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Abstract
We have been developing a light-weight X-ray telescope using micro electro mechanical systems technologies for future space missions. Micropores of 20 µm width are formed in a 4-inch Si wafer with deep reactive ion etching, and their sidewalls are used as X-ray reflection mirrors. The flatness of the sidewall is an important factor to determine the imaging performance, angular resolution. It is known that hydrogen annealing is effective to smooth a Si surface. We tested 150 hour annealing to achieve the ultimately smooth sidewalls. After 50 hour, 100 hour, and 150 hour annealing, the angular resolution improved 10.3, 4.0, and 2.6 arcmin in full width at half maximum (FWHM) and 17.0, 14.5, and 10.8 arcmin in half-power width (HPW). In spite of this improvement, the edge shapes of the sidewall were rounded. Therefore, both edges of the sidewall were ground and polished, and then the angular resolution was improved further to 3.2 arcmin (FWHM) and 5.4 arcmin (HPW).
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Telescopes are essential in space X-ray observations, especially X-ray astronomy. Since X-rays emitted from astronomical objects are absorbed by the Earth’s atmosphere, the main way to observe them is to launch a telescope on a satellite. A commonly used telescope configuration is Wolter type-I in which coaxial and confocal hyperboloid and paraboloid mirrors are combined [1]. X-rays are collected through twice total reflections on their surface.
One of the important indices of telescope performance is an angular resolution which represents imaging performance. The Wolter type-I telescopes have been fabricated in various ways where a telescope with higher angular resolution tends to be heavy. This is because the mirrors become thicker to achieve an accurate shape. For example, the angular resolution in half-power diameter and weight per effective area at 1.5 keV onboard Chandra [2] are 0.5 arcsec and $\sim$12000 kg/m$^2$, XMM-Newton [3] are 15 arcsec and $\sim$3000 kg/m$^2$, and Hitomi [4] are 72 arcsec and $\sim$600 kg/m$^2$, respectively. On the other hand, heavy telescopes are in general expensive to fabricate and launch, therefore a light one is demanded.
We have been developing an ultra light-weight X-ray telescope using micro electro mechanical systems (MEMS) technologies [5–18]. This type can break the conventional relationship between angular resolution and weight per effective area, and achieve a weight reduction of more than one order of magnitude.
Figure 1 shows its latest fabrication process flow. As a first step, micropores of 20 $\mu$m width are formed in a 4-inch diameter silicon wafer with deep reactive ion etching (DRIE). Their sidewalls are used as X-ray reflection mirrors. However, the root mean square (rms) surface roughness of the sidewalls after DRIE is tens of nm at 10 $\mu$m scale, which does not satisfy the required roughness on the order of 1 nm or less for total X-ray reflection. Therefore, as a second step, annealing is necessary to smooth the sidewalls. Annealing activates self-diffusion on the silicon surface at high temperatures in inert gases such as hydrogen, nitrogen, and argon. It has been reported that the silicon surface is spontaneously smoothed by exposing the wafer to near the melting point [19–24]. The third step is grinding and chemical mechanical polishing (CMP) process. The edges of the sidewall after the DRIE process are not actually ideal shapes for X-ray reflection. We can solve this issue by grinding and polishing both sides of the wafer [17]. The fourth step is to deform the entire wafer into a spherical shape in order to collect the parallel X-rays from astronomical objects. In the fifth step, the reflection surface is coated with a metal film by atomic layer deposition to enhance reflectivity. Finally, two wafers with different curvature radii are precisely stacked.
Because the ideal mirror surfaces of the Wolter type-I optic are parabolla/hyperbolla, this is a conical approximation. However, because of the thin wafer, this approximation does not contribute to the angular resolution significantly even at a short focal length (e.g., 1 arcsec when the wafer thickness is 300 $\mu$m and the focal length is 250 mm). The angular resolution is theoretically limited by X-ray diffraction. When the pore width is 20 $\mu$m, it is 13 arcsec when the X-ray energy is 1 keV. This limit is inversely proportional to the X-ray energy. Since this telescope is extremely light-weight ($\sim$15 g for two 4-inch Pt-coated wafers) and has a short focal length (e.g., 250 mm), this type is a good candidate for <50 kg class small satellites such as GEO-X [25] in which payload resources are limited.
There is, however, room for improvement of the angular resolution of the MEMS X-ray optics [26]. There are two main factors that determine the angular resolution: one is the accuracy of the mirror arrangement, and the other is the accuracy of the mirror shapes. The former represents the accuracy with which the mirrors are lined up on ideal curved surfaces, and is greatly affected by the verticality of the sidewalls in the DRIE process and deformation accuracy in the deformation process. The latter refers to the flatness of the mirror surface which is affected by the DRIE and the annealing process. The final imaging performance of a telescope is simply determined by the square root of the sum of squares of each accuracy when each value is independent.
This paper aims to improve the accuracy of the mirror shapes of MEMS-based X-ray optics. For this purpose, the sidewalls are extremely smoothed by annealing. The diffusion length $\lambda _{\rm D}$ of Si atoms, an index of surface smoothing, can be expressed as
where $D_{\rm s}$ is the surface diffusion coefficient which characterizes the surface diffusion rate depending on annealing conditions and $t$ is a processing time [27–29]. $D_{\rm s}$ is limited by experimental devices, however $t$ has infinite potential for extension. In general, the time is only several hours at most including our past development [16–18]. We can expect the longer the processing time, the larger the scale of Si surface flattening. Therefore, we made the processing time longer to an unprecedented long term 150 hours which is the longest hydrogen annealing time in the world as far as we know, and investigated how the Si surface changes with the time and how it affects the angular resolution.2. Experiments
2.1 DRIE process
Firstly, we fabricated a sample optic using a Si wafer (111) with a thickness of 300 $\mu$m. A number of micropores with a width of 20 $\mu$m were etched in concentric circles in a region of radius 7.5–30 mm by Bosch process [30]. Figure 2 shows the sample optic. The slits were taken from 6 different positions within the wafer to measure the sidewall shape. We obtained two-dimensional cross-sectional shapes of the sidewalls with Dektak stylus profiler as shown in Fig. 3(a). A typical sidewall profile measured after the DRIE process is shown in Fig. 3(b). Burrs can be seen at both edges of the sidewall. This is most likely due to the long Bosch process to etch high aspect micropores, which results in insufficient sidewall protection. However, it is difficult to avoid these structures while keeping the flatness and verticality of the sidewalls because burrs are small (<1 $\mu$m) relative to the sidewall length (300 $\mu$m) [17,31]. This tendency was similar within the optic.
Fig. 2. A sample X-ray optic. In the areas that look white, some slits are artificially sampled to measure the sidewall shape. The measurement results from the cyan rectangle region are shown in Figs. 3(b)-(h) and Figs. 5(b)-(h). The red rectangle region shows X-ray irradiation position.
Fig. 3. (a) A conceptual diagram of sidewalls of our X-ray optic and two-dimensional cross-sectional shape measurement by Dektak stylus profiler. Typical sidewall shapes after (b) DRIE, (c) 1 hour, (d) 50 hour, (e) 100 hour, (f) 150 hour annealing, (g) grinding and CMP, and (h) additional 2 hour annealing. In each panel, the left side corresponds to the upper side of the wafer during the annealing process.
2.2 Long-term annealing process
In the annealing process, we utilized the annealing machine developed by Dr. Yoshiaki Kanamori, Tohoku University. This heats a sample with infrared lamps as shown in Fig. 4. During the heating process, a thermocouple was contacted with the sample to measure the temperature. We have 3 variable parameters: gas type and flow rate, temperature, and pressure. Here, $D_{\rm s}$ in Eq. (1) is generally considered to be higher at higher temperatures and at lower pressures [21,32]. The conditions used in our experiments are shown in Table 1. Hydrogen was selected as the process gas because it has a suppressive effect on oxidation of silicon surface, and the flow rate was 2 SLM which was the maximum setting of the machine. The temperature was 1100$^{\circ }$C, which was a standard value and close to the upper limit of the lamp output. The pressure was set to 5 kPa, the lowest pressure at which we confirmed smoothing effect. We then proceeded to the long-term annealing. To reduce the load on the lamp, we limited the processing time to $\sim$3 hours at a time, achieving a total of 150 hours over 1.5 months.
Fig. 4. Appearance of the annealing machine, the inside of the main chamber (left), and the load-lock chamber (right). Using four SiC chips underneath the sample optic, the sample is floated from the ground in order to increase gas flow.
Table 1. Condition of the annealing experiment.
2.3 Observation of sidewalls
In order to verify the smoothing effect, we measured the three-dimensional surface profiles of the sidewalls with atomic force microscopy (AFM) as shown in Fig. 5(a). Before annealing, the surface was apparently rough as shown in Fig. 5(b). The roughnesses were $\sim$17, $\sim$19, and $\sim$19 nm rms at 1, 10, and 100 $\mu$m scale, respectively.
Fig. 5. (a) Same as Fig. 3(a) but for three-dimensional surface profile measurements by AFM. Typical surface profiles of the sidewalls after (b) DRIE, (c) 1 hour, (d) 50 hour, (e) 100 hour, (f) 150 hour annealing, (g) grinding and CMP, and (h) additional 2 hour annealing. In each panel, the measurement scales are $1 \times 1$ $\mu$m$^2$, $10 \times 10$ $\mu$m$^2$, and $100 \times 100$ $\mu$m$^2$ from left to right. All images are corrected for tilt angle of samples.
Figures 5(c)-(f) correspond to the sidewalls after 1 hour, 50 hour, 100 hour, and 150 hour annealing, respectively. Although these panels are not the same sidewall data, the trends should be similar since the nearby slits (inside the cyan rectangle in Fig. 2) are sampled. The surface had already been smoothed after 1 hour annealing. Periodic structures can be seen at 1 $\mu$m scale. They are interpreted as step-terrace structures on the Si surface and were also seen in our previous samples [17]. The directions of the periodic structure depend on the sampling position. Furthermore, larger waviness can be seen at 100 $\mu$m scale. This was formed during the DRIE process and extended after annealing. Both features suggest successful annealing. The surface roughnesses after 150 hour annealing were improved to $\sim$0.5, $\sim$1.0, and $\sim$11 nm rms and the improvement rate was $\sim$34, $\sim$19, and $\sim$1.7 at 1, 10, and 100 $\mu$m scale, respectively. We then observed the wafer surface around micropores as shown in Fig. 6. It was confirmed that the angular corners were rounded over processing time. That also suggests that annealing went well.
Fig. 6. SEM images of the micropores after (a) 1 hour, (b) 50 hour, (c) 100 hour, and (d) 150 hour annealing.
We also measured the cross-sectional shape of the sidewalls with Dektak stylus profiler. Figures 3(c)-(f) show the sidewalls after 1 hour, 50 hour, 100 hour, and 150 hour annealing, respectively. Here, the sample was put in the process chamber with the left side facing up in each panel. We found two major changes in the shape. One is that the back side (right side of panels (c)-(f) in Fig. 3) edge of the wafer is rounded with processing time. This suggests that there was a difference in the annealing effect between the front and back sides of the wafer. The other is that burr becomes taller over processing time. The growth rate slows down as time increases. Both changes were observed at 6 different positions on the wafer, and the trends were similar including the amount of change. These two changes are not desirable for X-ray reflection because the former makes the reflected X-ray images unclear and the latter blocks the incident X-rays.
2.4 X-ray measurements
X-ray irradiation tests were performed to measure the angular resolution at ISAS/JAXA 30 m beamline [33,34]. Here, we measured the sample optic after 50 hour, 100 hour, 150 hour annealing, respectively. Figure 7 shows the setup of the X-ray irradiation tests. X-rays from the generator are narrowed by slits to a width that can irradiate only a single mirror, and are incident at $\theta =0.8^{\circ }$. To compare with the shape of the sidewalls, we chose the mirror next to the sampling point as the measurement point (red rectangle in Fig. 2). X-rays reflected by the sidewall reach the detector with a certain degree of spread. The detector obtains the beam profile around $2\theta =1.6^{\circ }$. We used a CCD as a detector after 50 hour and 100 hour annealing however it was broken after the measurements. We therefore changed the detector to a new CMOS after 150 hour annealing. Pixel sizes and areas of these two detectors are similar but the new CMOS has lower electrical noise.
Fig. 7. Setup for the X-ray irradiation tests. X-rays are reflected from a single mirror of the sample optic.
We evaluated the one-dimensional profile of the reflected X-ray beam. There are 2 methods to evaluate an angular resolution. One is called full width at half maximum (FWHM). It is the angular width of a reflection profile measured between those points which are half the maximum intensity. It is unaffected by skirts of a reflection profile but exclusively determined by the vicinity of the maximum intensity. The other is called half-power width (HPW). It is the angular width of a reflection profile measured between those points which are chosen to have 50% intensity of the total. FWHM is an important index for point source detection while HPW is for detecting faint sources near bright sources.
2.5 Results
Figures 8(a)-(c) show the one-dimensional projection profiles of the reflected X-rays in the 2$\theta$ direction measured after 50 hour, 100 hour, and 150 hour annealing, respectively. The angular resolution was calculated in the range of $\pm 1^{\circ }$ from the maximum point of the reflection profile. The FWHM improved to 10.3 arcmin at 50 hours, 4.0 arcmin at 100 hours, and 2.6 arcmin at 150 hours, showing a steady improvement with processing time. This suggests that, as expected, the smoothing was achieved on a large scale by extending the annealing time. The HPW changed more slowly, 17.0 arcmin at 50 hours, 14.5 arcmin at 100 hours, and 10.8 arcmin at 150 hours. The reason for the difference between FWHM and HPW is sub-peak structures, which are located away from the main peak, as labeled I in Fig. 8(b) and II in Fig. 8(c). These weak peaks cause a loss of angular resolution (HPW). Since these components are only seen after 100 hour annealing and are reflected at a lower angle than the main peak, they are considered to be from the rounded area seen in Figs. 3(e) and (f).
Fig. 8. Projection profiles of the reflected X-ray photons on the sidewall after (a) 50 hour, (b) 100 hour, (c) 150 hour annealing, (d) grinding and CMP, and (e) additional 2 hour annealing. A CCD detector is used in panels (a) and (b), while the panels (c), (d), and (e) are taken with a CMOS.
Summarizing the above results, the center part of the sidewall could be flattened with processing time and then improved the angular resolution. However, one end of the sidewall was rounded due to long-term annealing, and there was room for improvement. If only the center of the sidewall was used for reflection, the angular resolution would be maximized. In addition, burrs are also unnecessary structures for X-ray reflection. Therefore, we introduced the grinding and CMP process to remove both edges of the sidewall.
2.6 Grinding and CMP process
By grinding and polishing our sample from both sides, we can eliminate the burrs and the rounded area on the sidewalls. A wafer becomes thinner by grinding both sides. Besides, the combination of mechanical removal by abrasive grains and chemical dissolution of the processing fluid called slurry polishes the wafer to a smooth surface. These are common methods used in wafer processing [35,36]. When we introduced this process for the first time, there had been a problem that the surface roughness of the sidewall was degraded due to chemical action during the grinding and CMP process [17]. To improve this, we updated the grinding and CMP process.
First, the Si surface was thermally oxidized at 1050$^{\circ }$C for 1 hour in O$_2$ atmosphere. This thin ($\sim$100 nm) oxide film can protect the Si sidewalls from the chemical action of the slurry. Second, the micropores were filled with resin. This prevents the sample from being damaged and broken by the stress of grinding and polishing. We filled the micropores with photoresist AZ P4620 while vibrating with ultrasonic waves and then baked it at 115$^{\circ }$C to cure it. Third, the wafer was thinned by grinding and CMP. We ground and polished 50 and 100 $\mu$m for the front and back sides, respectively. Finally, the wafer was cleaned with acetone and O$_2$ ashing to remove the photoresist and buffered hydrofluoric acid to remove the oxide film. The buffered hydrofluoric acid was diluted to less than 1% to suppress the roughness increase on the sidewalls.
Figure 3(g) shows the sidewall after the grinding and CMP process. We successfully removed 50 $\mu$m from the front side and 100 $\mu$m from the back side, and left only the flat part of the mirror. The three-dimensional surface profiles of the sidewall at scales larger than 10 $\mu$m were almost unchanged as shown in Fig. 5(g). However, the periodic structure seen at 1 $\mu$m scale disappeared. This was probably caused by the thermal oxidation step. The surface roughnesses after the grinding and CMP process were $\sim$0.7, $\sim$1.4, and $\sim$13 nm rms at 1, 10, and 100 $\mu$m scale, respectively. It was slightly worse than after 150 hour annealing, but was sufficient for X-ray reflection.
In order to check the effect on the angular resolution, an X-ray irradiation test was performed with the same setup as in Subsection 2.4. Figure 8(d) shows the result of the reflected projection profiles measured after the grinding and CMP process. The FWHM slightly degraded from 2.6 arcmin to 3.2 arcmin, which may be related to the increase in the surface roughness of the sidewall. On the other hand, the HPW improved significantly from 10.8 arcmin to 5.4 arcmin. This is due to the disappearance of the weak sub-peak at lower angle.
2.7 Second annealing process
We then performed annealing again to recover the roughened sidewalls during the grinding and CMP process. The conditions were the same as in Table 1, however the processing time was set to 2 hours to avoid rounding the corner edge. Figure 5(h) shows the surface profile of the sidewall after the second annealing process. As expected, the surface roughness appeared to have recovered, mainly on the 1 $\mu$m scale. The roughnesses after the second annealing process were $\sim$0.4, $\sim$1.1, and $\sim$12 nm rms at 1, 10, and 100 $\mu$m scale, respectively. However, burr-like structures of $\sim$200 nm were newly formed as shown in Fig. 3(h). These may be rounding due to annealing.
We conducted the same X-ray irradiation test again in this condition. The result is shown in Fig. 8(e). The FWHM changed from 3.2 arcmin to 3.4 arcmin and the HPW from 5.4 arcmin to 8.6 arcmin. Eventually, second annealing seems to have no positive effect on the angular resolution.
3. Discussion
Through 150 hour annealing, the height on the sidewalls varies on the order of hundreds of nm. We first focus on the shape change of the back side edge. The change in the top of the burr on the right side of Figs. 3(b)-(f) was 1.1 $\mu$m before and after the 150 hour annealing process. It was much smaller than the mirror length, however it was large enough to affect imaging performance. This can be interpreted as an excessive annealing effect. Only the one side showed a noteworthy change, suggesting that the temperature may have been higher on the lower side of the wafer. Since 150 hours are divided into 21 cycles in our experiment, it is undeniable that such a gradient can occur for a certain period of time during the rise and fall of the temperature.
Secondly, we found that the sub-peak III in Fig. 8(d) becomes more dominant than that of Fig. 8(c). This is likely a reflection from the sidewall that was blocked by the left burr in Fig. 3(f). Meanwhile, new sub-peaks IV in Fig. 8(e) are inferred to be associated with the small burrs by comparing Figs. 3(g) and (h). In this way, the burrs on the sidewalls are involved in the imaging performance of an optic. In order to examine the relationship between the burr and the processing time, we fabricated another sample optic without burrs using the DRIE and the grinding and CMP processes. As a result, the burrs became taller like a power-law shown in Fig. 9. However, burrs are not required in our optics. The grinding and CMP process is necessary after the long-term annealing process.
Fig. 9. Relationship between annealing time and burr height under the conditions in Table 1. The height of the burr at 0 hours is set to 0 $\mu$m for convenience. Error bars correspond to standard deviations of 20 measurement points. The solid line shows the best-fit power-law model ($h=100 t^{0.3}$) where the burr height is represented by $h$ in $\mu$m and the annealing time as $t$ in hour.
We plot the relationship between annealing time and angular resolution as shown in Fig. 10. The dotted points represent the angular resolution after the grinding and CMP process. We can see that the FWHM improves more drastically. By fitting a power-law curve, it is expected to reach 1 arcmin when the processing time is >300 hours. On the other hand, the grinding and CMP process is useful for significant improvement in HPW since it is affected by the rounding edge and the weak sub-peak. Either way, even higher angular resolution can be expected by extending the processing time.
Fig. 10. Relationship between annealing time and angular resolution under the conditions in Table 1. Blue and red points represent angular resolution in FWHM and HPW, respectively. The solid line shows the best-fit power-law model ($f=1719t^{-1.3}$) where the FWHM after the annealing is represented by $f$ in arcmin and annealing time as $t$ in hour. Dotted points represent the performance after the grinding and CMP process.
The theoretical limit on the angular resolution of our optics is 13 arcsec at 1 keV as written in Section 1. From the experimental results shown in Fig. 10, the angular resolution will be improved to this value when the annealing time exceeds $\sim$1000 hours. The better the initial shape of the mirror surface is, the shorter the processing time becomes. Therefore, the etching accuracy is equally important. If the angular resolution is less than 1 arcmin, hopefully 30 arcsec, our optics will be used in more various X-ray astronomy missions. For example, in the Japanese XRISM [37] mission to be launched in 2023, the angular resolution of the telescope for the X-ray microcalorimeter instrument is about 1 arcmin.
4. Conclusion
To the best of our knowledge, the longest term annealing was conducted on a silicon wafer. The surface roughnesses of the micropore sidewalls at small scales with AFM were successfully smoothed after the annealing process. The improvement rates were $\sim$34, $\sim$19, and $\sim$1.7 at 1, 10, and 100 $\mu$m scale, respectively. We also measured the sidewall shapes on larger scales with Dektak stylus profiler and found that structures at both edges of the sidewall changed significantly through 150 hour annealing. While the edge corresponding to the upper side in the process chamber got taller, the edge corresponding to the lower side was rounded. Since these were not desirable, we ground and chemical mechanical polished both sides of the wafer to remove them. At that time, no critical roughness degradation was observed due to sidewall protection by the oxide film.
The point spread function of the reflected photons on the sidewalls was measured as an index of imaging performance. The angular resolution of a single mirror achieved 2.6 arcmin (FWHM) and 10.8 arcmin (HPW) after the 150 hour annealing process. As for FWHM, it is close to the performance of the Wolter type-I telescope onboard X-ray astronomical satellite Suzaku [38]. After the grinding and CMP process, the angular resolution was 3.2 arcmin (FWHM) and 5.4 arcmin (HPW). The FWHM was slightly degraded however the HPW was significantly improved. These values are comparable to the level required for the future satellite GEO-X (5 arcmin in single reflection).
In conclusion, smoothing by ultra long-term annealing and removing unwanted mirrors by grinding and CMP are useful to maximize the angular resolution derived from mirror shapes of this MEMS-based X-ray optic. Here, note that for practical use, it is better to keep the wafer thickness since it directly leads to effective area. Therefore, it will be necessary to start by forming micropores in a thicker wafer (e.g., 400 $\mu$m) in future fabrication. Since it is also affected by the initial shape of the sidewalls, the annealing time, and other process conditions, there is a further possibility to improve the angular resolution even less than e.g., 1 arcmin in the near future.
Funding
Japan Society for the Promotion of Science (19J20910, 20H00177, 21H04972, 21J12023); Toray Science Foundation.
Acknowledgments
We are grateful to Jun-ichi Nishizawa Memorial Research Center and D-process Co., Ltd., for the annealing process and the grinding and CMP process. We also thank ISAS/JAXA nanoelectronics clean room and the X-ray telescope team for their great help in our microfabrication and X-ray measurements.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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