Sub-ppm Nanomechanical Absorption Spectroscopy of Silicon Nitride

Material absorption is a key limitation in nanophotonic systems; however, its characterization is often obscured by scattering and diffraction. Here we show that nanomechanical frequency spectroscopy can be used to characterize material absorption at the parts per million level and use it to characterize the extinction coefficient κ of stoichiometric silicon nitride (Si₃N₄). Specifically, we track the frequency shift of a high-Q Si₃N₄ trampoline in response to laser photothermal heating and infer κ from a model including stress relaxation and both conductive and radiative heat transfer. A key insight is the presence of two thermalization time scales: rapid radiative cooling of the Si₃N₄ film and slow parasitic heating of the Si chip. We infer κ ∼ 0.1-1 ppm for Si₃N₄ in the 532-1550 nm wavelength range, matching bounds set by waveguide resonators. Our approach is applicable to diverse photonic materials and may offer new insights into their potential.