Development of large Si mirrors and coating for application at 10-20 K
One of the unique features of the Einstein Telescope is the use of cryogenically cooled mirrors to significantly improve the detection rate for low gravitational wave frequencies (below 20 Hz) by reducing thermal noise in the mirror coatings and suspensions in particular. Crystalline silicon, a well-known material from the semiconductor industry, is ideal for this purpose: in addition to its excellent mechanical quality factor, silicon exhibits a negligible coefficient of thermal expansion at temperatures around 120 and below 20 K. More importantly, the material becomes an excellent low-temperature thermal conductor. Thermal mirror deformations will be greatly reduced compared to mirrors made of fused silica.
Concerning the crystalline silicon substrate or block, the bulk absorption of the laser light heating the mirrors must be kept below about 5 ppm/cm to maintain the mirrors, especially at 20 K operation, at a stable cryogenic temperature. Because residual free-charge carriers dominate absorption at the targeted wavelengths of 1.5 - 2.0 µm, substrates with high resistivity (better than 10 kΩ cm) are required. While silicon grown via float zone achieves the required high specific resistivity, this is technically limited to smaller diameters. Growth processes that achieve large substrate sizes with low impurities, for example the magnetically supported Czochralsky processes, should be further investigated.
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The polishing specifications of the silicon will be similar to the very demanding requirements currently met by fused silica for the LIGO and Virgo observatories: these mirrors (each about 40 kg) are polished to a radius of curvature of about 2 km, with flatness of ±2 nm and RMS roughness of less than 0.1 nm. This precision is achieved by electro-polishing, ion beam figuring and corrective (multilayer) coatings. The reflectivity of these mirrors is 99.999% and the measured bulk absorption per centimeter is below 1 ppm.
Polishing processes that can yield the same specifications on silicon substrates will need to be investigated and their quality proven by appropriate metrology, including parameters such as transmitted wavefront distortion and absorption. Given the different wavelengths and given the operation at cryogenic temperature, entirely new multilayer coatings must be developed. This is probably one of the most challenging issues related to mirrors and a current area of research in the global gravitational wave research community.
Key challenges in a nutshell:
- Development and interometric testing of large (10--50 cm diameter) silicon mirrors with bulk absorption for 1550 nm laser light below a few ppm/com;
- Superfine polished surfaces with a flatness of less than ±2 nm, and an RMS roughness of less than 100 pm;
- Coated with a low-noise and high reflectivity (T=10ppm) coating.
Goals
Mirrors:
- Crystalline silicon (negligible coefficient of thermal expansion and excellent thermal conductor)
Research objective | Substrates & multilayer coatings
- Given the different wavelengths and given the cryogenic temperature effects, entirely new multilayer coatings must be developed. This is probably one of the most challenging issues related to mirrors and a current area of research in the global gravitational wave research community;
- The reflection must be 99.999%;
- The bulk absorption of laser light heating the mirrors should be kept below about 5 ppm/cm;
- Substrates with high specific resistivity (better than 10 kΩ cm) are required;
- Growing large substrate sizes with low impurities, e.g. using magnetically assisted Czochralsky processes, needs further investigation.
Validation Goal | Polishing
Proposed Solution:
- Electrolytic polishing, ion beam processing and corrective (multilayer) coatings.
Requirements:
- Polishing with a radius of curvature of about 2 km;
- Flatness of ±2 nm;
- RMS roughness of less than 0.1 nm.