Stress-Dependent Optical Extinction in LPCVD Silicon Nitride Measured by Nanomechanical Photothermal Sensing

Abstract

Understanding optical absorption in silicon nitride is crucial for cutting-edge technologies like photonic integrated circuits, nanomechanical photothermal infrared sensing and spectroscopy, and cavity optomechanics. Yet, the origin of its strong dependence on film deposition and fabrication process is not fully understood. This Letter leverages nanomechanical photothermal sensing to investigate optical extinction $κ_{\mathrm{ext}}$ at 632.8 nm wavelength in LPCVD SiN strings across a wide range of deposition-related tensile stresses ($200-850$ MPa). Measurements reveal a reduction in $κ_{\mathrm{ext}}$ from 10$^3$ to 10$^1$ ppm with increasing stress, correlated to variations in Si/N content ratio. Within the band-fluctuations framework, this trend indicates an increase of the energy bandgap with the stress, ultimately reducing absorption. Overall, this study showcases the power and simplicity of nanomechanical photothermal sensing for low absorption measurements, offering a sensitive, scattering-free platform for material analysis in nanophotonics and nanomechanics.

Figures (3)

• Figure 1: (a) Sketch of the experimental set-up (LDV, Polytech GmbH MSA-500). A laser of wavelength $\lambda$ and input power $P_0$ impinges on the resonator, of absorption coefficient $\alpha_\mathrm{abs}(\lambda)$. This causes a frequency detuning of the nanomechanical resonator. BS: beam-splitter. BC: Bragg cell. PD: photodetector. (b) Mechanical frequency detuning measured by monitoring the shift of the thermomechanical noise peak of the string's fundamental mode as a function of $P_0$. (c) Optical micrograph of the SiN strings used in the present study. Orange/light blue regions are made of SiN; the grey regions are the Si substrate. (d) Photo of the cm-scale copper thermal equilibrium chamber used for the characterization of the linear coefficient of thermal expansion. A thermoelectric module is glued beneath to heat up the whole oven (thick red electrical connections) to guarantee a uniform temperature rise of the chips. The temperature is monitored and kept constant with a PID controller.
• Figure 2: (a) $\mathcal{R}_P$ for different SiN string structures. Circles: experimental responsivity \ref{['Rp_exp']}, divided by the corresponding mean absorption coefficient $\alpha_\mathrm{abs}$. Solid curve: theoretical model \ref{['Rp_theory']}. Material parameter assumed: $\rho = 3000\ \mathrm{kg/m^3}$, $\kappa=3$ W/(m K). Emissivity values are calculated from data reported in Ref. Cataldo2012: 0.05 ($h=56$ nm), 0.13 ($h=157$ nm), 0.133 ($h=177$ nm), 0.171 ($h=312$ nm), 0.176 ($h=340$ nm). (b) Example of Young's modulus estimation, following the procedure of Ref. Klass2022. (c) Experimental Young's modulus E as a function of the prestress $\sigma_0$. (d) Experimental linear coefficient of thermal expansion $\alpha_\mathrm{th}$ as a function of the prestress $\sigma_0$.
• Figure 3: (a) $\kappa_{ext}$ for different SiN string's tensile stresses at an excitation wavelength of $\lambda=(632.8 \pm 30)$ nm. Characterization techniques included in the figure are: nanomechanical photothermal absorption spectroscopy (NPAS) Land2024, direct absorption spectroscopy (DAS) in waveguides Inukai1994Bulla1999Daldosso2004Sacher2019, cavity absorption spectroscopy in microrings resonators (CAS-µring) Corato2024Worhoff2008, cutback Sorace2019, ellipsometry Poenar1997, and prism coupling Bonneville2021. Markers refer to LPCVD (circles), plasma-enhanced CVD (PECVD, diamonds), and electron-cyclotron resonance CVD (ECR-CVD, squares) deposited SiN films. For the reported values, the vertical lines indicate a relationship with stress $\sigma_0$ (intersection with the bottom x-axis) or Si/N (intersection with the top x-axis), explicitly given in (solid lines) or derived from (dashed lines) the original article. When none of these values could be extracted, a stress error bar has been used ($\sigma_0=865-1365$ MPa). (b) Absorption coefficient in the band-fluctuations model. The dashed blue and red curves represent the absorption due to electronic transition between extended states (Tauc regime), and absorption due to disorder-induced localized to extended state transitions (Urbach regime), respectively. (c) Energy bandgap $E_\mathrm{g}$ as a function of the Si/N ratio. The solid curve is a fitting function of the displayed reported values of the form $f(x)=a e^{b x} + c$, with $a= 95.94$ eV, $b=4.356$, and $c=1.633$ eV. Only LPCDV SiN films have been considered. Compilation: darkcyan, Ref. Bauer1977; blue, Ref. Corato2024; purple, Ref. Beliaev2022; orange, Ref. Krueckel2017. Dashed vertical lines indicate the Si/N ratios measured in this study with XPS. Intersections with the fitting curve are given in Table \ref{['tab:Strings']}. (d) Corresponding Urbach energy $\beta^{-1}$ of the thin films analyzed in this study (black circles). For comparison, data from Ref. Bauer1977 (darkcyan) and Ref. Corato2024 (blues) are displayed.