"Fabrication and characterization of high-Q silicon nitride membrane resonators".

This paper provides a comprehensive guide on the design, fabrication, and characterization of high-Q silicon nitride (SiN) membrane resonators, specifically focusing on centimeter-scale Si₃N₄ nanoribbons with torsion modes exhibiting a quality factor (Q) greater than 10⁸. These resonators are important in optomechanics and precision measurement applications.

Key Highlights:

1. Design & Simulation: The resonators are designed using COMSOL Multiphysics, where parameters such as frequency, mode shape, effective mass, and quality factor are optimized. The resonator geometry is adjusted to achieve desired performance, and simulations help predict the mechanical properties, including dissipation dilution, which influences the quality factor.

2. Fabrication Process: The fabrication involves several steps:

• Si₃N₄ Deposition: A high-stress Si₃N₄ thin film is deposited onto a silicon substrate using low-pressure chemical vapor deposition (LPCVD).

• Patterning: A layer of photoresist is applied, and photolithography is used to transfer the resonator design onto the wafer.

• Etching & Backside Patterning: Reactive ion etching (RIE) is used to carve the resonators into the Si₃N₄ film, followed by backside patterning to create windows for the resonators' release.

• Wafer Cleaving & KOH Etching: After dicing the wafer, a potassium hydroxide (KOH) etch is used to remove the silicon substrate beneath the resonators, leaving them free-standing.

3. Characterization: The membrane resonators are characterized using an optical lever (OL) setup. This method involves measuring the deflection of the resonator’s modes and calculating the quality factor (Q) from the energy ringdown and thermal noise measurement. The torsional and flexural modes of the resonators are measured, with results indicating a torsional mode Q of 200 million.

4. Challenges and Limitations: The process highlights challenges such as the difficulty in ensuring the survivability of complex resonator geometries during the release phase, as well as variations in etch rates depending on the geometry. Additionally, issues like substrate-mode coupling and clamping loss can affect the resonator’s performance, particularly in flexural modes.

5. Applications: SiN membrane resonators are used in a range of applications in quantum optomechanics, including force sensing, accelerometry, and precision measurements. They are also part of proposals for dark matter detectors and microwave-to-optical photon transducers.

The paper concludes by emphasizing the importance of this protocol for fabricating high-performance resonators and its potential for developing future optomechanical devices. The methods described provide a foundation for advanced resonator designs and enable precision fabrication with high-Q characteristics suitable for quantum and sensing applications.