Inductively Coupled Plasma Dry Etching of Silicon Deep Trenches with Extremely Vertical Smooth Sidewalls Used in Micro-Optical Gyroscopes

Micro-optical gyroscopes (MOGs) place a range of components of the fiber-optic gyroscope (FOG) onto a silicon substrate, enabling miniaturization, low cost, and batch processing. MOGs require high-precision waveguide trenches fabricated on silicon instead of the ultra-long interference ring of conventional F OGs. In our study, the Bosch process, pseudo-Bosch process, and cryogenic etching process were investigated to fabricate silicon deep trenches with vertical and smooth sidewalls. Different process parameters and mask layer materials were explored for their effect on etching. The effect of charges in the Al mask layer was found to cause undercut below the mask, which can be suppressed by selecting proper mask materials such as SiO2. Finally, ultra-long spiral trenches with a depth of 18.1 μm, a verticality of 89.23°, and an average roughness of trench sidewalls less than 3 nm were obtained using a cryogenic process at −100 °C.


Introduction
As the core of an inertial navigation system (INS), the gyroscope is responsible for providing angular velocity to assist in the calculation of velocity, position, and attitude information [1][2][3]. The interferometric fiber-optic gyroscope (IFOG) utilizes the Sagnac effect to measure rotational motions with light [4][5][6][7]. The interferometric ring inside the IFOG has two counterpropagating light beams with the same frequency, which will generate a phase difference as the IFOG rotates with the system, from which the angular velocity can be deduced. A longer interferometric ring is able to sense slighter motion, meaning a higher sensitivity of the gyroscope, but the resulting larger size limits further widespread applications [8][9][10]. With the development of optoelectronic and micro/nano processing technology, the miniaturization of optical gyroscopes became a major subject, and the micro-optical gyroscope (MOG) was launched [11,12]. The MOG relocates the entire set of FOG components, such as the photodetector, detection circuit, and fiber-optic waveguide, onto a substrate, typically silicon, integrating them into a monolithic device [12][13][14]. The migration of the ultra-long interference ring onto the silicon substrate is an essential part of the integration, as the accuracy of the ring directly affects the performance of the gyroscope [15]. Poor sidewall morphology of the silicon waveguide trenches can cause light wave loss when light passes through the trenches, thus decreasing measurement sensitivity and accuracy.
The fabrication technologies of silicon deep trenches include femtosecond laser processing [16][17][18], mechanical machining [19,20], and inductively coupled plasma (ICP) etching [21][22][23]. Femtosecond laser processing focuses a laser beam on the surface of a workpiece through an optical system, thereby melting and vaporizing the material to The silicon wafers from RDMICRO company (Suzhou, China) are 6-inch, crystal phase <100>, and 1500 µm thick. All silicon samples were cleaned sequentially with acetone, isopropanol, and anhydrous ethanol by ultrasonication for 3 min and baked at 100°C for 10 min before the experiment. AZ4620 is a thick photoresist (PR) used as a soft mask during the Bosch process, and AZ5214 is a thin PR used in preparation of hard mask layers. The developer AZ400K was diluted with deionized (DI) water at 1:4 for use. The three materials above were sourced from AZ Electronic Materials (Luxembourg). The N-Methylpyrrolidone (NMP) solution (99.9% purity) dissolved the photoresist for the purpose of removal and was purchased from Shanghai Aladdin (Shanghai, China).

Experimental Equipment
In this experiment, electron beam evaporation deposition (F.S.E. Corporation. FU-121, New Taipei, China) was used to plate Al films. The SiO 2 films on silicon wafers were grown on a PECVD device (Oxford, Plasma Pro System 100, Yatton, UK). The Bosch process and the pseudo-Bosch etching were carried out on the Plasma lab system 100 ICP 180 (Oxford, Yatton, UK), while the cryogenic etching process was investigated on the Estrelas Micromachines 2023, 14, 846 3 of 11 100 (Oxford, Yatton, UK). The tray in the working chamber of the latter is connected to a liquid nitrogen cooling system for cryogenic control of wafers.

Geometry Design of MOG Waveguide Trenches
The MOG waveguide adopted the Archimedean spiral structure, satisfying both ultralong length and low footprint. Also, the Archimedean spiral, known as the arithmetic spiral, ensures a constant trench width and pitch between adjacent trenches. The designed dimensions of the trench are 6 µm wide, 18 µm deep, and 24 µm apart, as shown in Figure 1. The spiral ring has a total length of 37.34 m with 250 laps (n = 250), using generated path data by MATLAB R2019a and drawn by AutoCAD 2020 and SOLIDWORKS 2016. The polar equations for the inner ring ρ 1 and outer ring ρ 2 are as follows (in mm): cess and the pseudo-Bosch etching were carried out on the Plasma lab system 100 ICP 180 (Oxford, Yatton, UK), while the cryogenic etching process was investigated on the Estrelas 100 (Oxford, Yatton, UK). The tray in the working chamber of the latter is connected to a liquid nitrogen cooling system for cryogenic control of wafers.

Geometry Design of MOG Waveguide Trenches
The MOG waveguide adopted the Archimedean spiral structure, satisfying both ultra-long length and low footprint. Also, the Archimedean spiral, known as the arithmetic spiral, ensures a constant trench width and pitch between adjacent trenches. The designed dimensions of the trench are 6 μm wide, 18 μm deep, and 24 μm apart, as shown in Figure  1. The spiral ring has a total length of 37.34 m with 250 laps (n = 250), using generated path data by MATLAB R2019a and drawn by AutoCAD 2020 and SOLIDWORKS 2016. The polar equations for the inner ring 1 ρ and outer ring 2 ρ are as follows (in mm):

ICP Etching of MOG Spiral Trenches
The three processes considered in this experiment, i.e., the Bosch process, pseudo-Bosch process, and cryogenic etching, are different in terms of the etchant gas type and the entry sequence into the reactor chamber, resulting in variations in their etching mechanisms.
The Bosch process, with SF6 as the etching gas and C4F8 as the passivation gas used alternately in the reactor chamber, cycles the etching and passivation steps for deep silicon etching [34][35][36][37]. During the passivation cycle, C4F8 is ionized by ICP power and deposited on all exposed surfaces forming a fluorocarbon polymer to prevent erosion. In the subsequent etching period, SF6 mainly ionizes into SFx (x = 1, 2, 3, 4, and 5) and F ions, which are attracted by the bias voltage out of the plasma ionization region above the chamber and accelerated downward to bombard the substrate [38,39]. The SFx ions physically sputter to remove the passivation polymer layer at the trench bottom, and Fsubsequently

ICP Etching of MOG Spiral Trenches
The three processes considered in this experiment, i.e., the Bosch process, pseudo-Bosch process, and cryogenic etching, are different in terms of the etchant gas type and the entry sequence into the reactor chamber, resulting in variations in their etching mechanisms.
The Bosch process, with SF 6 as the etching gas and C 4 F 8 as the passivation gas used alternately in the reactor chamber, cycles the etching and passivation steps for deep silicon etching [34][35][36][37]. During the passivation cycle, C 4 F 8 is ionized by ICP power and deposited on all exposed surfaces forming a fluorocarbon polymer to prevent erosion. In the subsequent etching period, SF 6 mainly ionizes into SF x (x = 1, 2, 3, 4, and 5) and F ions, which are attracted by the bias voltage out of the plasma ionization region above the chamber and accelerated downward to bombard the substrate [38,39]. The SF x ions physically sputter to remove the passivation polymer layer at the trench bottom, and Fsubsequently reacts with the exposed silicon to deepen the trench. As the cycles continue, the trench depth increases, while the sidewalls remain vertical, thanks to the presence of the passivation film. In the pseudo-Bosch process, SF 6 and C 4 F 8 are injected simultaneously; therefore, etching and passivation are performed together [40,41]. The cryogenic process operates below −100 • C and adopts O 2 as the passivation gas, working concurrently with SF 6 . O 2 ionizes to form O ions, which combine with Si and F atoms to deposit SiO x F y on the trench sidewalls to reduce over-etching. The SiO x F y polymer will decompose automatically as the reactor chamber recovers to room temperature after etching [42][43][44][45].
The Bosch process has a low etch rate for photoresists, i.e., a high selectivity (the ratio of the etching rate of silicon to the mask layer), as the result of alternating etching and passivation. Photoresists can be directly used as mask layer material for the Bosch process, as illustrated in Figure 2a. After spin-coating photoresist on the wafer surface (Step i), the spiral pattern on the photomask was transferred to the soft mask layer by lithography (Step ii, iii). During etching (Step iv), the area covering AZ4620 on the wafer was not etched; instead, the silicon material in the uncovered area was continuously removed to form trenches, eventually removing the photoresist by NMP solution. For the pseudo-Bosch and cryogenic processes, etching and passivation are running in parallel, and thus the etching rate of the photoresist becomes greater, which possibly causes the problem of depleting the mask layer before the etching step is finished. Consequently, the pseudo-Bosch and cryogenic processes utilized Al and SiO 2 as hard mask layer materials separately (shown in Figure 2b). An additional etching process (Step v) was required for transferring the target pattern to the hard mask layer before etching the silicon (Step vii). Al film was etched with Cl 2 /BCl 3, and SiO 2 with CHF 3 /Ar. After the whole etching process was complete, the Al film was stripped with a boiled sulfuric acid/peroxide mixture (SPM), and SiO 2 was stripped with buffered hydrofluoric acid (BHF).
The Bosch process has a low etch rate for photoresists, i.e., a high selectivity (the ratio of the etching rate of silicon to the mask layer), as the result of alternating etching and passivation. Photoresists can be directly used as mask layer material for the Bosch process, as illustrated in Figure 2a. After spin-coating photoresist on the wafer surface (Step ⅰ), the spiral pattern on the photomask was transferred to the soft mask layer by lithography (Step ⅱ, ⅲ). During etching (Step ⅳ), the area covering AZ4620 on the wafer was not etched; instead, the silicon material in the uncovered area was continuously removed to form trenches, eventually removing the photoresist by NMP solution. For the pseudo-Bosch and cryogenic processes, etching and passivation are running in parallel, and thus the etching rate of the photoresist becomes greater, which possibly causes the problem of depleting the mask layer before the etching step is finished. Consequently, the pseudo-Bosch and cryogenic processes utilized Al and SiO2 as hard mask layer materials separately (shown in Figure 2b). An additional etching process (Step ⅴ) was required for transferring the target pattern to the hard mask layer before etching the silicon (Step ⅶ). Al film was etched with Cl2/BCl3, and SiO2 with CHF3/Ar. After the whole etching process was complete, the Al film was stripped with a boiled sulfuric acid/peroxide mixture (SPM), and SiO2 was stripped with buffered hydrofluoric acid (BHF).

Characterization
The film thickness of SiO 2, Al, and PR, respectively, was measured by a spectroscopic ellipsometer (Semilab, GES5E, Budapest, Hungary) and a stylus profilometer (Bruker, DektakXT, Billerica, MA, USA). All SEM images were obtained by scanning electron microscopes (Hitachi, SU3900, Tokyo, Japan and FEI, Quanta 3D FEG, Hillsboro, OR, USA), and the surface morphology of MOG spiral trenches was observed by a metallographic microscope (Zeiss, Axiocam 208 color, Jena, Germany). A white light interferometer (Zygo, NewView 9000, Middlefield, CT, USA) was used to characterize the surface roughness of sidewalls after cutting the sample tangentially along the trench sidewall (illustrated in Figure 3).
DektakXT, Billerica, MA, USA). All SEM images were obtained by scanning electron microscopes (Hitachi, SU3900, Tokyo, Japan and FEI, Quanta 3D FEG, Hillsboro, OR, USA), and the surface morphology of MOG spiral trenches was observed by a metallographic microscope (Zeiss, Axiocam 208 color, Jena, Germany). A white light interferometer (Zygo, NewView 9000, Middlefield, CT, USA) was used to characterize the surface roughness of sidewalls after cutting the sample tangentially along the trench sidewall (illustrated in Figure 3). the sidewalls of marked area were completely exposed, allowing roughness characterization by white light interferometer, and (c) the sample was placed vertically under the measuring lens of the white light interferometer, which was then adjusted to focus on the exposed sidewall area for roughness measurement.

Bosch Process
As previously mentioned, the etching gas SF6 and passivation gas C4F8 are alternated in the Bosch process. To ensure process stability and repeatability, each gas was applied in small amounts during each etching or passivation cycle. SF6 was injected during deposition, and C4F8 during etching, both with a flow of 5 sccm. The soft mask layer AZ4620 was 6 μm thick (4000 rpm), and the optimized process parameters are listed in Table 1. After 100 cycles (30 min in duration), silicon trenches of 30.72 μm deep were obtained, with an etching rate of 1.02 μm/min. Although the trench depth was higher than 18 μm, which could be adjusted by reducing the number of cycles (total cycle time), the critical problem was the scalloped undulation of the sidewalls, as shown in Figure 4.
It is the result of lateral erosion acting on the newly etched sidewalls without the protection of passivation film during the etching cycle, leading to continuous undulations as the cycles persist. The size of the scallop microstructures was around 70-80 nm, not achieving low sidewall roughness.  the sidewalls of marked area were completely exposed, allowing roughness characterization by white light interferometer, and (c) the sample was placed vertically under the measuring lens of the white light interferometer, which was then adjusted to focus on the exposed sidewall area for roughness measurement.

Bosch Process
As previously mentioned, the etching gas SF 6 and passivation gas C 4 F 8 are alternated in the Bosch process. To ensure process stability and repeatability, each gas was applied in small amounts during each etching or passivation cycle. SF 6 was injected during deposition, and C 4 F 8 during etching, both with a flow of 5 sccm. The soft mask layer AZ4620 was 6 µm thick (4000 rpm), and the optimized process parameters are listed in Table 1. After 100 cycles (30 min in duration), silicon trenches of 30.72 µm deep were obtained, with an etching rate of 1.02 µm/min. Although the trench depth was higher than 18 µm, which could be adjusted by reducing the number of cycles (total cycle time), the critical problem was the scalloped undulation of the sidewalls, as shown in Figure 4. Cycles 1800

Pseudo-Bosch Process
Since the switching between etching and passivation caused scallops on the sidewalls of deep trenches, the pseudo-Bosch process was attempted instead. Separate passivation before etching in the Bosch process guarantees minimal corrosion of the soft mask layer, but when carried out together, the etching rate increases significantly. Metal films are highly resistant to fluorine-based plasma etching and have a good selectivity relative to silicon substrates, making it sufficient for use as a hard mask with only a thin film. A 400 nm thick Al film was therefore chosen as the hard mask for the pseudo-Bosch process in view of its simplicity for deposition by evaporation and ease-of-use for mask patterning

Pseudo-Bosch Process
Since the switching between etching and passivation caused scallops on the sidewalls of deep trenches, the pseudo-Bosch process was attempted instead. Separate passivation before etching in the Bosch process guarantees minimal corrosion of the soft mask layer, but when carried out together, the etching rate increases significantly. Metal films are highly resistant to fluorine-based plasma etching and have a good selectivity relative to silicon substrates, making it sufficient for use as a hard mask with only a thin film. A 400 nm thick Al film was therefore chosen as the hard mask for the pseudo-Bosch process in view of its simplicity for deposition by evaporation and ease-of-use for mask patterning by chlorine plasma etching. The experimental data and results are detailed in Table 2, and Figure 5 shows the SEM images of trench sections using different parameters in the pseudo-Bosch process. Groups 1-3 changed the flow of C 4 F 8, and Group 4 used the low flow of SF 6 and C 4 F 8 for verifying the effect of plasma density.

Pseudo-Bosch Process
Since the switching between etching and passivation caused scallops on the sidewalls of deep trenches, the pseudo-Bosch process was attempted instead. Separate passivation before etching in the Bosch process guarantees minimal corrosion of the soft mask layer, but when carried out together, the etching rate increases significantly. Metal films are highly resistant to fluorine-based plasma etching and have a good selectivity relative to silicon substrates, making it sufficient for use as a hard mask with only a thin film. A 400 nm thick Al film was therefore chosen as the hard mask for the pseudo-Bosch process in view of its simplicity for deposition by evaporation and ease-of-use for mask patterning by chlorine plasma etching. The experimental data and results are detailed in Table 2, and Figure 5 shows the SEM images of trench sections using different parameters in the pseudo-Bosch process. Groups 1-3 changed the flow of C4F8, and Group 4 used the low flow of SF6 and C4F8 for verifying the effect of plasma density.   It can be seen in Figure 5 that lateral etching occurred on the silicon beneath the mask, especially on the top sidewalls more severely, called undercut. Through searching literature and analysis, it was determined to be caused by the metal mask. The eddy current heating effect [46] and charges in the mask layer [47,48] are responsible for this result. For conductive metal masks, the RF power generates eddy currents inside the metal mask, causing heating that contributes to the desorption of the surrounding fluorocarbon film and thus speeding up the etching below the Al mask. But the heat flux caused by eddy currents is minor and not sufficient to dominate. The positive charge at the bottom of the Al mask deflects the CF x + ions that undertake a major role in the passivation deposition [49], reducing the thickness of the passivation layer at the top sidewall, which leads to increased lateral etching of this region. Figure 5a-c reveal that undercut was suppressed with the increase of passivation gas C 4 F 8 flow, confirming that this defect is mainly controlled by the passivation stage. An additional group that reduced the flow of both gases, as displayed in Figure 5d, also occurred with undercut, excluding the disturbance of higher ion densities due to high fluxes in Groups 1-3.
Finally, SiO 2 was determined as a reliable hard mask material. The thickness of the SiO 2 layer prepared by PECVD was around 2 µm, and the final process parameters are presented as the fifth recipe in Table 2. The undercut under the mask was alleviated as the mask material changed to SiO 2 (as shown in Figure 5e), and the etching rate was reached at 1.62 µm/min, but the verticality of the sidewall remains to be improved.

Cryogenic Etching
Although the pseudo-Bosch process using SiO 2 as a mask layer has been proven to achieve micro-trenches with good morphological sidewalls, the etching rate is still undesirable. For further improvement, we investigated cryogenic etching for deep trenches. SF 6 and O 2 are used for etching and passivation, respectively, in which SF 6 provides F radicals to react with silicon, and meanwhile, O 2 combines with other particles to generate SiF x O y film, the passivation layer in the cryogenic etching process.
In this experiment, SiO 2 remained as the hard mask layer, and the working temperature of cryogenic etching was set to −100 • C. The work aimed to obtain vertical and smooth sidewalls by varying the flow of O 2 and the process time, keeping ICP power, RF power, temperature, and chamber pressure constant (as shown in Table 3). In both Bosch and pseudo-Bosch processes, the high-energy plasma bombardment and etching of the silicon wafer increase the substrate temperature, contributing to nonuniformity of etching. The cryogenic process allows the wafer to be connected with a liquid nitrogen cooling system, which provides a consistent cryogenic environment over the entire wafer, thereby improving the etch profile.
The results of cryogenic etching are concentrated in Figure 6. With an oxygen flow of 8 sccm, a depth of 32.81 µm can be reached after 10 min of etching. But from its SEM image (as shown in Figure 6a), the profile is observed as narrow at the top and wide at the bottom, resembling a bottle, and the magnified view of sidewalls shows an uneven morphology, measured to undulate at 40-60 nm. The trench profile evolved towards a V-shaped structure as O 2 flow increased (Figure 6d), and the undulations on the sidewalls gradually disappeared. This can be summarized as the increase in O 2 flow improves passivation efficiency and enhances the protection of sidewalls. It was also found that the etching rate should theoretically decrease with increasing O 2 flow, but the data from the previous three groups are controversial, indicating that the average etching rate is also related to the process time. For this, a fourth group was built as the comparison group for the first group, with identical parameters, except the process time was shortened to 3.5 min.
The differences in etching rates and profiles between these two groups confirmed our guess. We speculate that the gradual deepening of the trench and the property of the high aspect ratio of the trench contribute to the reduced efficiency of the plasma in reaching the trench bottom and removing the silicon material, intuitively expressed as an effect of process time, i.e., the shorter the process time, the faster the average etching rate. cess time. For this, a fourth group was built as the comparison group for the first group, with identical parameters, except the process time was shortened to 3.5 min. The differences in etching rates and profiles between these two groups confirmed our guess. We speculate that the gradual deepening of the trench and the property of the high aspect ratio of the trench contribute to the reduced efficiency of the plasma in reaching the trench bottom and removing the silicon material, intuitively expressed as an effect of process time, i.e., the shorter the process time, the faster the average etching rate. A Partial Least Squares (PLS) regression model was created to analyze the correlation between gas flow, process time, and etching profile. The SF6 to O2 ratio and the process time were selected as the independent variables x1 and x2, and the etching depth and tilt angle as the dependent variables y1 and y2. Based on the experimental data in Table 3, the regression model was established as follows: The histogram of the regression coefficients (shown in Figure 7a) visualizes that the regression coefficients of the ratio of SF6 to O2 flow x1 is much larger than the process time x2 for both etching depth y1 and tilt angle y2, meaning that the gas flow has a more significant effect on the etching profiles. Figure 7b and c, respectively, display the prediction graphs of etching depth and tilt angle based on the regression equation, and the horizontal and vertical coordinates of data points separately represent the fitted values and the actual values. Data points closer to the diagonal line mean that the predicted value is closer to the actual value, implying the higher confidence of the regression equation. Compared with Figure 7c, the fitted results of Figure 7b about the etching depth are better, indicating the regression equation of the etching depth is more desirable, which is because the regression coefficients of the tilt angle are both lower than those of the etching depth. Overall, the minor differences between the fitted values of the equation and the original data demonstrate that the model created is acceptable. According to the model, for obtaining a A Partial Least Squares (PLS) regression model was created to analyze the correlation between gas flow, process time, and etching profile. The SF 6 to O 2 ratio and the process time were selected as the independent variables x 1 and x 2 , and the etching depth and tilt angle as the dependent variables y 1 and y 2 . Based on the experimental data in Table 3, the regression model was established as follows: The histogram of the regression coefficients (shown in Figure 7a) visualizes that the regression coefficients of the ratio of SF 6 to O 2 flow x 1 is much larger than the process time x 2 for both etching depth y 1 and tilt angle y 2 , meaning that the gas flow has a more significant effect on the etching profiles. Figure 7b and c, respectively, display the prediction graphs of etching depth and tilt angle based on the regression equation, and the horizontal and vertical coordinates of data points separately represent the fitted values and the actual values. Data points closer to the diagonal line mean that the predicted value is closer to the actual value, implying the higher confidence of the regression equation. Compared with Figure 7c, the fitted results of Figure 7b about the etching depth are better, indicating the regression equation of the etching depth is more desirable, which is because the regression coefficients of the tilt angle are both lower than those of the etching depth. Overall, the minor differences between the fitted values of the equation and the original data demonstrate that the model created is acceptable. According to the model, for obtaining a trench with 90 • sidewalls, the gas ratio should be 13.1, namely an O 2 flow of 7 sccm, as in the fifth recipe in Table 3. After successive explorations, the desirable silicon spiral trench sample is displayed in Figure 8, with a sidewall verticality of 89.2 • , an average width of 6.1 µm, and an average depth of 18.1 µm. Moreover, the average roughness of the trench sidewall characterized by the white light interferometer is only about 2.5 nm, which is significant for future light wave conduction. trench with 90° sidewalls, the gas ratio should be 13.1, namely an O2 flow of 7 sccm, as in the fifth recipe in Table 3. After successive explorations, the desirable silicon spiral trench sample is displayed in Figure 8, with a sidewall verticality of 89.2°, an average width of 6.1 μm, and an average depth of 18.1 μm. Moreover, the average roughness of the trench sidewall characterized by the white light interferometer is only about 2.5 nm, which is significant for future light wave conduction.

Conclusions
In this study, the Bosch process, pseudo-Bosch process, and cryogenic etching were used to fabricate silicon spiral deep trenches. The Bosch process, with its inherent characteristic of alternate etching and passivation, could produce 70-80 nm scallops on the sidewalls of the deep trenches. Undercut of the silicon beneath the Al mask occurred in the pseudo-Bosch process. The charges in the mask are responsible for this result, achieved by interference passivation, and this negative effect was mitigated by replacing Al with SiO2 as the hard mask. A cryogenic process with a higher etching rate was demonstrated as a viable method in which cryogenic control ensures the stable temperature of the wafer trench with 90° sidewalls, the gas ratio should be 13.1, namely an O2 flow of 7 sccm, as in the fifth recipe in Table 3. After successive explorations, the desirable silicon spiral trench sample is displayed in Figure 8, with a sidewall verticality of 89.2°, an average width of 6.1 μm, and an average depth of 18.1 μm. Moreover, the average roughness of the trench sidewall characterized by the white light interferometer is only about 2.5 nm, which is significant for future light wave conduction.

Conclusions
In this study, the Bosch process, pseudo-Bosch process, and cryogenic etching were used to fabricate silicon spiral deep trenches. The Bosch process, with its inherent characteristic of alternate etching and passivation, could produce 70-80 nm scallops on the sidewalls of the deep trenches. Undercut of the silicon beneath the Al mask occurred in the pseudo-Bosch process. The charges in the mask are responsible for this result, achieved by interference passivation, and this negative effect was mitigated by replacing Al with SiO2 as the hard mask. A cryogenic process with a higher etching rate was demonstrated as a viable method in which cryogenic control ensures the stable temperature of the wafer

Conclusions
In this study, the Bosch process, pseudo-Bosch process, and cryogenic etching were used to fabricate silicon spiral deep trenches. The Bosch process, with its inherent characteristic of alternate etching and passivation, could produce 70-80 nm scallops on the sidewalls of the deep trenches. Undercut of the silicon beneath the Al mask occurred in the pseudo-Bosch process. The charges in the mask are responsible for this result, achieved by interference passivation, and this negative effect was mitigated by replacing Al with SiO 2 as the hard mask. A cryogenic process with a higher etching rate was demonstrated as a viable method in which cryogenic control ensures the stable temperature of the wafer during the process and etching uniformity. It was found that the etching rate of the deep trenches was also dependent on the process time. The association of the etching rate with gas flow and process time was revealed by a PLS regression model. The optimal silicon trench with a verticality of 89.23 • was fabricated, and the sidewall roughness was only 2.5 nm on average. Our future work includes the selection and deposition into silicon trenches of optical waveguide materials, the construction of optical platforms for measuring light wave transmission, and the combination of silicon trenches with an MOG.