Optical Loss Measurements of Silicon-Nitride Membranes using Photothermal Common-Path Interferometry

Materials that feature low optical loss and relatively high refractive index are important for applications such as on-chip photonics¹, free-space optics for sensitive experiments like LIGO^2,3 and, more recently, laser-driven light sails comprising thin membrane-like structures that efficiently reflect a high-power drive laser⁴. We have been investigating stoichiometric silicon nitride (Si₃N₄) membranes as a candidate material for such laser-light sails, due to its [a] low loss in the near infrared, [b] a moderately high refractive index (~2), [c] a large bandgap (~4.5 eV) that prevents two-photon absorption^5,6, and [d] vibrational resonances in the mid infrared that can enable radiative cooling⁷. To our knowledge, the optical absorption of Si₃N₄ membranes has not been directly measured.<br/><br/>We used photothermal commonpath interferometry (PCI)⁸, a sensitive pump-probe technique, to measure the absorption of Si₃N₄ membranes in the near infrared. We characterized membranes because they are the closest form factor to laser sails, and conventional techniques such as variable-angle spectroscopic ellipsometry are not sensitive enough to measure optical absorption in such thin low-loss membranes. PCI characterizes optical loss in a material by measuring the effect of the sample's absorption of a chopped pump beam on a probe beam via the thermo-optic effect. The amount of modulation in the probe beam carries information about the sample’s absorptivity at the pump wavelength.<br/><br/>Translation of the PCI signal to the actual absorption value depends on the sample geometry and material properties, including the thermo-optic coefficient and thermal conductance of the sample. The translation is most-easily done using a reference similar to the sample in terms of optical and thermal properties, except with a higher, known absorbance. Here, we transferred a monolayer of graphene onto the SiN membranes we want to measure. Because it is thin and grown by chemical vapor deposition, the graphene does not significantly affect the overall thermal conductance of the sample; however, the presence of graphene increases the optical absorption from the ppm level to the ~1% level (the latter easily measurable using ellipsometry or reflection/transmission spectroscopy), and thus the resulting graphene/SiN structure can be used as a reference for PCI measurements of the SiN alone. To our knowledge, this technique of using a highly absorbing monolayer as a reference for PCI measurements has not been proposed or demonstrated previously.<br/><br/>Using graphene-referenced PCI, we found the absorption coefficient of stoichiometric Si₃N₄ to be ~1.3 x 10^-2 cm^-1 and that of non-stoichiometric SiN_x (x~1) to be ~6.7 cm^-1. These values of absorption are close to those reported in literature for waveguides.^1,3 Based on our measurements, stoichiometric Si₃N₄ is indeed a promising candidate for laser-light sails and other applications where low optical absorption is required.<br/><br/>¹ X. Ji, et al., APL Photonics <b>6</b>(7), (2021).<br/>² J. Steinlechner, et al., Class Quantum Gravity <b>32</b>(10), (2015).<br/>³ J. Steinlechner, et al., Physical Review D <b>96</b>(2), 022007 (2017).<br/>⁴ K.L.G. Parkin, Acta Astronaut <b>152</b>, 370–384 (2018).<br/>⁵ H.R. Philipp, J Electrochem Soc <b>120</b>(2), 295 (1973).<br/>⁶ G.R. Holdman, et al., Adv Opt Mater <b>10</b>(19), 2102835 (2022).<br/>⁷ K. Luke, et al., Opt Lett <b>40</b>(21), 4823 (2015).<br/>⁸ A. Alexandrovski, et al., in <i>Solid State Lasers XVIII: Technology and Devices</i>, edited by W.A. Clarkson, N. Hodgson, and R.K. Shori (SPIE, 2009), p. 71930D.