High-$Q$ membrane resonators using ultra-high-stress crystalline TiN films

High-quality-factor ($Q$) mechanical resonators are essential components for precise sensing and control of mechanical motion at a quantum level. While amorphous materials such as SiN have been widely used in high-$Q$ mechanical resonators utilizing stress-induced dissipation dilution, crystalline materials have emerging potential to achieve higher quality factors by combining low intrinsic loss and high tensile stress. In this paper, we demonstrate high-Q membrane resonators using ultra-high-stress crystalline TiN. Our membrane resonator exhibits a tensile stress exceeding 2.3 GPa and a quality factor of $Q = 8.0 \times 10^6$ at 2.2 K. By estimating the dilution factor, we infer that our TiN resonator has a intrinsic quality factor comparable to that of SiN membrane resonators. With its ultra-high stress and crystalline properties, our TiN films can serve as a powerful tool for opto- and electromechanical systems, offering highly dissipation-diluted mechanical resonators.

💡 Research Summary

In this work the authors demonstrate a high‑quality‑factor (Q) mechanical membrane resonator based on ultra‑high‑stress crystalline titanium nitride (TiN) thin films. By exploiting the large tensile stress (>2.3 GPa) that can be generated in epitaxial TiN on silicon through lattice‑mismatch and differential thermal expansion, they achieve a dilution‑enhanced Q of 8.0 × 10⁶ for the fundamental (1,1) mode at a temperature of 2.2 K. The TiN film (100 nm thick, (200) oriented) is grown by DC magnetron sputtering at 880 °C on a 300‑µm Si(100) substrate, then patterned into a 420‑µm‑square membrane surrounded by a phononic crystal (PC) designed to open bandgaps around the membrane’s resonant frequencies. Finite‑element simulations (COMSOL) guide the PC geometry, and anisotropic wet etching combined with deep reactive‑ion etching releases the membrane while preserving the PC.

Mechanical characterization is performed with a Michelson interferometer inside a cryostat. The fundamental mode frequency shifts from 1.008 MHz at room temperature to 1.132 MHz at 2.2 K, remaining within the PC bandgap, which suppresses acoustic radiation loss. Ring‑down measurements reveal Q = 8.0 × 10⁶ for the (1,1) mode, and Q > 10⁶ for higher‑order (2,2) and (3,3) modes, even when those modes lie outside the PC bandgap. Temperature sweeps from 2.2 K to 150 K show that Q decreases with increasing temperature, while the tensile stress stays roughly constant up to ~50 K. This indicates that the observed Q degradation is dominated by a reduction in the intrinsic material loss (Q_int) rather than by stress‑induced dilution changes.

Using the standard dissipation‑dilution model Q_mn = Q_int · D_Q, where D_Q =