Passive TCF compensation in high Q silicon micromechanical resonators

This paper reports on passive temperature compensation techniques for high quality factor (Q) silicon microresonators based on engineering the geometry of the resonator and its material properties. A 105 MHz concave silicon bulk acoustic resonator (CBAR) fabricated on a boron-doped substrate with a resistivity of 10^-3 ¿-cm manifests a linear temperature coefficient of frequency (TCF) of -6.3 ppm/°C while exhibiting a Q of 101,550 (fQ = 1.06×10¹³). The TCF is further reduced by engineering the material property via a wafer-level aluminum thermomigration process to -3.6 ppm/°C while maintaining an fQ of over 4×10¹². Such high fQ products with low TCF values are being reported for the first time in silicon and are critical for successful insertion of these devices into low-power low-phase noise frequency references and high performance resonant sensors.