Zero temperature coefficient of frequency in extensional-mode highly doped silicon microresonators

For the first time we demonstrate the existence of a turnover temperature in extensional-mode silicon microresonators, fabricated on highly n-type doped substrates and aligned to the [100] crystalline orientation. This behavior is commonly observed in quartz resonators and is a key to achieving exceptional temperature stability in oven-controlled crystal oscillators. In order to show the effect of doping concentration and resonator alignment to different crystalline orientations, the thin-film piezoelectric-on-silicon (TPoS) platform is utilized. It is shown through both theoretical analysis and finite element simulation that the turnover temperature is a function of doping concentration and orientation. In order to experimentally validate this result, similar resonators are fabricated on silicon-on-insulator (SOI) substrates and the temperature variation of frequency is measured. The trends are shown to agree with theory. An overall temperature-induced frequency variation of less than 150ppm is measured over the range of -40 to 85°C for a ~25MHz TPoS resonator aligned to the [100] plane; this shows more than 24 fold reduction with respect to the uncompensated conventional silicon resonators reported before. Our work is a significant step toward strengthening silicon´s position as an alternative resonator technology in the quartz-dominated stable oscillator market.