Frequency and damping effect of suspended silicon nitride membranes in water near the megahertz range

Abstract

Understanding the behavior of water-immersed membranes in the megahertz range is critical to develop novel acoustic metamaterials compatible with biomedical ultrasound applications. Herein, we study the influence of water on the resonance frequency and quality factor near the megahertz range of silicon nitride membranes fully immersed in water using laser Doppler vibrometry. The resonance frequency of silicon nitride membranes significantly decreases in water compared to air. For a 40 µm wide membrane, the resonance frequency is reduced from 11.2 MHz in air to 1.24 MHz after immersion in water, which is confirmed by finite element method simulations. Our results indicate that the water mass loading plays a major role in the resonance frequency reduction, with a ratio of water mass to membrane mass of m w a t e r / m m e m b r a n e ∼ 102 and NAVMI factors of Γ∼1.3. We attribute the main losses to acoustic radiation with small contributions from viscous damping. We estimate that silicon nitride membranes with widths below 50 µm are required to build negative metamaterials operating above 1 MHz. The large NAVMI factors suggest strong coupling between membrane motion and acoustic waves in water, which is important to develop metamaterials able to manipulate acoustic fields.

Negative‐Index Acoustic Metamaterial Operating above 100 kHz in Water Using Microstructured Silicon Chips as Unit Cells

“…Based on previous reports, membranes below 40 microns in width may be required to achieve operation above 1 MHz. [41,43] However, this will require addressing more fabrication challenges, overcoming membrane damping and water viscosity limitations, and developing new alignment/ assembling methods.…”

“…This was determined from measurements of the resonance frequency of the (1,1) mode of the membranes in air by LDV measurements as described in Note S3, Supporting Information giving a value of 1.2 GPa. [ 43 ] This residual stress is produced during the chemical vapor deposition at 800 o C of the 200 nm thick SiN x film. This stress is due to the thermal expansion and lattice mismatch between Si and SiN x .…”