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

Abstract

A setup for measuring mechanical losses of silicon wafers has been fully characterized from room temperature to 4 K in the frequency range between 300 Hz and 4 kHz: it consists of silicon wafers with nodal suspension and capacitive and optical vibration sensors. Major contributions to mechanical losses are investigated and compared with experimental data scanning the full temperature range; in particular, losses due to the thermoelastic effect and to the wafer clamp are modeled via finite element method analysis; surface losses and gas damping are also estimated. The reproducibility of the measurements of total losses is also discussed and the setup capabilities for measuring additive losses contributed by thin films deposited on the wafers or bonding layers. For instance, assuming that additive losses are due to an 80-nm-thick wafer bond layer with Young modulus about ten times smaller than that of silicon, we achieve a sensitivity to bond losses at the level of 5x10(-3) at 4 K and at about 2 kHz.