Passive Self-Temperature Compensating Diamond Ring Resonator

An$85.1-\text{MHz}$capacitive-gap transduced diamond ring resonator using gap-dependent electrical stiffness to passively compensate its temperature dependence achieves an unassisted frequency excursion of only -15.1 ppm over 300 K to$380 \mathrm{K}\left(189 \text{ppb} /{}^{\circ} \mathrm{C}\right)$. This is$10 \times$smaller than a recent diamond resonator [1] and, when extrapolated over a$-40^{\circ} \mathrm{C}$to 85° C range,$2 \times$better than the 20 ppm achieved by the best heavily doped silicon [2]. It also surpasses the previous best passively compensated resonator [3] while operating at$8.6 \times$higher frequency and$11 \times$higher$Q$, all while obviating the need for gold. The key to this performance lies in the thermal-expansion mismatch between the diamond structural layer and the silicon substrate, which induces a temperature-dependent change in electrode-to-resonator gap. This gap change shifts electrical stiffness in a direction that counteracts the Young's modulus-dominated mechanical stiffness temperature dependence, thereby passively nulling frequency drift without consuming DC power. Combined with diamond's inherent advantages (high frequency-$Q$product, chemically inert, and high fracture strength), this built-in compensation mechanism positions diamond as an exceptionally promising platform for stable, low-power resonant sensors and timing devices.