Simultaneous dual-mode excitation of piezo-on-silicon micromechanical oscillator for self-temperature sensing

This paper demonstrates a dual-mode (DM) oscillator which simultaneously excites the fundamental and third-order modes of a micromachined, piezo-on-silicon bulk acoustic wave (BAW) resonator for real-time self-temperature measurement. By concurrently measuring the temperature coefficient of frequency (TCF) at 30 MHz (f₁) and 87 MHz (f₃), a beat frequency (f_b) with TCF of 162 ppm/°C is extracted. Phase measurements of the third-order harmonic before and after DM excitation show signal degradation close to carrier and improvement far from carrier. This is attributed to the loaded Q of both modes and the introduction of spurious modes near resonance. In addition, the beat frequency linearity is compared over several devices with varying Q, confirming that Q of each individual mode directly affects the oscillator stability and ultimately temperature measurement accuracy.