Fabrication and tolerances of moth-eye structures for perfect antireflection in the mid-infrared wavelength region

Mid-infrared, 25 - 45 microns, is a very important wavelength region to investigate the physics of lower temperature environments in the universe. There are few transparent materials in the range of mid-infrared except silicon. However, the reflection on a silicon surface reaches 30 % because of its high refractive index (~3.4). To apply silicon to mid-infrared astronomical instruments, we need a way of antireflection and have adopted a moth-eye structure. This structure keeps durable under cryogenic environments, which is advantageous to mid-infrared instruments. We have fabricated three samples of the moth-eye structure on plane silicon surfaces by electron-beam photo-lithograph and reactive ion etching. The structures consist of many cones standing on silicon surfaces. We have substantiated the transmittance of 96 % or higher in the wide range of 20 - 50 microns and higher than 98 % at the maximum. The transmittance of moth-eye surfaces, however, is theoretically expected as 100 %. We have examined the discrepancy between the transmittance of the theory and fabrications with electromagnetic simulations. It has been revealed that shapes of the cones and gaps at the bottom of the cones seriously affect the transmittance. We have estimated a few tolerances for manufacturing the moth-eye structures achieving sufficient transmittance of nearly 100 %.