Investigation of Side Wall Roughness Effect on Optical Losses in a Multimode Si3N4 Waveguide Formed on a Quartz Substrate

This article presents the results of the study of the influence of the most significant parameters of the side wall roughness of an ultra-thin silicon nitride lightguide layer of multimode integrated optical waveguides with widths of 3 and 8 microns. The choice of the waveguide width was made due to the need to provide multimode operation for telecommunication wavelengths, which is necessary to ensure high integration density. Scattering in waveguide structures was measured by optical frequency domain reflectometry (OFDR) of a backscattering reflectometer. The finite difference time domain method (FDTD) was used to study the effect of roughness parameters on optical losses in fabricated waveguides, the roughness parameters that most strongly affect optical scattering were determined, and methods of its significant reduction were specified. The prospects for implementing such structures on a quartz substrate are justified.


Introduction
Silicon photonics, which is a synergy of two groups of technologies-optics and electronics-is among the most well-known technological platforms for implementing photonic integrated circuits today [1]. Among the main advantages of such circuits is compatibility with standard silicon technologies. This makes it possible to manufacture silicon photonics devices using standard technological processes using existing production lines used for the production of electronic integrated circuits. This method allows the possible financial costs caused by the launch of specialized production to be minimized [2].
Recently, multimode photonics has attracted increasing attention; the introduction of higher-level modes allows an increase in the number of channels for data transmission in systems with mode-division-multiplexed systems (MDM). Multimode waveguides involve not only the fundamental mode but also higher-level modes. The mode dispersion in a multimode integrated optical waveguide is extremely large. This allows efficient mode manipulation to be realized-among the most important properties for multimode integrated photonics [3]. Most integrated photonics devices are designed on the basis of single-mode integrated optical waveguide structures, since higher-level modes cause crosstalk and losses because of multimode interference (MMI) [4,5]. However, the technology based on MMI allows the implementation of highly sensitive temperature sensors [6], chemical sensors, biosensors [7,8], which have many advantages, such as ease of operation and high sensitivity [9].
One of the ways to implement integrated optical waveguide structures is based on SOI-technology (silicon on insulator) assuming the use of silicon as a waveguide layer and silicon oxide as a cladding [10,11]. Interest in this method of implementation consisted mainly of the high contrast index for a silicon waveguide with a silicon oxide cladding (n Si = 3.46 vs. n SiO2 = 1.46) and CMOS (complementary metal-oxide-semiconductor) compatibility. However, although such a high contrast index makes it possible to implement a unique function on a very compact area, it leads to significant internal losses in the material of the lightguide layer, which is associated with the intrinsic structural features of the silicon crystal (scattering of radiation by free carriers in silicon) [2,12]. So, the implementation of photonic integrated circuits (PIC) based on such waveguides is extremely inefficient.
Thus, there is an interest in exploring alternative material combinations that meet the same requirements. Previously, asymmetrical waveguide structures using a covering layer made of tellurium oxide were considered [13,14]. We draw our attention in this work to symmetrical waveguides, demonstrating better localization of guided mode in Si 3 N 4 waveguide core with the waveguide cladding made of SiO 2 [15][16][17]. Such waveguide structures have a number of undeniable advantages. First, a moderately high contrast index (n Si3N4 = 2.0 vs. n SiO2 = 1.46) reduces the impact of manufacturing defects on the devices [2]. Second, the negligible two-photon scattering inherent of silicon nitride in the near-infrared region of the spectrum allows waveguide structures with low optical losses, as well as resonators with high Q-factors to be demonstrated [18][19][20][21]. Finally, due to the promising nonlinear properties of silicon nitride waveguides and wide transparency window spanning from visible to far-infrared spectra, they benefit from parametric amplification [22][23][24][25], soliton microcomb [26], broadband supercontinuum generation [27], etc. Thus, the use of such waveguide structures opens up a wide range of new possibilities for CMOS-compatible integrated photonics [17]. In particular, this technology can be an optimal solution for manufacturing biosensors in the visible and near-infrared ranges [28][29][30], where low losses and low sensitivity to thermal changes have a crucial role. In addition, it also benefits gas sensors, which are critical for a variety of applications, including medical diagnostics, pollution monitoring, and quality control of the manufacturing process [31,32].
In the manufacture of waveguide structures from silicon nitride, there are a number of problems preventing their effective use for the applications described above. One such problem is the roughness of the edge of the lightguide layer from both silicon and silicon nitride. Ways to solve this problem have previously been the subject of special attention [33][34][35]. In our article, we propose a method for identifying the most significant parameters of the side wall roughness of an ultra-thin silicon nitride lightguide layer in terms of the degree of their effect on optical losses in the waveguide structure. We show that changing these parameters also changes the value of optical loss. This leads to the conclusion of which specific technological operations should be optimized during the manufacturing. In addition, following the path of reducing optical losses, we propose a way to implement such waveguide structures based on a quartz substrate, citing the justification of the undeniable advantages of using such a material system while maintaining the possibility of their manufacture within existing CMOS-productions sites.

Fabrication
When choosing the geometric parameters of the studied waveguides, we were guided by the possibility of implementing such structures in standard silicon technologies. The width of the lightguide layer was chosen in such a way that the formed waveguide supports a multimode mode of operation for telecommunications wavelengths (1.55 microns), and also meets the condition to provide a high density of integration of devices that are planned to be manufactured on their basis in the future. We chose the thickness of the lightguide layer made of silicon nitride to be 200 nm, which ensures a strong interaction of the field with the upper cladding and a high level of integration [28][29][30]36]. When creating waveguide structures, we used bilaterally polished semiconductor quartz wafers with a surface roughness (Ra): <0.5 nm, in contrast to the standard approach implying the use of a silicon substrate followed by the formation of a lower cladding from thermal oxide [36]. Such a low surface roughness of the wafer allows us to form subsequent layers of the waveguide structure with minimal roughness. This makes the upper and lower interfaces almost perfect, so scattering at these interfaces can be neglected. In addition, the use of a quartz wafer as a substrate allows formation of a silicon nitride waveguiding layer to begin immediately. It reduces the possibility of introducing additional defects at the production stages, as well as the cost and production time significantly. Additionally, this way of implementing waveguide structures is fully compatible with silicon technology.
When using silicon wafers as a substrate, there is always a risk of guided wave leakage into the substrate. This is due to the fact that (as mentioned earlier) the contrast index in the Si-SiO 2 structure is significantly higher than the contrast index of the Si 3 N 4 -SiO 2 structure [2]. In this case, the slightest error in choosing the thickness of the lower cladding of the waveguide structure made of thermal oxide, as well as with minimal deviations of the angle at which the radiation enters the device, significantly increases the risk of radiation leakage into the substrate. The use of quartz wafers instead of silicon ones completely eliminates the possibility of such leakage due to difference in contrast indices and allows a reduction in entering losses of the optical device. Figure 1 shows a diagram of the route for fabricating silicon nitride waveguide structures on a quartz substrate. At the first stage, a 200-nm-thick Low-pressure Chemical Vapor Deposition (LPCVD) layer of silicon nitride was formed on a quartz substrate. Precipitation was carried out using a precursor consisting of a mixture of gaseous dichlorsilane (DCS) (SiH 2 Cl 2 ) and ammonia (NH 3 ). LPCVD nitride was chosen for its better uniformity and thickness due to the fact that lowered pressure reduces the probability of undesirable reactions in the gas phase and leads to more uniform deposition of the film on the substrate [37,38]. The refractive index of the film obtained was investigated by spectral ellipsometry and is equal to n = 2.0. Comparative characteristics of silicon, nitride and silicon oxide are shown in Table 1.
At the next stage, a waveguide layer of silicon nitride was formed using photolithography and plasma-chemical etching of Si 3 N 4 .
Photonics 2020, 7, x FOR PEER REVIEW 3 of 11 wafers with a surface roughness (Ra): <0.5 nm, in contrast to the standard approach implying the use of a silicon substrate followed by the formation of a lower cladding from thermal oxide [36]. Such a low surface roughness of the wafer allows us to form subsequent layers of the waveguide structure with minimal roughness. This makes the upper and lower interfaces almost perfect, so scattering at these interfaces can be neglected. In addition, the use of a quartz wafer as a substrate allows formation of a silicon nitride waveguiding layer to begin immediately. It reduces the possibility of introducing additional defects at the production stages, as well as the cost and production time significantly. Additionally, this way of implementing waveguide structures is fully compatible with silicon technology. When using silicon wafers as a substrate, there is always a risk of guided wave leakage into the substrate. This is due to the fact that (as mentioned earlier) the contrast index in the Si-SiO2 structure is significantly higher than the contrast index of the Si3N4-SiO2 structure [2]. In this case, the slightest error in choosing the thickness of the lower cladding of the waveguide structure made of thermal oxide, as well as with minimal deviations of the angle at which the radiation enters the device, significantly increases the risk of radiation leakage into the substrate. The use of quartz wafers instead of silicon ones completely eliminates the possibility of such leakage due to difference in contrast indices and allows a reduction in entering losses of the optical device. Figure 1 shows a diagram of the route for fabricating silicon nitride waveguide structures on a quartz substrate. At the first stage, a 200-nm-thick Low-pressure Chemical Vapor Deposition (LPCVD) layer of silicon nitride was formed on a quartz substrate. Precipitation was carried out using a precursor consisting of a mixture of gaseous dichlorsilane (DCS) (SiH2Cl2) and ammonia (NH3). LPCVD nitride was chosen for its better uniformity and thickness due to the fact that lowered pressure reduces the probability of undesirable reactions in the gas phase and leads to more uniform deposition of the film on the substrate [37,38]. The refractive index of the film obtained was investigated by spectral ellipsometry and is equal to n = 2.0. Comparative characteristics of silicon, nitride and silicon oxide are shown in Table 1    After the formation of the waveguide layer, the roughness of its side walls was studied. The roughness measurement of the silicon nitride waveguide samples was performed by analyzing the side wall roughness of identical control silicon waveguide formed in the same technological process as the silicon nitride ones using a (SEM). This method of estimation was chosen due to the fact that when studying fully dielectric structures, which the waveguide structures we describe made on quartz substrates are, a charge accumulates in the dielectric layers in a scanning electron microscope, which causes the frame to "light up" and hinders the analysis. Performing the analysis on similar control structures made on a silicon substrate reduces the effect of charge accumulation due to the "flow" of charge into silicon. As a result, it was found that the roughness of the side wall of the silicon nitride etching profile has a wavelike shape with a period of about 30-33 nm and a deviation of the edge from the vertical plane to 64 nm ( Figure 2).
Photonics 2020, 7, x FOR PEER REVIEW 4 of 11 At the next stage, a waveguide layer of silicon nitride was formed using photolithography and plasma-chemical etching of Si3N4.
After the formation of the waveguide layer, the roughness of its side walls was studied. The roughness measurement of the silicon nitride waveguide samples was performed by analyzing the side wall roughness of identical control silicon waveguide formed in the same technological process as the silicon nitride ones using a (SEM). This method of estimation was chosen due to the fact that when studying fully dielectric structures, which the waveguide structures we describe made on quartz substrates are, a charge accumulates in the dielectric layers in a scanning electron microscope, which causes the frame to "light up" and hinders the analysis. Performing the analysis on similar control structures made on a silicon substrate reduces the effect of charge accumulation due to the "flow" of charge into silicon. As a result, it was found that the roughness of the side wall of the silicon nitride etching profile has a wavelike shape with a period of about 30-33 nm and a deviation of the edge from the vertical plane to 64 nm ( Figure 2). Then, the upper layer of the waveguide structure was formed by deposition of the silicon oxide film. The refractive index of this silicon oxide film was also studied by spectral ellipsometry and was defined to be 1.46, which is as close as possible to the refractive index of the quartz substrate. This allows us to conclude that the resulting waveguide structure is as close to symmetric as possible.

Study of Fabricated Waveguides
Optical loss was estimated using optical frequency domain reflectometry (OFDR) in optical backscatter reflectometer (OBR). OFDR is an interferometric measurement technique that uses a highly coherent, continuously tunable laser light source. The analysis of the interference pattern is carried out using the Fourier transform that makes it possible to obtain the dependence of the reflection intensity on the distance to the point of introduction of the probe radiation. This method is optimal for solving problems that require a combination of high speed, sensitivity and resolution in Then, the upper layer of the waveguide structure was formed by deposition of the silicon oxide film. The refractive index of this silicon oxide film was also studied by spectral ellipsometry and was defined to be 1.46, which is as close as possible to the refractive index of the quartz substrate. This allows us to conclude that the resulting waveguide structure is as close to symmetric as possible.

Study of Fabricated Waveguides
Optical loss was estimated using optical frequency domain reflectometry (OFDR) in optical backscatter reflectometer (OBR). OFDR is an interferometric measurement technique that uses a highly coherent, continuously tunable laser light source. The analysis of the interference pattern is carried out using the Fourier transform that makes it possible to obtain the dependence of the reflection intensity on the distance to the point of introduction of the probe radiation. This method is optimal for solving problems that require a combination of high speed, sensitivity and resolution in the analysis of short and intermediate transmission line lengths [40,41]. Figure 3 shows a scheme of studying optical losses for fabricated waveguide samples. the analysis of short and intermediate transmission line lengths [40,41]. Figure 3 shows a scheme of studying optical losses for fabricated waveguide samples.  Figure 4 shows a reflectogram of the test waveguide structure with a width of 8 microns and a length of 60 mm, which has the lowest optical losses. Table 2 shows the results of the study of waveguides that were also made in this research. The waveguide parameters were measured using a Luna OBR 5T-50 optical backscattering reflectometer connected through the FPC562 fiber polarization controller (FPC). Optical radiation entered the waveguide using an SMF-28 lensed fiber. FPC was used to adjust the polarization of light, since the optical radiation coming out of the reflectometer has an arbitrary form of polarization (a common case of polarization is elliptical type of polarization of light). Monitoring of changes in polarization was made by the response of the reflectogram. Horizontal linear polarization corresponds to minimal optical losses-i.e., the minimum slope of the reflectogram (Figure 4a), which is also associated with a high aspect ratio of the waveguide. Due to the sufficient noise level of the obtained reflectograms (Figure 4a), as well as in order to obtain more reliable values of optical losses in the waveguide, linear extrapolation was performed (Figure 4b). Additionally, dead zones for events, such as reflections from the crystal ends at the input and output of the waveguide, were excluded.  Figure 4 shows a reflectogram of the test waveguide structure with a width of 8 microns and a length of 60 mm, which has the lowest optical losses. Table 2 shows the results of the study of waveguides that were also made in this research. The waveguide parameters were measured using a Luna OBR 5T-50 optical backscattering reflectometer connected through the FPC562 fiber polarization controller (FPC). Optical radiation entered the waveguide using an SMF-28 lensed fiber. FPC was used to adjust the polarization of light, since the optical radiation coming out of the reflectometer has an arbitrary form of polarization (a common case of polarization is elliptical type of polarization of light). Monitoring of changes in polarization was made by the response of the reflectogram. Horizontal linear polarization corresponds to minimal optical losses-i.e., the minimum slope of the reflectogram (Figure 4a), which is also associated with a high aspect ratio of the waveguide. Due to the sufficient noise level of the obtained reflectograms (Figure 4a), as well as in order to obtain more reliable values of optical losses in the waveguide, linear extrapolation was performed (Figure 4b). Additionally, dead zones for events, such as reflections from the crystal ends at the input and output of the waveguide, were excluded.

Calculation of the Influence of the Side Walls' Roughness of a Silicon Nitride Layer on Optical Losses in the Waveguide
To calculate the effect of the roughness of the side walls of a silicon nitride lightguide layer on optical losses in a multimode optical waveguide, a finite-difference time-domain (FDTD) method was used. The data obtained during the study of the roughness of the lightguide layer of previously

Calculation of the Influence of the Side Walls' Roughness of a Silicon Nitride Layer on Optical Losses in the Waveguide
To calculate the effect of the roughness of the side walls of a silicon nitride lightguide layer on optical losses in a multimode optical waveguide, a finite-difference time-domain (FDTD) method was used. The data obtained during the study of the roughness of the lightguide layer of previously manufactured waveguides were used as a basis. The σ (mean square deviation of roughness) and δ (longitudinal size of roughness) parameters used to calculate are clearly represented in Figure 5 Photonics 2020, 7, x FOR PEER REVIEW 7 of 11 Figure 5. Schematic of the waveguide with "rough"side wall.
The roughness on side walls of the waveguide was set as a random variable with a standard deviation and a longitudinal roughness size. The results of calculations for waveguides with widths of 3 and 8 microns are shown in Table 3 and Figure 6. Figure 6 shows that when the waveguide is wider, the field strength on its side walls is less. That means better localization of energy in the center of the waveguide, and leads to significantly less attenuation on the roughness of the side walls (Table 3). The roughness on side walls of the waveguide was set as a random variable with a standard deviation and a longitudinal roughness size. The results of calculations for waveguides with widths of 3 and 8 microns are shown in Table 3 and Figure 6. Figure 6 shows that when the waveguide is wider, the field strength on its side walls is less. That means better localization of energy in the center of the waveguide, and leads to significantly less attenuation on the roughness of the side walls (Table 3). Table 3. Comparison of the measured and calculated attenuation of the TE00 mode in silicon nitride waveguides; σ-mean square deviation of roughness; δ-longitudinal size of roughness.     Table 3 shows that for waveguides with widths of 3 and 8 microns, reducing the roughness height by three times leads to a decrease in attenuation by an order of magnitude. The study of silicon Photonics 2020, 7, 104 7 of 9 nitride waveguide's profile structure SEM images revealed that there is a significant variation in the longitudinal size of the roughness. Regarding this, calculations were also performed for various longitudinal roughness sizes. It can be seen ( Table 3) that an increase in the longitudinal size of the roughness with a constant transverse size leads to a certain decrease in attenuation, but this parameter affects the attenuation significantly less than the transverse size. Apparently, some averaged longitudinal roughness sizes can be used for numerical estimates in this case.

Conclusions
Based on the data obtained, it was found that the optical losses for a waveguide with widths of 3 and 8 µm were 1.43 and 0.31 dB/cm, respectively. Loss values are consistent with the values of analogs [42][43][44]. Losses in a waveguide with a width 8 µm are minimal, since the intensity of the mode field at the ends is much lower than in a 3 µm wide waveguide with the same thickness. The calculation of the effect of the roughness of the side walls of the lightguide layer made of silicon nitride is sufficiently consistent with the data obtained experimentally. Based on this, we can conclude that the value of the optical loss in the waveguide is significantly affected by the transverse size of the waveguide-layer's side wall roughness. This means that to improve the surface quality of multimode integrated optical waveguides it is necessary to improve methods for forming the lightguide layer.
To calculate the effect of the roughness of the side walls of a silicon nitride lightguide layer on optical losses in a multimode integrated optical waveguide, a finite-difference time-domain (FDTD) method was used. The data obtained during the study of the roughness of the lightguide layer of previously manufactured waveguides were used as a basis.