Experimental verification of internal friction at GHZ frequencies in doped single-crystal silicon

This paper reports on the experimental verification of the intrinsic loss mechanisms present in degenerately doped single-crystal silicon. Previous work reported at the Hilton Head Workshop 2010 experimentally showed the dominant acoustic loss mechanism in a 3.72-GHz silicon resonator (Fig. 1) to be Landau-Rumer phonon-phonon dissipation as seen from the 1/T⁴ temperature dependence for temperatures as low as 77K. This work extends these measurements to lower temperature (1.5K) and finds that free electron scattering due to degenerate doping affects the Q of silicon micromechanical resonators at low temperatures and in some cases, such as in the current resonator design, becomes comparable to anchor loss even at room temperature.