A 62 Hz high-Q 4-spiral mechanical resonator fabricated of a silicon wafer

High purity silicon is considered as the test mass material for future cryogenic gravitational-wave detectors, in particular Einstein Telescope-low frequency and LIGO Voyager [(LIGO) Laser Interferometer Gravitational-Wave Observatory]. To reduce the thermal noise of the test masses, it is necessary to study the sources of corresponding losses. Mechanical resonators with frequencies 300 Hz-6 kHz are successfully used for studying, for example, losses in optical coatings of the test mass. However, the frequency range of the interferometric gravitational-wave detectors starts at 10 Hz, and the investigation of different dissipation mechanisms for the test masses in the low-frequency region is relevant. We developed a design of a four-spiral mechanical resonator for studying dissipation and noise in the low frequency range. The resonator was fabricated of a 3-in. silicon wafer using an anisotropic wet etching technique. It consists of four spiral cantilevers on a common base, linked together with additional coupling beams for increasing the frequency difference between the resonator normal modes corresponding to the fundamental flexural off-plane mode of a single spiral cantilever. The measured Q-factor of the 62 Hz out-of-phase mode of the four-spiral silicon resonator at room temperature is limited mainly by the thermoelastic loss. At 123 K, the measured Q = (1.5 ± 0.3) × 107. The main contribution to the total loss comes from clamping and surface losses.