Loss budget of a setup for measuring mechanical dissipations of silicon wafers between 300 and 4 K

A setup for measuring mechanical losses of silicon wafers has been fully characterized from roomtemperature to 4 K in the frequency range between 300 Hz and 4 kHz: it consists of silicon waferswith nodal suspension and capacitive and optical vibration sensors. Major contributions tomechanical losses are investigated and compared with experimental data scanning the fulltemperature range; in particular, losses due to the thermoelastic effect and to the wafer clamp aremodeled via finite element method analysis; surface losses and gas damping are also estimated. Thereproducibility of the measurements of total losses is also discussed and the setup capabilities formeasuring additive losses contributed by thin films deposited on the wafers or bonding layers. Forinstance, assuming that additive losses are due to an 80-nm-thick wafer bond layer with Youngmodulus about ten times smaller than that of silicon, we achieve a sensitivity to bond losses at thelevel of 510−3 at 4 K and at about 2 kHz.