Long term stability and quality factors of degenerately n-type doped silicon resonators

Effect of degenerate doping on the long term stability and quality factors of silicon resonators was studied. The long term stability of electrostatically coupled tuning fork and width extensional mode resonators was found to be better than 1 ppm during a measurement spanning 220 days. Resonators were phosphorus doped to a carrier concentration of 4.1×10¹⁹cm^-3. Quality factors of ~10-MHz Lamé mode resonators on wafers doped up to a concentration of 7.5 × 10¹⁹cm^-3 were found to range from 900,000 to 1,500,000, which is comparable to that reported for similar resonators with moderate doping. The results indicate that the effect from heavy phosphorus doping on resonator stability or on silicon intrinsic losses is low at the studied doping levels.