Thermo-Optic Coefficient of Silicon Nitride, Silicon, and Other Photonic Materials: dn/dT Reference Table

Scope

The thermo-optic coefficient $dn\mathrm{/}dT$ (how refractive index moves with temperature) sets how far every filter drifts per kelvin, how much power every thermal phase shifter needs, and how hard athermal design has to work. The values are scattered across decades of papers; this page collects the working numbers for the common photonic materials at telecom wavelengths and room temperature, gives silicon nitride the fuller treatment its search traffic asks for, states the formulas the numbers plug into, and flags where "the" coefficient is a family of values that depends on the film.

The reference table

Values near 1550 nm and 295–300 K unless noted. Each headline value has a primary source in the references; per-material context is on the materials pages.

Three structural facts come out of the table. The semiconductors cluster near $+2\times {10}^{-4}$ K⁻¹, an order of magnitude above the dielectrics. Silica and stoichiometric nitride sit at $+0.85$–$2.5\times {10}^{-5}$ K⁻¹. And the polymers are negative at semiconductor-like magnitude, which is the basis of polymer-overlay athermalization.

Silicon nitride in detail

The number most people arrive here for is $dn\mathrm{/}dT=(2.45\pm 0.09)\times {10}^{-5}$ K⁻¹ for LPCVD Si₃N₄ at 1550 nm, measured by Arbabi and Goddard from the temperature shift of microring resonances in a film of index $1.977\pm 0.003$. The same paper gives $(0.95\pm 0.10)\times {10}^{-5}$ K⁻¹ for the PECVD SiOₓ cladding. Two later measurements land on the same value from different directions: Elshaari and colleagues found $(2.51\pm 0.08)\times {10}^{-5}$ K⁻¹ for a 200 nm PECVD film at 850–880 nm, and a 2022 effective-index study of LPCVD nitride reported $(2.51\pm 0.08)\times {10}^{-5}$ K⁻¹ at 300 K over a 300–460 K characterization range. For stoichiometric nitride of either deposition type, $2.4$–$2.5\times {10}^{-5}$ K⁻¹ is the number to use.

That agreement disappears once the film is silicon-rich. Nejadriahi and colleagues measured PECVD films at 1550 nm and found the coefficient climbing from about $1.8\times {10}^{-5}$ K⁻¹ at $n=1.92$ to $5.85\times {10}^{-5}$ K⁻¹ at $n=2.25$ and $1.65\times {10}^{-4}$ K⁻¹ at $n=3.1$, which is silicon's value in a film that still looks like nitride on the wafer. Pruiti and colleagues found the same trend in 500 nm PECVD films, $4.0\times {10}^{-5}$ K⁻¹ at $n=2.26$ rising to $1.1\times {10}^{-4}$ K⁻¹ at $n=2.73$. A sputtered amorphous film measured by Zanatta and Gallo gave $4.7\times {10}^{-5}$ K⁻¹ at 1510 nm. The practical rule: if the film index is above about 2.05, do not assume the stoichiometric coefficient; the index is a proxy for silicon content, and the coefficient follows it.

Wavelength dependence is mild for the stoichiometric film. A 2026 measurement on 670 nm thick Si₃N₄ rings found about 7 % variation across 780–1550 nm; the same sputtered film measured $6.2\times {10}^{-5}$ K⁻¹ at 620 nm against $4.7\times {10}^{-5}$ K⁻¹ at 1510 nm. Temperature dependence is the larger effect: both silicon and nitride lose roughly an order of magnitude between room temperature and 18 K, so cryogenic circuits cannot be designed from room-temperature coefficients.

What the coefficient buys, measured on real rings at 1550 nm:

The thick-nitride value is close to the bulk-coefficient estimate ($\lambda \mathrm{/}{n}_g\cdot dn\mathrm{/}dT$ with $n_g\approx 2.1$ gives 18 pm/K); the thin film sits lower because a third of the mode energy is in the oxide. Silicon's measured drift runs above the same estimate (66 pm/K with $n_g=4.2$ and the bulk coefficient) because in a high-contrast wire the mode's sensitivity to the core index exceeds 1. First-order perturbation theory gives $d\lambda \mathrm{/}dT=\lambda {\sum }_i{\eta }_i(d{n}_i\mathrm{/}dT)\mathrm{/}{n}_i$, with ${\eta }_i$ the share of the mode's electric energy in each material: a 500 × 220 nm strip, with about 90% of its electric energy in the silicon, shifts by 75 pm/K in a mode calculation, or 77 pm/K once thermal expansion is added. Because the shares add up to one, no silica-clad silicon guide can drift by more than about 87 pm/K at room temperature: 83 pm/K from the index and 4 pm/K from expansion. About 80 pm/K is the figure for budgets.

The formulas the table feeds

Waveguide devices respond through the effective index. What a ring or MZI feels is $d{n}_{eff}\mathrm{/}dT$, an energy-weighted average over core and cladding:

$$\frac{d{n}_{eff}}{dT}\approx {\mathrm{\Gamma }}_{core}\frac{d{n}_{core}}{dT}+{\mathrm{\Gamma }}_{clad}\frac{d{n}_{clad}}{dT}$$

with the confinement factors taken as field-energy fractions, which in a high-contrast waveguide can sum to more than one. A silicon strip waveguide lands at $1.8$–$2.3\times {10}^{-4}$ K⁻¹; a thin-core Si₃N₄ guide with much of its mode in oxide sits below the nitride bulk value. Geometry is a thermal design variable.

Resonance and filter drift. A resonant wavelength moves as

$$\frac{d\lambda }{dT}=\frac{\lambda }{n_g}\frac{d{n}_{eff}}{dT}$$

At 1550 nm one picometer is 125 MHz, so the nitride rings above drift at 1.9–2.4 GHz/K and silicon rings at about 10 GHz/K. The silicon number is the reason silicon rings ship with heaters and servos; the nitride number is why a nitride filter can often be left free-running in a temperature-controlled module. The same arithmetic for a silica AWG gives the 11 pm/K familiar from athermal-package datasheets.

Phase-shifter efficiency. A heater's $P_{\pi }$ scales inversely with $d{n}_{eff}\mathrm{/}dT$, and the measured values track the coefficient ratio. A doped-silicon heater 61.6 µm long needs 24.8 ± 0.4 mW per π (Harris 2014); a 200 µm titanium heater on 220 nm LPCVD nitride needs about 195 mW, or 65 mW with isolation trenches (Serkin 2026, preprint), and conventional nitride heaters in the literature span 64–300 mW per π. Both platforms drop below 1 mW per π once the waveguide is suspended: 0.49 mW in undercut silicon (Fang 2011) and 0.98 mW in a suspended nitride spiral (Zeng 2025). Silicon's large coefficient is therefore a 5–10× advantage in tuning power and a 5–10× penalty in drift; the two are the same number.

Silicon nitride versus silicon: the platform numbers

The thermo-optic coefficient is one row of a longer comparison. The others most often needed when choosing a platform:

The pattern is consistent: silicon buys density and active devices with its index contrast and pays in scattering loss, drift, and nonlinear absorption; nitride gives those back and pays in footprint and passivity. The silicon nitride photonics and silicon-on-insulator entries carry the rest of the comparison.

Caveats that keep this honest

$dn\mathrm{/}dT$ is wavelength-dependent (mildly, away from band edges), temperature-dependent (silicon's coefficient falls by an order of magnitude from 300 K to below 100 K and is near ${10}^{-8}$ K⁻¹ at 5 K), and for films, process-dependent: silicon-rich compositions shift the nitride coefficient by up to a factor of seven, and polymer formulations vary by tens of percent. Anisotropic crystals (LiNbO₃) have per-axis values; quote the axis with the number. For design sign-off, measure on your platform: a ring resonance tracked over a 20 °C sweep hands you $d{n}_{eff}\mathrm{/}dT$ in one afternoon, which is how most of the film values above were obtained.

Athermal design in one paragraph

Passive athermalization balances a positive-coefficient core against a negative-coefficient cladding (polymer overlays on SOI, heavily silica-loaded Si₃N₄ geometries) so that $d{n}_{eff}\mathrm{/}dT\to 0$ at the design point; mechanical athermalization (AWG packages that shift the fiber with a bimetal element) cancels drift without touching the optics; and active stabilization spends heater power to hold the setpoint, the standard answer in silicon at the cost of the power budget discussed under thermo-optic phase shifters and worked through for rings in Ring resonator thermal tuning and locking.

Per-material context lives on the materials pages: silicon, silicon nitride, fused silica, indium phosphide, gallium arsenide, and lithium niobate.

References: A. Arbabi and L. L. Goddard, "Measurements of the refractive indices and thermo-optic coefficients of Si₃N₄ and SiOₓ using microring resonances," Optics Letters 38, 3878 (2013). A. W. Elshaari, I. E. Zadeh, K. D. Jöns, and V. Zwiller, "Thermo-optic characterization of silicon nitride resonators for cryogenic photonic circuits," IEEE Photonics Journal 8, 2701009 (2016). K. Johnson, N. Alshamrani, D. Almutairi, A. Grieco, C. Horvath, J. N. Westwood-Bachman, A. McKinlay, and Y. Fainman, "Determination of the nonlinear thermo-optic coefficient of silicon nitride and oxide using an effective index method," Optics Express 30, 46134 (2022). H. Nejadriahi et al., "Thermo-optic properties of silicon-rich silicon nitride for on-chip applications," Optics Express 28, 24951 (2020). N. Pruiti et al., "Thermo-optic coefficient of PECVD silicon-rich silicon nitride," Optics Letters 45, 6242 (2020). A. R. Zanatta and I. B. Gallo, "The thermo optic coefficient of amorphous SiN films in the near-infrared and visible regions," Applied Physics Express 6, 042402 (2013). B. J. Frey, D. B. Leviton, and T. J. Madison, "Temperature-dependent refractive index of silicon and germanium," Proc. SPIE 6273, 62732J (2006). J. Komma et al., "Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures," Applied Physics Letters 101, 041905 (2012). D. B. Leviton and B. J. Frey, "Temperature-dependent absolute refractive index measurements of synthetic fused silica," Proc. SPIE 6273, 62732K (2006). T. Zheng, R. Yin, J. Xin, S. Li, M. Li, and X. Wang, "Nonlinear thermal drift characteristics in temperature-insensitive silicon nitride microring resonators," Photonics 13, 371 (2026) (silica-clad reference ring, 14.9 pm/K). C. Zhang et al., "Photonic thermometer by silicon nitride microring resonator with milli-kelvin self-heating effect," Measurement 188, 110494 (2022) (800 nm Si₃N₄ ring, 19.37 pm/K). G. Kim et al., "Silicon photonic temperature sensor employing a ring resonator manufactured using a standard CMOS process," Optics Express 18, 22215 (2010). N. C. Harris et al., "Efficient, compact and low loss thermo-optic phase shifter in silicon," Optics Express 22, 10487 (2014). Q. Fang et al., "Ultralow power silicon photonics thermo-optic switch with suspended phase arms," IEEE Photonics Technology Letters 23, 525 (2011). Z. Zeng et al., Optics Letters 50, 3768 (2025) (suspended Si₃N₄ heater, 0.98 mW). A. Rahim et al., "Expanding the silicon photonics portfolio with silicon nitride photonic integrated circuits," Journal of Lightwave Technology 35, 639 (2017). J. Liu et al., "High-yield, wafer-scale fabrication of ultralow-loss, dispersion-engineered silicon nitride photonic circuits," Nature Communications 12, 2236 (2021). J. F. Bauters et al., "Planar waveguides with less than 0.1 dB/m propagation loss fabricated with wafer bonding," Optics Express 19, 24090 (2011). Y. A. Vlasov and S. J. McNab, "Losses in single-mode silicon-on-insulator strip waveguides and bends," Optics Express 12, 1622 (2004). P. Dong et al., "Low loss shallow-ridge silicon waveguides," Optics Express 18, 14474 (2010). J. Cardenas et al., "Low loss etchless silicon photonic waveguides," Optics Express 17, 4752 (2009). D. Serkin et al., "Thermo-optic modulator with ultra-high extinction ratio for low-loss silicon nitride integrated photonics," arXiv:2601.19732 (2026). K. Ikeda, R. E. Saperstein, N. Alic, and Y. Fainman, "Thermal and Kerr nonlinear properties of plasma-deposited silicon nitride/silicon dioxide waveguides," Optics Express 16, 12987 (2008). M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Applied Physics Letters 82, 2954 (2003).