Temperature Compensation of Silicon Resonators via Degenerate Doping

This paper demonstrates the dependence of temperature coefficient of frequency (TCF) of silicon micromechanical resonators on charge carrier concentration. TCF compensation is demonstrated by degenerate doping of silicon bulk acoustic resonators (SiBARs) using both boron and aluminum dopants. The native TCF of -33×ppm/^°C for silicon resistivity of >; 10³ Ω · is shown to reduce to -1.5×;ppm/^°C at ultralow resistivity of ~10×^-4;Ω·cm using relatively slow diffusion-based boron doping. However, the faster thermomigration-based aluminum doping offers TCF reduction to as low as -2.7×;ppm/^°C with much reduced processing time. A very high Q of 28 000 at 100 MHz is measured for a temperature-compensated SiBAR.