for the calculation are presented briefly. Figure 5 shows a graphical representation of the results of numerical simulation of the Q-factor of the resonator, taking into account the measured value of the surface roughness of its profile, performed using the formula:
, (2)
where fR is the resonant frequency, e is the base of the natural logarithm, m is the pulse attenuation parameter.
The results of numerical Q-factor modeling for the studied mesa structures of optical resonators are presented in Table 2.
Conclusions
It follows from the results obtained that after optimizing the technological process of manufacturing mesa structures from Si and SiO2, it is possible to count on achieving a high Q-factor of optical resonators operating in the whispering-gallery-mode regime. The presented research results show that a decrease in the roughness from 30–40 nm to 2–3 nm leads to an increase in the Q-factor of a resonator with a light-guide layer of SiO2 to 109. The Q-factor of silicon oxide resonators increases more with a decrease in the roughness value than in the case of silicon, which is due to the manifestation of nonlinear optical properties of this material.
ACKNOWLEDGEMENT
This article was prepared with the financial support of the Ministry of Education and Science of the Russian Federation as part of the state task for 2021 (Project No. FNRM‑2020-0008) “Theoretical and Experimental Studies of Constructive and Technological Methods for CreatinG Elements of Integrated Optics Compatible with Silicon Technology”. When performing the work, the equipment of the collective use of Functional Control and diagnostics of Micro- and Nanosystem Equipment Center” was used, with the equipment housed by Scientific-Manufacturing Complex “Technological Center”.
INFORMATION ABOUT THE AUTHORS
A. V. Yakukhina, Researcher at Scientific-Manufacturing Complex “Technological Center”, Moscow, Zelenograd, Russia, A. Yakuhina@tcen.ru,
ORCID: 0000-0002-0729-9653
V. V. Svetukhin, Doctor of Ph.D., Professor, Director of Scientific-Manufacturing Complex “Technological Center”, Moscow, Zelenograd, Russia, V. Svetukhin@tcen.ru.
ORCID: 0000-0003-0831-9254
A. S. Kadochkin Ph.D., Research Associate, Scientific-Manufacturing Complex “Technological Center”, Moscow, Zelenograd, Russia.
ORCID: 0000-0002-7960-1583
CONTRIBUTION OF THE AUTHORS
The article was prepared on the basis of the work of all members of the team of contributors: A. V. Yakukhina – conducting experiments, processing and discussion of results; V. V. Svetukhin – organization of work, discussion of results; A. S. Kadochkin – mathematical modeling, processing of results.
CONFLICT OF INTEREST
The authors herewith declare that there is no conflict of interest. All authors participated in the writing of the manuscript in terms of the contribution of each of them to the work and agree with the full text of the manuscript.
A. V. Yakuhina, V. V. Svetukhin, A. S. Kadochkin
Scientific-Manufacturing Complex “Technological Centre”, Zelenograd, Moscow, Russia
The results of a study of the influence of the surface roughness of the fiber layer on the Q-factor of the mesa structures of optical resonators operating in the whispering gallery mode, manufactured using silicon technology are presented. Two variants were studied as the material of the fiber layer: SiO2 and Si. The study of the influence of the value of the roughness of the lateral surface of the light-guide layer on the value of the figure of merit for each variant of the structure has been carried out. The roughness of the lateral surface of the light guide layer was investigated using AFM and SEM. For mesa structures of optical resonators with a fiber layer made of both silicon and silicon oxide, as a result of optimization of the basic technological processes, it was possible to achieve a decrease in the roughness value from 30–40 nm to 1–3 nm. The evaluation carried out by numerical simulation showed that the Q-factor of optical resonators with a light-guide layer of SiO2 can be achieved 109, by reducing the roughness of the side surface of the light-guide layer.
Key words: integrated optics, whispering gallery modes, photonics, SiO2, Si, silicon technology, optical loss, quality factor, roughness
Received on: 17.12.2021
Accepted on: 27.12.2021
Introduction
Silicon photonics is the main platform for creating optoelectronic integrated circuits (OEIC). Due to the extremely large bandwidth and high speed of optical communication, integrated optical waveguides are used in optical interconnects to transmit data at the crystal level [1]. The practical deployment of silicon optoelectronic devices and integrated photonic circuits in computing and telecommunication systems has become possible thanks to the introduction of a number of innovative ideas [2]. The commercialization of silicon photonics is occasioned by the mass application in the field of telecommunications, as well as the prospects for consumption by the computer industry. Examples of this can be new technologies developed in the USA by Intel and Luxtera for a series of photonic transceiver systems [3].
The development of research in the field of silicon photonics has allowed CMOS manufacturing enterprises to launch the production of integrated nanophotonic components for a wide range of applications, including high-speed communication [4]. This made it possible to proceed to the creation of a number of prototypes of powerful highly integrated optical transmitters and receivers [5–7], monolithically integrated with processors and memory [8, 9]. Recent studies have shown that silicon photonic channels provide a bandwidth of the order of Tbit / s while maintaining an overall energy efficiency of less than 2 pJ / bit [10–12].
Silicon photonics is actively used for microwave photonics applications focusing on the use of photonic methods and technologies for generation, processing and analysis / characterization of microwave signals [12–15]. Considerable efforts are directed to the development of integrated photonic technologies for the implementation of the functions of processing microwave photonic signals [16–18].
To date, silicon-containing materials, including silicon-on-insulator (SOI) structures, as well as InP, LiNbO3 and chalcogenide glasses are considered as the main integrated platforms [20]. Very complex systems based on InP [20], Si3N4 [21] and SOI [19] have been implemented. In addition, nonlinear integrated microwave photonic circuits in chalcogenide for the implementation of highly selective filters have been demonstrated [18].
Among the various microphotonic components actively used in silicon photonics, microdisc and micro-ring resonators are distinguished [22–26] due to the long photon lifetime (high Q-factor) and a significant increase in the electric field inside. Optical microresonators [27] are universal micro photonic structures characterized by compact size, selectivity, and amplification [28]. Over the past two decades, the research of devices based on microresonators has found application as the main building blocks for integrated photonic applications in optical communication, on-chip optical interconnects, and biosensorics [29].
A special role is given to research in the field of creating ultra-high-frequency resonators that operate in the whispering gallery mode. In such resonators, it is possible to achieve the maximum photon lifetime, in other words, large Q-factor values, which is one of the most significant parameters of their operation, with small volumes of modes [30].
Optical resonators operating in the whispering-gallery-mode (WGM) regime can be used to create various biosensors [30, 31], phonon lasers [33], lasers with an ultra-low generation threshold [34]. At the same time, such resonators are widely used in the field of nonlinear optics [35–37].
This paper presents a comparative analysis of the effect of the surface roughness of the mesa structure of the light guide layer made on the basis of silicon-containing materials on the Q-factor of optical resonators operating in the whispering-gallery-mode regime (WGM).
Methods for Investigating the Effect of Roughness on Q
To conduct a comparative analysis, waveguide structures were made from a light-conducting layer of SiO2 and Si at the domestic production site of the Scientific-Manufacturing Complex “Technological Center”. Figure 1 shows the cross-sections and appearance of the studied mesa structures of optical resonators with a light guide layer of Si (Fig. 1a, c) and SiO2 [32, 38].
The main contribution to the decrease in Q-factor and the increase in optical losses in integral structures is made by scattering at the interface [39]. As the main technological parameter at this stage of research, the value of the surface roughness of the light-conducting layers of waveguide structures is chosen.
In practice, achieving a minimum surface roughness of the structure of both silicon oxide and silicon is associated with a number of technological difficulties. This has to do with the fact that when creating most silicon microelectronics devices, roughness requirements are either not imposed, or are limited to values of the order of tens of nanometers. Therefore, the standard technological processes of silicon technology preclude ensuring the minimum roughness of the formed structures. However, in the manufacture of optical devices, this technological factor is extremely significant, due to the fact that the formed surface of the light guide layer is the interface of optical media.
Achieving optimal optical properties of the mesa structures under consideration is possible in the case of minimal losses at the interface of optical media. The formula given in [40] makes it possible to estimate the Q-factor of optical resonators through insertion loss:
Qint–1 = Qmat–1 + Qsurf–1 + Qscatt–1 + Qbend–1, (1)
where Qmat is the proper absorption in the material (attenuation of waves in the material); Qsurf is the loss due to absorption on the surface; Qscatt – scattering losses, mainly due to defects such as roughness; Qbend – losses due to bending.
It is obvious that the losses caused by the imperfection of the surface make a significant contribution (about 50%) to the total loss of the optical structure and, accordingly, to its optical properties, in a particular case, the Q-factor.
Therefore, in order to form structures with a minimum amount of roughness (on the order of units of nanometers), it is necessary to resort to non-standard methods of processing structures. In the case of silicon oxide, some manufacturers use a CO2 laser to melt dielectric structures.
Indeed, in this case, a toroidal fused structure is obtained, which makes it possible to effectively use devices made on its basis in optical applications. However, this method has a number of disadvantages associated with the performance of expensive equipment, as well as the impossibility of creating an array of such resonators on a chip, since this method is designed for piece processing.
To date, in the case of silicon optical structures the smallest amount of surface roughness has been demonstrated only on single-crystal, free-standing structures [41].
Technological approaches have been developed at the Scientific-Manufacturing Complex “Technological Center”, which make it possible to reliably form arrays of optical whispering-gallery-mode resonators with a light-guide layer of silicon or silicon oxide with minimal roughness (1–3 nm), using a special complex of technological processes.
As a rule, it is customary to estimate the amount of roughness by examining samples using atomic force microscopy. However, each of the structures under consideration has a number of specific design and technological features. Due to the fact that it is necessary to investigate non-standard inclined surfaces made of silicon oxide and silicon, in order to obtain the most reliable information about roughness, the surface analysis was carried out using a combined technique. This technique includes research using a Helios 650 scanning electron microscope (SEM) and a Bruker atomic force microscope (AFM).
The basis of this roughness analysis technique using the Helios 650 SEM is the research of Japanese authors [42; 43], as well as previously presented own developments [44]. The essence of the method is to analyze the horizontal edge of the metal-test material interface in the etched area. The presentation of the stages of the methodology for analyzing the roughness of the inclined surface of mesa structures is shown in Fig. 2.
At the first stage, a contrast layer was formed in the area of the inclined plane of the mesa structure by successive spraying of thin metal layers Cr and Pt directly in the Helios 650 SEM chamber (Fig. 2a, 1). It is worth noting the special significance of this approach in the quantitative analysis of the surface roughness of dielectric structures. This is due to the fact that when studying such structures in a scanning electron microscope, charge accumulates in the dielectric layers, which causes the frame to flare and prevents analysis [44].
With the help of an ion beam, a part of the structure at the edge of the inclined plane was removed (Fig. 2a, 2) [38], and then the metal – Si interface was analyzed. Figure 2b shows the area where the points are highlighted and the graph is plotted (Fig. 2c). To quantify the amount of roughness, the average value of the spread of values along the Y axis is taken.
During the control analysis of the mesa structure surface using the Bruker atomic force microscope (AFM), the main difficulty was in positioning the cantilever and interpreting the results obtained (Fig. 3). The samples were scanned with a ScanAsyst Air probe equipped with a V-shaped cantilever.
For each of the structures under consideration, the optimization of the manufacturing process was carried out, aimed at reducing the surface roughness of the light-guide layer of the masa structures. For comparison, Fig. 4 shows SEM photographs of mesa structures from SiO2 before and after optimizing the technological process of their formation.
Table 1 provides the results of quantitative analysis of the roughness values for Si and SiO2 structures obtained using the combined technique described above.
Based on the data on the surface roughness of mesa structures and the method of finite time differences, the Q-factor of the studied mesa structures was calculated. The Q-factor calculation is based on the method of determining the attenuation of a short pulse introduced into the study subject [42]. Such a pulse contains a certain frequency spectrum, the width of which directly depends on its length (the shorter the pulse is, the wider the frequency spectrum is). This makes it possible not to pay special attention to the diameter of the structure and the frequency of the input wave at the design stage of the resonator design parameters, since in the case of a wide spectrum, several resonant frequencies can be excited [42].
Considering that the method of calculating the Q-factor of resonators from SiO2 is similar to the method used in our earlier article for resonators from Si [38], explanations for the calculation are presented briefly. Figure 5 shows a graphical representation of the results of numerical simulation of the Q-factor of the resonator, taking into account the measured value of the surface roughness of its profile, performed using the formula:
, (2)
where fR is the resonant frequency, e is the base of the natural logarithm, m is the pulse attenuation parameter.
The results of numerical Q-factor modeling for the studied mesa structures of optical resonators are presented in Table 2.
Conclusions
It follows from the results obtained that after optimizing the technological process of manufacturing mesa structures from Si and SiO2, it is possible to count on achieving a high Q-factor of optical resonators operating in the whispering-gallery-mode regime. The presented research results show that a decrease in the roughness from 30–40 nm to 2–3 nm leads to an increase in the Q-factor of a resonator with a light-guide layer of SiO2 to 109. The Q-factor of silicon oxide resonators increases more with a decrease in the roughness value than in the case of silicon, which is due to the manifestation of nonlinear optical properties of this material.
ACKNOWLEDGEMENT
This article was prepared with the financial support of the Ministry of Education and Science of the Russian Federation as part of the state task for 2021 (Project No. FNRM‑2020-0008) “Theoretical and Experimental Studies of Constructive and Technological Methods for CreatinG Elements of Integrated Optics Compatible with Silicon Technology”. When performing the work, the equipment of the collective use of Functional Control and diagnostics of Micro- and Nanosystem Equipment Center” was used, with the equipment housed by Scientific-Manufacturing Complex “Technological Center”.
INFORMATION ABOUT THE AUTHORS
A. V. Yakukhina, Researcher at Scientific-Manufacturing Complex “Technological Center”, Moscow, Zelenograd, Russia, A. Yakuhina@tcen.ru,
ORCID: 0000-0002-0729-9653
V. V. Svetukhin, Doctor of Ph.D., Professor, Director of Scientific-Manufacturing Complex “Technological Center”, Moscow, Zelenograd, Russia, V. Svetukhin@tcen.ru.
ORCID: 0000-0003-0831-9254
A. S. Kadochkin Ph.D., Research Associate, Scientific-Manufacturing Complex “Technological Center”, Moscow, Zelenograd, Russia.
ORCID: 0000-0002-7960-1583
CONTRIBUTION OF THE AUTHORS
The article was prepared on the basis of the work of all members of the team of contributors: A. V. Yakukhina – conducting experiments, processing and discussion of results; V. V. Svetukhin – organization of work, discussion of results; A. S. Kadochkin – mathematical modeling, processing of results.
CONFLICT OF INTEREST
The authors herewith declare that there is no conflict of interest. All authors participated in the writing of the manuscript in terms of the contribution of each of them to the work and agree with the full text of the manuscript.
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