Fabrication and tolerances of moth-eye structures for perfect ...

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Figure 1. (a) A schematic illustration of moth-eye structure. The transmittance depends on D and H. (b) The SEM image of the sample No. 1 taken right above the protuberances. (c) The side image of the sample No. 1. The flared shape is observed. The sample No.2 has a similar shape to that of No. 1. (d) The side image of the sample No. 3. The shape of the protuberances is straight. where n Si is the refractive index of silicon, and n Si ∼ 3.42. 3 This high reflectance arises from its extremely high refractive index. Antireflection is strongly needed for astronomical applications. Although there are many ways for antireflection, most of them cannot be applied to mid-infrared instruments. Muti-layer coating, for example, is one of the most popular ways to achieve antireflection but needs various kinds of materials, each having a different refractive index. In addition, multi-layer structure can be broken due to bimetal effect under cryogenic environment which is needed in order to suppress the thermal radiation from instruments. We therefore have difficulty in applying multi-layer coating. Another example is a sub-wavelength structure which consists of bulk and porous layers piled by turns. 4 It is suitable for antireflection but not easy to fabricate because it is necessary to pile many layers in order to achieve broadband antireflection. A moth-eye structure is also one of effective structures for antireflection. This structure is a surface-relief structure which needs only one material. We think this structure is the best because it does not have problems mentioned above. We have designed moth-eye structures on silicon for 25-40 µm. The moth-eye structure has many protuberances placed on a plane surface next to each other like Fig. 1(a). The protuberances have nearly a conical shape. A similar structure can be found on corneas of nocturnal insects, such as moths, after which it is called moth-eye structure. Bernhard 5 showed that the structures on the corneas of moths worked to suppress reflection by experiments using a model scaled up properly for microwave. In case of visible light, they have been applied to a surface on crystalline silicon for solar cells (e.g. Forberich et al. 6 ). Moth-eye structures on a GaAs substrate have been analyzed in detail in the near-infrared up to 17 µm. 7 In this paper, 25-40 µm is the band in which we would like to attain transmittance of more than 99 % for normal incidence. The next section includes how we have determined the design of the moth-eye structure and have fabricated them. In section 3, it is shown how we have made measurements and have corrected the measurements for getting precise transmittance. In section 4, the results of measurements after analysis are
shown. Simulations with Rigorous Coupled Wave Analysis (RCWA) have been carried out to investigate what makes the spectra of the measurements in section 5. Finally, we summarize a few tolerances for fabrication of moth-eye structures. 2. DESIGN AND FABRICATION OF MOTH-EYE STRUCTURE The principle of antireflection by moth-eye structure is understood qualitatively well. The essence of reflection is that a refractive index is discontinuous at an interface between two media. If the wavelength λ is longer than the period D between the protuberances (Fig. 1 (a)), the refractive index appears to be an effective value between those of silicon n Si and vacuum. Moreover, if the effective refractive index varies so gradually at the interface that the light cannot recognize the discontinuity or variation of it, reflection should not be generated. Rayleigh 8 investigated the relation between the wavelength λ and the effective thickness H of the layer of graded refractive index. H corresponds to the height of the moth-eye protuberances. Clapham et al. 9 calculated the reflectance of the graded interface and showed the results (see fig. 3 in Clapham et al.). When H/λ ≪ 1, the refractive index appears to be discontinuous and the reflectance is not zero. As H/λ increases, the reflectance falls monotonically and reaches 0% at H/λ ∼ 0.4. When H/λ is larger than 0.3, that is, λ < ∼ 3H, the reflectance is less than 1 %. Diffraction is another concern to design the shape of the protuberances. When the wavelength λ is equal to or shorter than n Si D, the moth-eye structure acts as a grating and the higher orders of the transmitted diffraction are generated, which makes the 0th order diffraction decreased. Detailed and strict discussions about the effective index of refraction and diffraction can be found in Brückner et al. 10 In the consideration above, approximately n Si D < λ < 3H is the range in which the transmittance of the 0th order diffraction is almost 100 % theoretically. We have designed moth-eye structures to attain transmittance of more than 99% in the wavelengths from 25 µm to 40 µm. For normal incidence, one of the limits of the transmitted wavelength is given by n Si D ≤ 25 µm, which yields D ≤ 7.3 µm. The other is 40µm ≤ 3H, that is, H ≥ 13.3 µm. We have adopted D = 5 µm and H =15 - 20 µm as a goal in fabricating. The shape of protuberances we have intended to fabricate is a cone, which is easier to process. The substrates are high resistivity silicon, the diameter is 4 inches and the thickness is 600 µm. One side of the substrates was processed and the other side was not. Electron-beam lithograph and Reactive Ion Etching (RIE) was used. The first process was to make metal masks by electron-beam lithograph on the silicon surface where the protuberances should stand. Then, a silicon surface was etched by optimizing ion energies of reactive ions. As a result, the area without the metal masks was carved, then protuberances like cones appeared on the surface of the silicon. Finally, the metal masks were removed. We have acquired three moth-eye samples. The diameter of the processed area of No.1 and No.2 is 25mm, and that of No. 3 is 40mm. Fig. 1 (b) is a scanning electron microscope (SEM) image taken right above protuberances. The period D and the height H of all the samples were measured as 5 µm and 16 µm, respectively. Fig. 1 (c) and Fig. 1 (d) of SEM images show the side views of the protuberances. There is a difference in the shape of the cones among the samples. The samples No.1 and No.2 have flared shape: they have spindly tops and become fat as getting close to the bottom (Fig. 1 (c)). By contrast, No. 3 is straight shapes from the tops to the bottoms (Fig. 1 (d)). Note that the tops of the protuberances remain flat, not pointed, due to the metal masks in processing. Fig. 2 was a photo taken in visible light. The area with moth-eye structure seems to have no reflection in visible light range and the other area looks like a mirror. 3. MEASUREMENT AND ANALYSIS Transmittance spectra of the samples were obtained by Fourier Transform Infrared spectroscopy (FT-IR). The incident angle was 0 degrees. The 0th order transmitted diffraction was measured in a vacuum. The mylar beam splitter was used. The samples were at the room temperature around 300 K. The resolution was 2 cm −1 . For getting better S/N, we have averaged 6 successive measurement points relative to wavenumbers, therefore the effective resolution was 12 cm −1 .
Page 1: Fabrication and tolerances of moth-
Page 5 and 6: Figure 3. (a) The refractive index
Page 7 and 8: Figure 6. (a) A model of straight s
Page 9: [4] Wada, T., Makitsubo, H., and Mi

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