Optical constants

Refractive index of Si₃N₄, SiN (Silicon nitride)

Luke et al. 2015: n 0.310–5.504 µm

Data: formula 1
Range: 0.31–5.504 µm
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.0458
Extinction coefficient k: 0

Permittivity ε₁: 4.18531
Permittivity ε₂: 0

Absorption coefficient α: 0 cm⁻¹
Penetration depth δ = λ/(2πk): — nm

Abbe number V_d: 34.364
Chromatic dispersion dn/dλ: -0.156402 µm⁻¹

Group index n_g: 2.1377
Group velocity dispersion: 284.562 fs²/mm

Dispersion parameter D: -1552.44 ps/(nm·km)
Photon energy: 2.11001 eV

ε = (n + ik)², α = 4πk/λ, n_g = n − λ dn/dλ, GVD = λ³/(2πc²) d²n/dλ², D = −(λ/c) d²n/dλ². Group-velocity dispersion is given for formula data only.

Use it in Lightsmith

Load this data in Python, simulate in one more line

pip install lightsmith

import lightsmith as ls

# Si3N4, SiN (Silicon nitride): Luke et al. 2015: n 0.310–5.504 µm
si3n4_sin = ls.fetch_refractiveindex("main", "Si3N4", "Luke", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si3n4_sin.range_nm)  # (310, 5504) nm
eps = si3n4_sin.eps([633])  # complex permittivity

Downloads the original record once (pinned to the imported snapshot) and caches it.

import json, urllib.request
import lightsmith as ls

url = "https://materials.lightsmith.dev/v1/datasets/ds_614ff551b289/lightsmith"
si3n4_sin = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(si3n4_sin.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (si3n4/luke-2015).

# ... load si3n4_sin as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=si3n4_sin)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=1000, num=81),
)
res = ls.solve(sim)  # exact Mie for a sphere
print(res.q_ext)     # extinction efficiency at each wavelength

Same spec runs with DDA, FDTD, BEM or T-matrix: ls.compare(sim, ["mie", "dda"]).

import json, urllib.request
import lightsmith as ls

url = "https://materials.lightsmith.dev/v1/datasets/ds_614ff551b289/lightsmith?model=drude_lorentz"
si3n4_sin_dl = ls.DrudeLorentz.model_validate(json.load(urllib.request.urlopen(url)))

A dispersive Drude–Lorentz model for time-domain solvers.

Materials guide Open a sphere of it in Studio Quick start Ask the community

Lightsmith is open source (MIT): Mie, T-matrix, BEM, DDA, FDTD, RCWA, TMM, mode solvers and inverse design behind one spec, on CPU or GPU. GitHub.

Dispersion formula

Sellmeier (formula 1), λ in µm

n^{2} - 1 = \frac{3.0249 λ^{2}}{λ^{2} - {0.1353406}^{2}} + \frac{40314.0 λ^{2}}{λ^{2} - {1239.842}^{2}}

Valid from 0.31 to 5.504 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	3.0249
C3	0.1353406
C4	40314.0
C5	1239.842

Comments and conditions

340 nm Si₃N₄ on 3.1 μm of thermal SiO₂ on silicon.

References

K. Luke, Y. Okawachi, M. R. E. Lamont, A. L. Gaeta, M. Lipson. Broadband mid-infrared frequency comb generation in a Si₃N₄ microresonator. Opt. Lett. 40, 4823-4826 (2015)

doi:10.1364/ol.40.004823 Broadband mid-infrared frequency comb generation in a Si_3N_4 microresonator, Optics Letters (2015)

Cite

Kevin Luke, Yoshitomo Okawachi, Michael R. E. Lamont, Alexander L. Gaeta and Michal Lipson. Broadband mid-infrared frequency comb generation in a Si_3N_4 microresonator. Optics Letters, 40, 4823 (2015), doi:10.1364/ol.40.004823; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 400 wavelengths, the same grid as the API and the library

CSV comma separated TXT tab separated YAML n, k Full database record original YAML All quantities CSV JSON metadata

Si3N4, SiN (Silicon nitride), Luke et al. 2015: n 0.310–5.504 µm: n and k versus wavelength
λ (µm)	n
0.31	2.175939
0.312243	2.173044
0.314502	2.170204
0.316778	2.16742
0.31907	2.16469
0.321379	2.162011
0.323704	2.159384
0.326046	2.156807
0.328406	2.154279
0.330782	2.151798
0.333175	2.149364
0.335586	2.146976
0.338014	2.144632
0.34046	2.142331
0.342924	2.140072
0.345405	2.137856
0.347904	2.135679
0.350421	2.133543
0.352957	2.131445
0.355511	2.129385
0.358083	2.127362
0.360674	2.125375
0.363284	2.123424
0.365913	2.121508
0.36856	2.119625
0.371227	2.117776
0.373913	2.115959
0.376619	2.114174
0.379344	2.112421
0.382089	2.110698
0.384853	2.109004
0.387638	2.10734
0.390443	2.105705
0.393268	2.104098
0.396114	2.102518
0.39898	2.100965
0.401867	2.099439
0.404774	2.097938
0.407703	2.096463
0.410653	2.095012
0.413625	2.093586
0.416618	2.092184
0.419632	2.090805
0.422668	2.089448
0.425727	2.088115
0.428807	2.086803
0.43191	2.085513
0.435035	2.084244
0.438183	2.082996
0.441353	2.081768
0.444547	2.08056
0.447764	2.079371
0.451004	2.078202
0.454267	2.077052
0.457554	2.07592
0.460865	2.074806
0.464199	2.073709
0.467558	2.072631
0.470941	2.071569
0.474349	2.070524
0.477781	2.069495
0.481238	2.068483
0.48472	2.067486
0.488227	2.066505
0.49176	2.065539
0.495318	2.064589
0.498902	2.063652
0.502512	2.062731
0.506148	2.061823
0.509811	2.060929
0.5135	2.060049
0.517215	2.059182
0.520958	2.058328
0.524727	2.057487
0.528524	2.056659
0.532348	2.055843
0.5362	2.055039
0.54008	2.054248
0.543988	2.053468
0.547924	2.052699
0.551888	2.051942
0.555882	2.051196
0.559904	2.050461
0.563955	2.049736
0.568036	2.049022
0.572146	2.048318
0.576286	2.047624
0.580456	2.046941
0.584656	2.046267
0.588886	2.045602
0.593147	2.044947
0.597439	2.044301
0.601762	2.043665
0.606116	2.043037
0.610502	2.042417
0.614919	2.041807
0.619369	2.041204
0.62385	2.04061
0.628364	2.040024
0.632911	2.039446
0.63749	2.038876
0.642103	2.038314
0.646749	2.037759
0.651429	2.037211
0.656142	2.03667
0.66089	2.036137
0.665672	2.03561
0.670489	2.035091
0.67534	2.034578
0.680227	2.034071
0.685149	2.033571
0.690106	2.033078
0.6951	2.03259
0.700129	2.032109
0.705195	2.031634
0.710298	2.031164
0.715437	2.0307
0.720614	2.030242
0.725828	2.029789
0.73108	2.029342
0.73637	2.0289
0.741698	2.028463
0.747065	2.028031
0.75247	2.027604
0.757915	2.027182
0.763399	2.026765
0.768923	2.026352
0.774487	2.025944
0.780091	2.025541
0.785735	2.025142
0.79142	2.024747
0.797147	2.024356
0.802915	2.02397
0.808725	2.023587
0.814576	2.023208
0.82047	2.022834
0.826407	2.022463
0.832387	2.022095
0.83841	2.021731
0.844476	2.021371
0.850586	2.021014
0.856741	2.02066
0.86294	2.02031
0.869184	2.019963
0.875473	2.019619
0.881808	2.019278
0.888189	2.018939
0.894615	2.018604
0.901088	2.018272
0.907608	2.017942
0.914176	2.017614
0.92079	2.01729
0.927453	2.016967
0.934164	2.016648
0.940923	2.01633
0.947731	2.016015
0.954589	2.015702
0.961496	2.015391
0.968453	2.015082
0.975461	2.014775
0.982519	2.01447
0.989628	2.014167
0.996789	2.013866
1.004	2.013566
1.01127	2.013268
1.01858	2.012972
1.02595	2.012677
1.03338	2.012383
1.04085	2.012091
1.04839	2.0118
1.05597	2.011511
1.06361	2.011223
1.07131	2.010935
1.07906	2.010649
1.08687	2.010364
1.09473	2.01008
1.10265	2.009797
1.11063	2.009514
1.11867	2.009232
1.12676	2.008951
1.13491	2.008671
1.14313	2.008391
1.1514	2.008112
1.15973	2.007833
1.16812	2.007554
1.17657	2.007276
1.18509	2.006998
1.19366	2.00672
1.2023	2.006443
1.211	2.006165
1.21976	2.005888
1.22859	2.00561
1.23748	2.005333
1.24643	2.005055
1.25545	2.004777
1.26453	2.004499
1.27368	2.00422
1.2829	2.003942
1.29218	2.003662
1.30153	2.003382
1.31095	2.003102
1.32043	2.002821
1.32999	2.002539
1.33961	2.002256
1.3493	2.001973
1.35907	2.001689
1.3689	2.001404
1.37881	2.001117
1.38878	2.00083
1.39883	2.000542
1.40895	2.000252
1.41915	1.999962
1.42942	1.999669
1.43976	1.999376
1.45018	1.999081
1.46067	1.998785
1.47124	1.998487
1.48189	1.998187
1.49261	1.997886
1.50341	1.997583
1.51429	1.997278
1.52524	1.996972
1.53628	1.996663
1.5474	1.996352
1.55859	1.99604
1.56987	1.995725
1.58123	1.995408
1.59267	1.995089
1.60419	1.994767
1.6158	1.994443
1.62749	1.994116
1.63927	1.993787
1.65113	1.993455
1.66308	1.993121
1.67511	1.992784
1.68723	1.992444
1.69944	1.992101
1.71174	1.991755
1.72412	1.991406
1.7366	1.991054
1.74916	1.990698
1.76182	1.99034
1.77457	1.989978
1.78741	1.989612
1.80034	1.989243
1.81337	1.988871
1.82649	1.988494
1.83971	1.988114
1.85302	1.987731
1.86642	1.987343
1.87993	1.986951
1.89353	1.986555
1.90723	1.986155
1.92103	1.985751
1.93493	1.985342
1.94893	1.984929
1.96304	1.984512
1.97724	1.984089
1.99155	1.983663
2.00596	1.983231
2.02047	1.982794
2.03509	1.982353
2.04982	1.981906
2.06465	1.981454
2.07959	1.980997
2.09464	1.980535
2.10979	1.980067
2.12506	1.979593
2.14043	1.979114
2.15592	1.978629
2.17152	1.978138
2.18723	1.977641
2.20306	1.977138
2.219	1.976629
2.23506	1.976113
2.25123	1.975591
2.26752	1.975063
2.28392	1.974527
2.30045	1.973985
2.3171	1.973437
2.33386	1.972881
2.35075	1.972318
2.36776	1.971747
2.38489	1.97117
2.40215	1.970584
2.41953	1.969992
2.43704	1.969391
2.45467	1.968782
2.47243	1.968166
2.49032	1.967541
2.50834	1.966908
2.52649	1.966266
2.54477	1.965616
2.56318	1.964957
2.58173	1.96429
2.60041	1.963613
2.61923	1.962927
2.63818	1.962231
2.65727	1.961527
2.6765	1.960812
2.69586	1.960088
2.71537	1.959354
2.73502	1.958609
2.75481	1.957854
2.77474	1.957089
2.79482	1.956313
2.81504	1.955527
2.83541	1.954729
2.85592	1.95392
2.87659	1.9531
2.8974	1.952268
2.91837	1.951425
2.93948	1.95057
2.96075	1.949702
2.98218	1.948822
3.00375	1.94793
3.02549	1.947025
3.04738	1.946107
3.06943	1.945176
3.09164	1.944232
3.11401	1.943274
3.13654	1.942302
3.15924	1.941316
3.1821	1.940316
3.20512	1.939302
3.22831	1.938273
3.25167	1.937229
3.2752	1.93617
3.2989	1.935095
3.32277	1.934005
3.34681	1.932899
3.37103	1.931776
3.39542	1.930638
3.41999	1.929482
3.44473	1.92831
3.46966	1.92712
3.49476	1.925913
3.52005	1.924688
3.54552	1.923444
3.57118	1.922183
3.59702	1.920903
3.62304	1.919603
3.64926	1.918285
3.67566	1.916947
3.70226	1.915589
3.72905	1.91421
3.75603	1.912811
3.78321	1.911391
3.81058	1.90995
3.83815	1.908487
3.86593	1.907002
3.8939	1.905495
3.92207	1.903965
3.95045	1.902413
3.97904	1.900836
4.00783	1.899236
4.03683	1.897612
4.06604	1.895962
4.09546	1.894288
4.12509	1.892589
4.15494	1.890863
4.185	1.889111
4.21529	1.887333
4.24579	1.885527
4.27651	1.883694
4.30745	1.881832
4.33862	1.879942
4.37001	1.878023
4.40163	1.876074
4.43348	1.874095
4.46556	1.872086
4.49787	1.870046
4.53042	1.867974
4.5632	1.865869
4.59622	1.863733
4.62947	1.861562
4.66297	1.859359
4.69671	1.85712
4.73069	1.854847
4.76492	1.852538
4.7994	1.850193
4.83413	1.847811
4.86911	1.845392
4.90434	1.842934
4.93983	1.840438
4.97557	1.837902
5.01157	1.835326
5.04783	1.832709
5.08436	1.830051
5.12115	1.82735
5.1582	1.824607
5.19553	1.821819
5.23312	1.818987
5.27098	1.816109
5.30912	1.813186
5.34754	1.810215
5.38623	1.807196
5.42521	1.804128
5.46446	1.801011
5.504	1.797843

Optical transmission calculator

Free-standing sample in vacuum, normal incidence

Transmittance T: —
Reflectance R: —

Fresnel reflection calculator

R_p: —
R_s: —
R = (R_p+R_s)/2: —
Phase φ_p: —
Phase φ_s: —
Brewster angle θ_B: —
Critical angle θ_C: —

Si₃N₄, SiN (Silicon nitride): all datasets

Si3N4 films (stoichiometric)

Non-stoichiometric SiN films

About Si3N4, SiN (Silicon nitride)

Silicon nitride (Si₃N₄) is a synthetic, high-performance ceramic material known for its impressive mechanical properties even at elevated temperatures. It exhibits excellent thermal shock resistance, and its hardness makes it resistant to wear and abrasion. In the realm of electronics, it's utilized as an insulator and as a dielectric for advanced microelectronics applications due to its electrical properties. Owing to its resistance to oxidation and chemical corrosion, it's also used in challenging environments, such as in the manufacturing of ball bearings, turbine blades, and other engine components. Additionally, in the optical domain, silicon nitride is transparent in the infrared range and has been studied for potential uses in optoelectronic devices. Its combination of strength, temperature resistance, and electrical properties make it a sought-after material for various high-tech applications.

Silicon nitride - Wikipedia

More about Si3N4, SiN (Silicon nitride) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Si3N4/nk/Luke.yml
ID: ds_614ff551b289
API: /v1/datasets/ds_614ff551b289

Plot