Tunable turning point of the frequency--temperature response in suspended bilayer SiN_x/Al nanofilms

Abstract

Non-invasive thermometry is highly desirable in cryogenic experiments to avoid the self-heating inherent in conventional sensors. In previous work, temperature was probed via the vibrational eigenfrequency of a suspended single-layer SiNx nanofilm. However, the turning point of the frequency-temperature curve limited the usable measurement range. Moreover, the slow thermal response confined measurements to a stepwise protocol with only discrete temperature points. Here, we show that these limitations can be overcome with a suspended bilayer SiNx/Al nanofilm, whose temperature-dependent vibrational eigenfrequency provides a monotonic, continuous, and repeatable temperature readout. The frequency-temperature dependence is governed by the mismatch between the effective coefficients of thermal expansion (CTE) of the bilayer and the substrate, which makes the turning point tunable through the thickness ratio of the two layers. Over the 90 K to 300 K range, we characterize three bilayer nanofilms with different Al layer thicknesses and show how the turning point shifts with the thickness of the Al layer. For the sample with 72 nm Al, the turning point is pushed beyond 300 K, yielding a monotonic negative temperature coefficient over the entire 90 K to 300 K range. Combining a thin Al layer on the SiNx film with improved thermal anchoring of the chip shortens the thermal response to below 1 s, enabling continuous frequency tracking at a ramp rate of 3 K/min. We also demonstrate that the nanofilm with a 72 nm Al layer achieves a repeatability better than 150 mK above 175 K, and the frequency resolution of 1 Hz corresponds to a temperature resolution of ~5 mK.