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Abstract
The etching uniformity of diffractive membrane optical elements with an irregular shape was investigated. A deteriorative uniformity of electron number density and electron temperature was found according to finite element analysis of plasma discharge. A designable equivalent electrode was proposed to weaken the influence of introducing the unconventional, irregular sample. Improved uniformity of etching depths was demonstrated experimentally, assisting by the designable equivalent electrode. The demonstration of the designable equivalent electrode provides a beneficial solution for the fabrication of unconventional optical elements and an effective means for adjusting and controlling plasma characteristics.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Diffractive membrane optics has been proposed for large aperture telescopes, which is expected to significantly reduce system mass and cost scaling due to lightweight optical materials [1–3]. However, fabrication of a single precision diffractive membrane optic, especially a large aperture membrane element, still is a challenging task, due to the difference between the novel flexible membrane and the traditional rigid substrate. Basically, to meet the optical performance objectives, a membrane needs to be held dimensionally stable like a rigid substrate and remains lightweight, so that a designed frame, which holds the membrane around its entire boundary, has to be used to minimize the distortion of the etched pattern [4]. Therefore, the sample, composed of a frame and a membrane, has a quite different shape and material property from conventional regular and uniform ones, so that the etching results of the membrane optical element showed a quite different etching rate and uniformity from the conventional samples in reactive ion etching (RIE).
Generally, the state-of-the-art fabrication process of the phase-type diffractive optical elements contains two steps: the generation of a diffractive pattern on a photoresist via photolithography and its transfer to a substrate by etching [5]. The etching step determines the vertical depth of the diffractive pattern, furthermore, diffraction efficiency of that. However, owing to the lack of specialized etching equipments and technologies matched with the unconventional, large aperture diffractive membrane optical elements, it is difficult to simultaneously achieve both accurate etching depths and high uniformity of etching, which will lead to poor distribution of diffraction efficiency over the full aperture. Non-uniform pattern transfer would cause fluctuations of the diffraction efficiency across the entire membrane surface, while the variations in etching depth significantly decrease the diffraction efficiency of the membrane optical elements [6–8]. For instance, the diffraction efficiency of a 4-level FZP would decrease ∼8.5% theoretically during each overlay process if the etching depth exhibits a 10% deviation from the designed value [9].
Reactive ion etching (RIE) is a typical etching technology used for the fabrication of diffractive optical elements [5–8]. However, most of the commercial RIE equipments were designed for 300 mm diameter substrate or smaller. The influence of the diameter increase and the change on the shape of the sample required to be evaluated for the current equipment and technology, when the pattern transfer of the diffractive membrane optical elements were achieved in a capacitively coupled plasma (CCP) tool. Already for 300 mm tools, there is evident that wave behavior such as propagation and interference will affect the uniformity of processing. The increase in diameter up to 400mm or larger is likely to exacerbate these effects [10]. The uniformity of CCP etching is usually determined by the radial uniformity of plasma parameters, mainly including electron number density and electron temperature [11–13], which directly affect the ionization and excitation reaction rate in the plasma so that the uniformity of their radial distribution in the discharge chamber seriously affects the uniformity of pattern transfer [10,14].
Here, we evaluated the etching uniformity of an unconventional, irregular membrane optical element in a customized CCP reactor experimentally, and the experimental results suggested that the etching non-uniformity deteriorated dramatically down to ±20.0% due to the introduction of the unconventional, irregular sample, relative to a conventional, regular quartz element whose etching non-uniformity was usually expected in ±3%∼±5%. Based on the simulation of the radial distribution of electron number density and electron temperature by finite element analysis (FEA), a serious deterioration of the uniformity of electron number density and electron temperature was found, which was believed to be the main reason that the etching uniformity deteriorated. In order to weaken the influence of introducing the unconventional, irregular sample in the etching process, a solution based on variable auxiliary metal fillers was proposed, which arose from the consideration that plasma distribution characteristics can be adjusted by changing related parameters and structures of discharge chamber [15]. The optimized parameters of the auxiliary metal filler were determined by the simulated results of the radial distribution of electron number density and electron temperature in COMSOL, and an obvious improvement on the radial uniformity of electron number density and electron temperature was achieved by choosing an appropriate auxiliary metal filler with optimized parameters in simulation. Finally, an etching experiment of the unconventional, irregular membrane optical element with the auxiliary metal filler was demonstrated, and the etching non-uniformity was improved from ±20.0% to ±8.5% due to the optimized solution. A distribution of diffraction efficiency for a 4-level FZP on the membrane optical element was also obtained experimentally based on the designable equivalent electrode composed of the bottom electrode, the ring-like metal frame and the designable auxiliary metal filler.
2. Apparatus and sample
As shown in Fig. 1(a), the plasma discharge structure of the CCP tool used in COMSOL simulation is a 2-D axisymmetric structure, which is composed of a power electrode, a substrate, a base, and a cavity. The top and sides of the chamber are grounded. A power source is applied below the electrode, V = V0sin(2πft), where RF frequency is f=13.56 MHz and power is P=160 W. The pressure in the chamber is p=0.665 Pa, the temperature T=300 K, the distance between the plates d=5.5 cm, the radius of the chamber r1=45 cm, the radius of the lower plate r2=32.5 cm, and the radial monitoring line z=0.5d.
The photogram of the membrane optical element is shown in Fig. 1(b). In order to keep the polyimide (PI) membrane dimensionally stable and minimize the distortion of the etched pattern, a metal ring with a height of 20 mm, a thickness of 25 mm, and an inner radius of 400 mm, was designed to fix the membrane substrate. A homemade Polyimide membrane, which has a thickness of about 25 µm, Young’s modulus of above 7 GPa and a transmittance of more than 80% at 632.8 nm, was fixed onto the 400-mm aperture metal frame by glues and mechanical clamp devices. Therefore, a chamber structure is formed, and its axisymmetric cross-sectional view is shown in Fig. 1(a). The metal ring is made of 304 stainless steel (height h1 = 2 cm, thickness h2 = 2.5 cm), and the distance Rr from the center axis of the chamber to the left edge of the metal ring is 20 cm.
RIE performed in a customized, 650-mm aperture capacitively coupled plasma (CCP) reactor (Beijing jinshengweina Technology Co., Ltd). The distribution of measurement points is along a radius of the sample and etching masking layers on each measurement point were fabricated. The etching depths on each point were measured by a 3D optical surface profiler (NewView 7300 by Zygo).
3. Results and discussions
The etching uniformity of a pristine membrane was investigated experimentally using the same parameters as those for conventional regular ones, as shown in Fig. 2. The etching non-uniformity of the sample is ±20.0%, which is far from the normal level in conventional etching. The simulation suggested that poor etching uniformity in the fabrication of 4-level FZP would lead to poor uniformity of diffraction efficiency, which would be a non-uniformity of ∼±24.6%, even if only etching depth errors were considered [9].
Fig. 2. Radial distribution of etching depth without the metal filler. 5 samples and 18 measurement points per sample were applied in the measurement experiment to ensure reproducibility.
The simulated results of plasma discharge in COMSOL suggested that the radial uniformity of electron number density and electron temperature deteriorated seriously, as shown in Fig. 3, and the calculated values of non-uniformity are ±35.4% and ±7.32%, respectively, which was believed to result in the deterioration of etching uniformity and root in the edge effect caused by the irregular equivalent electrode composed of the bottom electrode and the ring-like metal frame.
Fig. 3. Radial distribution of CCP with a metal ring: (a) radial distribution of electron number density; (b) radial distribution of electron temperature.
In order to improve the etching uniformity of the unconventional membrane optical element, a variable metal filler was used to constitute a designable equivalent electrode together with the bottom electrode and the ring-like metal frame, supposing that the ideal contacts among them were formed. The schematic of the membrane optical element without and with the metal filler are shown in Fig. 4. The size and shape of the metal filler can be designed to form equivalent electrodes with various shapes and structures and obtain required distributions of electron number density and electron temperature.
As the attempt to improve the uniformity of electron number density and electron temperature by adjusting the structure of the equivalent electrode, the radial distributions of electron number density and electron temperature was simulated in COMSOL. The influence of main parameters of the auxiliary metal filler, including the height of the filler, the height of metal ring with the metal filler, and the gap between the filler and the metal frame, were investigated.
As Fig. 5 shown, the radial uniformity of electron number density and electron temperature shows apparent dependency with the height of the metal filler, when the radius of the metal filler are set as same as the inner radius of the ring-like frame. The radial non-uniformity of electron number density is ±26.8%, ±19%, ±17.5%, and ±16.1%, respectively, at the height of 5 mm, 10 mm, 15 mm, and 20 mm, as shown in Fig. 5(a). Similarly, the radial non-uniformity of electron temperature is ±5.71%, ±3.62%, ±1.36%, and ±1.85%, respectively, at the height of 5 mm, 10 mm, 15 mm, and 20 mm, as shown in Fig. 5(b). The simulated results in Fig. 5 suggested that the radial uniformity of electron number density and electron temperature could be improved by introducing a designed metal filler to form various equivalent electrodes, and the optimal value of the uniformity appeared when the height of the metal filler was the same as one of the metal frame in the simulation about height of metal fillers.
Fig. 5. Radial distribution of CCP when the height of the metal filler is set as different values: (a) radial distribution of electron number density; (b) radial distribution of electron temperature.
The influence of the height of the equivalent electrode on the radial distribution of plasma characteristics are shown in Fig. 6, at the height of 8 mm, 12 mm, 16 mm, and 20 mm, respectively, when the metal filler has the same height as the metal frame. The radial non-uniformity of electron number density is ±17.9%, ±18.2%, ±15%, and ±16.1%, respectively, as shown in Fig. 6(a). Similarly, the radial non-uniformity of electron temperature is ±1.49%, ±1.82%, ±1.71%, and ±1.85%, respectively, as shown in Fig. 6(b). The simulated results in Fig. 6 suggested that the radial uniformity of electron number density and electron temperature were hardly affected by the height of the equivalent electrode.
Fig. 6. Radial distribution of CCP at different metal ring heights: (a) radial distribution of electron number density; (b) radial distribution of electron temperature.
Considering the practical manufacturing and application, a gap between the metal filler and the metal frame would be unavoidable. The influence of different gap (2, 4, 6, 8 mm) on the radial distribution of plasma characteristics are shown in Fig. 7. The simulated results of in Fig. 7 suggested that the radial uniformity of electron number density and electron temperature were hardly affected by the gap between the metal filler and the metal frame, which means that the fabrication and installation of the metal filler have so loose tolerances that no special requirements need to be satisfied and conventional levels for working accuracy and aligning precision can be directly applied into this designable device.
Fig. 7. Radial distribution of plasma under different gap: (a) radial distribution of electron number density; (b) radial distribution of electron temperature.
In order to verify the feasibility of improving etching uniformity by adjusting plasma characteristics, a metal filler with a radius of 200 mm and a height of 18 mm was fabricated by 304 stainless steel, as shown in Fig. 8(a), and applied into the etching experiment of the irregular membrane optical element. The radial etching non-uniformity of the sample with the metal filler is ±8.5%, as shown in Fig. 8(b), which has been drastically improved relative to that without the metal filler. Theoretically, designed fillers with more complicated and finer shapes and structures can be introduced to improve the etching uniformity further, even up to the level of conventional samples, or obtain the desired distribution of etching depths, depending on a more accurate relation between the etching uniformity and the plasma characteristics which can be obtained from further simulations and experiments.
Fig. 8. (a) photogram of the metal filler; (b) Radial distribution of etching depth with the metal filler in an etching experiment. 5 samples and 18 measurement points per sample were applied in the measurement experiment to ensure reproducibility.
A 4-level FZP on the 400-mm membrane optical element has been fabricated by photolithography and RIE, assisting by the method of constituting a designable equivalent electrode. The non-uniformity of diffraction efficiency over the full aperture is ±10.7% and mean value is 75.8%, as shown in Fig. 9, which have some difference with the theoretical value, that is ∼±7.1%, estimated from the data in [9]. The extra fluctuation of uniformity was believed to root in the alignment errors in the fabrication, which need to investigate further and find corresponding methods for improving alignment accuracy, furthermore, diffraction efficiency.
4. Conclusions
In this paper, the etching uniformity of diffractive membrane optical elements with an irregular shape was investigated and a deteriorative etching uniformity of the unconventional sample was found. A deterioration of the uniformity of electron number density and electron temperature owing to the introduction of the unconventional sample was found according to FEA of plasma discharge in RIE. Considering that the plasma characteristics are closely related to the properties of the chamber structure, a designable equivalent electrode composed of the bottom electrode, a ring-like metal frame and a variable auxiliary metal filler was proposed to weaken the influence of introducing the unconventional, irregular sample in the etching process. According to simulated results in COMSOL, a metal filler with a radius of 200 mm and a height of 18 mm was fabricated and applied into the etching experiment of the irregular membrane optical element. Improved uniformity of etching and diffraction efficiency was demonstrated experimentally, assisting by the designable equivalent electrode. Furthermore, simulated results suggested that the fabrication and installation of the metal filler have loose tolerances and can be easily applied into practical manufacture. Better uniformity compared with conventional sample or desired distribution of etching depths can be achieved by an equivalent electrode with more complicated and finer shapes and structures. The demonstration of improving etching uniformity by the designable equivalent electrode provided a beneficial solution for the fabrication of unconventional optical elements and an effective means for adjusting and controlling plasma characteristics.
Funding
National Natural Science Foundation of China (62075220); National Key Research and Development Program of China (2016YFB0500200).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. P. D. Atcheson, C. Stewart, J. L. Domber, K. Whiteaker, J. Cole, P. Spuhler, A. Seltzer, J. A. Britten, S. N. Dixit, B. Farmer, and L. Smith, “MOIRE: initial demonstration of a transmissive diffractive membrane optic for large lightweight optical telescopes,” Proc. SPIE 8442, 844221 (2012). [CrossRef]
2. P. D. Atcheson, J. L. Domber, and K. Whiteaker, “MOIRE: ground demonstration of a large aperture diffractive transmissive telescope,” Proc. SPIE 9143, 914311 (2014). [CrossRef]
3. J. L. Domber, P. D. Atcheson, and J. Kommers, “MOIRE: Ground Test Bed Results for a Large Membrane Telescope. Spacecraft Structures Conference,” Proc. AIAA2014, 1510 (2014).
4. W. Tandy, P. D. Atcheson, J. L. Domber, and A. Seltzer, “MOIRE Gossamer Space Telescope - Structural Challenges and Solutions,” Aiaa/asme/asce/ahs/asc Structures, Structural Dynamics & Materials Conference Aiaa/asme/ahs Adaptive Structures Conference, Proc. AIAA2012, 1670 (2012).
5. C. Guo, Z. Zhang, D. Xue, L. Li, R. Wang, X. Zhou, F. Zhang, and X. Zhang, “High-performance etching of multilevel phase-type Fresnel zone plates with large apertures,” Opt. Commun. 407, 227–233 (2018). [CrossRef]
6. J. Wang, F. Zhang, Q. Song, A. Zeng, J. Zhu, and H. Huang, “Fabrication error analysis for diffractive optical elements used in a lithography illumination system,” Opt. Eng. 54(4), 045102 (2015). [CrossRef]
7. R. Wang, Z. Zhang, C. Guo, D. Xue, and X. Zhang, “Effects of fabrication errors on diffraction efficiency for a diffractive membrane,” Chin. Opt. Lett. 14(12), 120501 (2016). [CrossRef]
8. J. C. Adam, B. Markus, J. W. Andrew, and R. T. Mohammad, “Analysis of multimask fabrication errors for diffractive optical elements,” Appl. Opt. 46(12), 2180–2188 (2007). [CrossRef]
9. P. Xu, X. Zhang, L. Guo, Y. Guo, X. Zhou, C. Du, and M. Zhou, “Fabrication errors analysis and simulation of binary optical element,” Acta Opt. Sin. 16(6), 833–838 (1996).
10. Y. Yang and M. J. Kushner, “450 mm dual frequency capacitively coupled plasma sources: Conventional, graded, and segmented electrodes,” J. Appl. Phys. 108(11), 113306 (2010). [CrossRef]
11. Y. X. Liu, Y. S. Liang, D. Q. Wen, Z. H. Bi, and Y. N. Wang, “Experimental diagnostics of plasma radial uniformity and comparisons with computational simulations in capacitive discharges,” Plasma Sources Sci. Technol. 24(2), 025013 (2015). [CrossRef]
12. Y. R. Zhang, A. Bogaerts, and Y. N. Wang, “Fluid simulation of the phase-shift effect in Ar/CF4 capacitively coupled plasmas,” J. Phys. D: Appl. Phys. 45(48), 485204 (2012). [CrossRef]
13. Y. R. Zhang, X. Xu, A. Bogaerts, and Y. N. Wang, “Fluid simulation of the phase-shift effect in hydrogen capacitively coupled plasmas: II. Radial uniformity of the plasma characteristics,” J. Phys. D: Appl. Phys. 45(1), 015203 (2012). [CrossRef]
14. H. Caquineau and B. Despax, “Influence of the reactor design in the case of silicon nitride PECVD,” Chem. Eng. Sci. 52(17), 2901–2914 (1997). [CrossRef]
15. Y. S. Liang, Y. R. Zhang, and Y. N. Wang, “Influence of dielectric materials on uniformity of large-area capacitively coupled plasmas for N2 /Ar discharges,” Chin. Phys. B 25(10), 105206 (2016). [CrossRef]
