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UV-Vis-NIR Complex Refractive Index Characterization of Silicon Nitride Thin Films
Silicon nitride ($\mathrm{SiN_x}$) is a widely used material in nanomechanics and integrated photonics due to its favorable mechanical and optical properties. In photonics, it serves as a low-loss platform for optical waveguides owing to its low extinction coefficient $k(\lambda)$ in the infrared (IR).
Conventional determination of the complex refractive index $\tilde{n}(\lambda)$ relies on measurements of transmittance $T$ and reflectance $R$, which are interpreted using optical models to extract $n(\lambda)$ and $k(\lambda)$. Absorptance is often inferred as $A = 1 - T - R$. In the low-loss regime, $A$ becomes very small and difficult to distinguish from scattering contributions and measurement noise, limiting the reliability of such extraction methods.
Here, we use tensile-stressed $\mathrm{SiN_x}$ nanomechanical resonators as photothermal sensors. Monochromatic UV–NIR illumination induces heating proportional to optical absorption, leading to thermal expansion and a corresponding shift in resonance frequency. This shift scales with absorptance, $\Delta f_0 / f_0 \propto A(\lambda)$, enabling an alternative route to quantify optical absorption. Combining this with transmission measurements improves the robustness of the determination of the complex refractive index, in particular the extinction coefficient $k(\lambda)$.