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

Abstract

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.

Figures (4)

• Figure 1: A membrane resonator using ultra-high stressed TiN films.(a) A stress map of the TiN film on a Si substrate at room temperature. (b) A photograph of the TiN membrane resonator device.(c) A photograph of the TiN membrane taken from the backside of (b). The side length of the membrane resonator is 420$\mathrm{\mu m}$.
• Figure 2: Characterization of an ultra-high-stress TiN membrane resonator at 2.2 K. (a) Frequency response of the membrane resonator recorded at 2.2 K. Gray shaded areas indicate phononic bandgaps. Inset shows an aluminum sample mount to fix the resonator and piezo actuator. The peaks of the membrane modes are not shown due to their extremely narrow linewidth. (b) Quality factors of the membrane modes up to the (3,3) mode measured at 2.2 K. Modes inside phononic bandgaps (shaded) are shown by orange stars. Modes outside bandgaps are shown by blue circles. High-$Q$ ($>10^6$) modes outside bandgaps are shown by green triangles. Inset shows ringdown data of the fundamental mode of the membrane resonator. Time constant $\tau$ is obtained by fitting. The extracted quality factor is $8.0\times10^6$.
• Figure 3: Temperature dependence of the mechanical properties of the membrane resonator. (a) Temperature dependence of the tensile stress on the membrane. The tensile stress is extracted from the frequency of the fundamental mode using Eq. \ref{['eq:1']}. (b) Temperature dependence of the quality factor of the fundamental mode. Measurement data are shown with orange filled circles. The expected reduction in quality factor with increasing temperature from 2.2 K is displayed with blue open circles, assuming only the tensile stress in Eq. \ref{['eq:3']} has the temperature dependence.
• Figure 4: Comparison of achievable quality factors as a function of frequency for different materials and designs. Estimated achievable quality factors of SiN and our TiN membrane resonators with 100 nm thickness and below 1000 $\mathrm{\mu m}$ side lengths are shown as colored regions. Solid lines represent the upper limit of $Q$ for SiN, while dashed lines represent that for TiN. A yellow filled circle corresponds to the measured quality factor of the TiN membrane resonator (fundamental mode).