Bulk mode piezoresistive thermal oscillators: time constants and scaling

This paper presents design and analysis for engineering the thermal and mechanical time constants of piezoresistive thermal oscillators. The optimal design is obtained by minimizing the threshold current density required to initiate self-sustained oscillations. Optimizing the oscillator geometry is of extreme practical importance given that the threshold current densities (GA/m(2)) are close to the breakdown current densities observed in silicon. The equivalent circuit model of the oscillator is used along with the lumped thermal, mechanical, and piezoresistive parameters to calculate the threshold current density of the oscillator. The optimal ratio of the thermal and mechanical time constants is found to be √3 for bulkmode oscillators where the in-plane dimensions control the mechanical resonant frequency. The final frequency of oscillations is obtained as a function of the mechanical resonant frequency, quality factor (Q), and the ratio of the time constants. Results show that scaling the dimension (or frequency) has a weak sub-linear effect on the oscillator performance. Finally, we compare different bulk modes, based on the calculated threshold dc currents for a 1-GHz oscillator.