Verification of the controllability of refractive index by subwavelength structure fabricated by photolithography: toward single-material mid- and far-infrared multilayer filters Hironobu Makitsubo* a,b, Takehiko Wada b, Makoto Mita b a Department of Astronomy, Graduate School of Science, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; b Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan ABSTRACT We are developing high performance mid-infrared (especially 30-40μm wavelength regions) multilayer interference filters with mechanical strength and robustness for thermal cycling toward cryogenic infrared astronomical missions. Multilayer interference filters enable us to design a wide variety of spectral response by controlling refractive index and thickness of each layer. However, in mid- and far-infrared (MIR/FIR) regions, there are a few optical materials so that we can only use limited refractive index values to design filters, which makes difficult to realize high performance filters. It is also difficult to deposit thick layers required for MIR/FIR multilayer filters. Furthermore, deposition of two materials, which have different coefficients of thermal expansion, makes filters fragile for thermal cycling. To clear these problems, we introduce sub-wavelength structures (SWS) for controlling the refractive index. Then, only one material is necessary for fabricating filters, which enables us to fabricate filters with mechanical strength and robustness for thermal cycling. According to the effective medium approximation (EMA) theory, the refractive index of randomly mixing materials in sub-wavelength scale is controllable by changing the ratio of mixing materials. However, it is not clear that EMA can be applied to such simple SWS, periodic cylindrical holes on a bulk material, which is easily fabricated by photolithography. In order to verify the controllability of refractive index by simple SWS, we have fabricated simple SWS on a silicon substrate and measured its transmittance. Comparing measured transmittance with theoretical transmittance calculated by EMA, we confirm that EMA can be applied to simple SWS fabricated by photolithography. Keywords: multilayer filters, sub-wavelength structure, silicon, photolithography, mid-infrared, far-infrared 1. INTRODUCTION In astronomical instruments, optical filters such as bandpass filters and dichroic beam splitters are essential optical components in order to obtain both spectral and spatial information. In optical and near-infrared (NIR) wavelength regions, thin film coating multilayer interference filters are commonly used to realize optical filters. Multilayer interference filters enable us to design a wide variety of spectral response by controlling refractive index and thickness of each layer 1,2. In optical and NIR wavelength regions, there are a lot of transparent and chemically stable optical materials so that we can use many values of refractive index, which enables us to design high performance filters. It is also established to fabricate multilayer structures by using vacuum deposition technology. Recently, multilayer interference filters are applied to longer (mid-infrared/mir) wavelength regions. Thin film coating MIR (5-28μm) multilayer interference bandpass filters are developed for the James Webb Space Telescope 3. However, in MIR (30-40μm) wavelength regions, there are a few transparent materials 4,5 so that we can only use limited values of refractive index to design multilayer filters, which becomes difficult to design high performance filters. It is also difficult to deposit thick layers required for MIR multilayer filters. Furthermore, in case of the thin film coating multilayer interference filters, filters are fabricated by deposition of two or more materials whose coefficients of thermal expansion are different, which makes filters fragile for thermal cycling. The robustness for thermal cycling is essential for high sensitivity astronomical observation, because astronomical optics must be extremely cooled (< 10 K) *makitsu@ir.isas.jaxa.jp; phone +81-50-336-23909; fax +81-42-786-7202
in order to decrease thermal background radiations which prevent high sensibility observation. Therefore it is difficult to realize thin film coating multilayer interference filters in 30-40μm wavelength regions for cryogenic infrared astronomical missions. In this paper, so as to overcome these difficulties, we propose single-material (all-silicon) multilayer interference filters with sub-wavelength structures (SWS) for cryogenic infrared astronomical missions. 2. SINGLE-MATERIAL MULTILAYER INTERFERENCE FILTERS 2.1 Concept In order to realize high performance MIR (especially 30-40μm wavelength regions) bandpass filters with mechanical strength and robustness for thermal cycling, we are trying to develop multilayer interference filters using only one material. Using only one material, it is expected that we can realize multilayer interference filters with robustness for thermal cycling because a coefficient of thermal expansion is same all over the filters. Adopting multilayer interference filters, it is expected that we can fabricate filters with mechanical strength because the thickness of substrate is commonly 0.5 mm. Furthermore, multilayer interference filters enable rectangular spectral response as the number of layers is increased. In 30-40μm wavelength regions there are a few transparent materials, but fortunately silicon is transparent in 30-40μm wavelength regions and furthermore silicon is chemically stable and adequate material for microfabrication, that is we can use very suitable optical material for realizing single-material multilayer interference filters with SWS. Using only one material, however, we cannot use different refractive index values other than that of a bulk material. Then we introduce sub-wavelength structures (SWS) for controlling the refractive index which is essential for making multilayer interference filters. According to the effective medium approximation (EMA) theory, the refractive index of randomly mixing materials in sub-wavelength scale is controllable by changing the ratio of mixing materials 6-9. In this case, we can make mixing materials which consist of silicon and vacuum. Using vacuum as a mixing material, we can realize multilayer interference filters which is composed of only one material (silicon). Therefore, it is expected that we can get the medium whose refractive index is arbitrary value of 1.0 to 3.4 by changing the ratio of silicon and vacuum i.e. porosity. Figure 1. Conceptual schematic of single-material (all-silicon) multilayer interference filters with SWS. In order to realize mechanically tough filters we propose alternate structures of bulk silicon layers and SWS silicon layers.
Figure 1 shows the conceptual schematic of single-material (all-silicon) multilayer interference filters with SWS. Multilayer structures are composed of SWS layers and bulk layers alternately, which is expected to make filters mechanically tough. We can also design high performance filters by taking advantage of the fact that we can use arbitrary refractive index values by changing the porosity of SWS layers 9. 2.2 Fabrication Fabrication of single-material multilayer interference filters is following three steps; dry etching, wafer bonding, and wafer thinning. At first, to make mixing materials layers in sub-wavelength scale, we use MEMS technology: photolithography and reactive ion etching. Photolithography enables us to manufacture easily simple SWS (such as periodic cylindrical holes on a bulk material) and to control the porosity precisely. Furthermore, we are also plannig to control the thickness of SWS layers by adjusting etching condition and etching time. Then we can fabricate SWS layers with expected porosity (i.e. refractive index) and thickness at the same time, which are key point to realize the expected multilayer interference filters. The next step is to fabricate multilayer structures. Making multilayer filters which consists of only one material is the key of our research, so we cannot use a different material such as adhesive to bond a SWS layer and a bulk layer. That is why we use MEMS technology: wafer direct bonding technique. To obtain stronger bonding, we are planning to use surface activated room temperature wafer bonding technique 10. In this technique, surfaces of two silicon substrates are activated by argon beam etching and bonded in a vacuum. Surface activated bonding is so strong that in the tensile test fracture occurred not at the bonding surface but mainly in the bulk of silicon. To obtain adequate thickness of bulk layers, we use wafer thinning technique. Controlling the polishing time and polishing condition, we will get bulk layers having expected thicknesses. Figure 2. The proposed fabrication method of single-material multilayer interference filters with SWS. We plan to use MEMS technology: photolithography and dry etching, wafer bonding technique, and wafer thinning technique.
3. VERIFICATION OF THE CONTROLLABILITY OF REFRACTIVE INDEX BY SUBWAVELENGTH STRUCTURE According to the effective medium approximation (EMA) theory, the mixing materials in sub-wavelength scale are regarded as a homogeneous medium having effective refractive index determined by the ratio of mixing materials. Then, it is expected that we can regard sub-wavelength periodic cylindrical holey structures on a bulk silicon as a homogeneous thin film having effective refractive index n eff (1.0 < n eff < 3.4) determined by porosity. However, it is not clear that the EMA theory can be applied to such simple SWS, periodic cylindrical holes on a bulk material, which is easily fabricated by photolithography and dry etching. In order to verify the controllability of refractive index by such simple SWS, we have fabricated such simple SWS on a silicon substrate by photolithography and dry etching, and have measured its transmittances. Comparing measurement transmittances with theoretical transmittances calculated by the EMA theory, we verify whether the refractive index control by such simple SWS is possible or not. 3.1 Fabrication of sub-wavelength structure We have fabricated two simple SWS (periodic cylindrical holes on a silicon substrate) samples at ISAS/JAXA by using photolithography and inductively coupled plasma reactive ion etching (ICP-RIE) in order to examine whether or not the effective medium approximation theory can be applied and the refractive index control by such simple SWS is possible. Fabricated samples are Sample 1 (porosity: 59%) and Sample 2 (porosity: 30%). See Figure 4 for more details. Figure 5 shows the scanning electron microscope (SEM) images of Sample 1. Figure 3. Optical image of SWS (porosity: 59%) fabricated on the surface of a silicon wafer. Dry etchings are processed within the central square region. Figure 4. Optical microscope images (top view) of SWS fabricated on the surface of a silicon wafer. Left figure is Sample 1 (porosity: 59%, hole diameter: 4.2μm, hole separation: 5.2μm) and Right figure is Sample 2 (porosity: 30%, hole diameter: 4.2μm, hole separation: 7.3μm). Hole separation means the distance between the centers of two adjacent holes.
Figure 5. SEM images of SWS Sample 1 (porosity: 59%) fabricated on the surface of a silicon wafer. Left figure is cross section image. The depth of holes (Sample 1; porosity 59%) is 12.3 ± 0.1μm. The depth of holes (Sample 2; porosity 30%) is 14.3 ± 0.1μm. 3.2 Measurement of transmittance We have measured transmittances of the fabricated samples between 25 to 120μm wavelength regions using Fourier transform spectrometer (BOMEM DA8) at ISAS/JAXA. The transmittances are measured with a mercury lamp beam (aperture is 7 mm) at a room temperature. A Mylar beam splitter of 6μm thickness and a deuterated triglycine sulfate (DTGS) pyroelectric detector are used. The measured transmittances are plotted in Figure 6. Measured samples are Sample 1 (59% porosity SWS on a silicon substrate), Sample 2 (30% porosity SWS on a silicon substrate), and a silicon substrate. The thickness of a silicon substrate is 0.5 mm. Anti-reflection effects by SWS are easily confirmed. Figure 6. Measured transmittances of SWS Sample 1 (porosity: 59% red lines), SWS Sample 2 (porosity: 30% blue lines), and a bulk silicon wafer (green lines).
3.3 Verification of the controllability of refractive index by sub-wavelength structure In order to verify the controllability of refractive index by simple SWS, we compare measured transmittances of SWS samples with theoretical transmittances of one-layer thin film anti-reflection filters (See Figure 7). The results are shown in Figure 8 and Figure 9. Figure 8 and 9 shows Sample 1 (porosity: 59%) and Sample 2 (porosity: 30%) respectively. Relative transmittance means SWS sample transmittance divided by silicon transmittance as a function of wavelength. The transmittances of 59% and 30% porosity SWS samples fit well with the theoretical calculation in case of refractive index n=1.95 and n=2.6 respectively. Furthermore, in the case of 59% porosity SWS sample, relative transmittance is 130% at the peak wavelength, which means that 59% porosity sub-wavelength periodic cylindrical holey structures play a nearly perfect anti-reflection layer. That is we have realized a nearly perfect AR coat on a silicon substrate by photolithography and dry etching. Figure 7. Conceptual schematic of the effective medium approximation theory. Figure 8. Relative transmittance of SWS Sample 1 (porosity 59%) on a silicon substrate compared with that of a bulk silicon wafer. The lines show the theoretical calculations of one-layer thin film AR filters whose refractive index is 1.85 (blue dotted lines), 1.95 (red solid lines), and 2.05 (black dotted lines). The thickness of the SWS layer (d=12.3μm) is given by the SEM observation. Note that 59% porosity SWS sample is worked as a nearly perfect AR coat, because relative transmittance is 130% at the peak wavelength.
Figure 9. Relative transmittance of SWS Sample 2 (porosity 30%) on a silicon substrate compared with that of a bulk silicon wafer. The lines show the theoretical calculations of one-layer thin film AR filters whose refractive index is 2.5 (blue dotted lines), 2.6 (red solid lines), and 2.7 (black dotted lines). The thickness of the SWS layer (d=14.3μm) is given by the SEM observation. 4. SUMMARY We are developing high performance MIR (especially 30-40μm wavelength regions) and FIR multilayer interference bandpass filters for cryogenic infrared astronomical missions. The requirements for the filters are having mechanical strength and robustness for thermal cycling. In order to realize these filters, we introduce sub-wavelength structures (SWS) to control the refractive index, and we are trying to develop single-material (all-silicon) multilayer interference bandpass filters. As a first step to realize these filters, we have fabricated one-layer simple SWS (periodic cylindrical holes on a silicon substrate) so as to confirm the controllability of refractive index by sub-wavelength structures the key point to develop single-material multilayer interference filters with mechanical strength and robustness for thermal cycling. The results show that the simple SWS fabricated easily by photolithography have refractive index different from that of bulk silicon, so we conclude that simple SWS (periodic cylindrical holes on bulk silicon) can be applied for single-material multilayer interference filters. We also confirm that 59% porosity sub-wavelength periodic cylindrical holey structures play a nearly perfect anti-reflection layer.
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