Optical constants

Refractive index of Si (Silicon)

Franta et al. 2013: n,k 0.138–26.9 µm

Data
tabulated nk
Range
0.138–26.92 µm
Points
230
State
amorphous
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.138–26.92 µm
Refractive index n
4.46097
Extinction coefficient k
0.173354
Permittivity ε1
19.8702
Permittivity ε2
1.54666
Absorption coefficient α
37073.5 cm⁻¹
Penetration depth δ = λ/(2πk)
539.47 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-4.26544 µm⁻¹
Group index ng
6.96735
Group velocity dispersion
— fs²/mm
Dispersion parameter D
— ps/(nm·km)
Photon energy
2.11001 eV

ε = (n + ik)², α = 4πk/λ, ng = 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

# Si (Silicon): Franta et al. 2013: n,k 0.138–26.9 µm
si = ls.fetch_refractiveindex("main", "Si", "Franta", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si.range_nm)  # (138.038, 26915.3) nm
eps = si.eps([633])  # complex permittivity

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

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.

Comments and conditions

Film a-Si:H; Multi-sample method; Heterogenous data processing combining ellipsometric and spectrophotometric measurements on films deposited on c-Si and glass; Experimental data of the films deposited on c=Si are taken from D. Franta, D. Nečas, L. Zajíčková, I. Ohlídal, J, Stuchlík, D. Chvostová. Application of sum rule to the dispersion model of hydrogenated amorphous silicon, Thin Solid Films 539, 233-244 (2013). Room temperature."

References

D. Franta, D. Nečas, L. Zajíčková, I. Ohlídal, J, Stuchlík. Advanced modeling for optical characterization of amorphous hydrogenated silicon films, Thin Solid Films 541, 12-16 (2013) (Numerical data kindly provided by Daniel Franta)

Cite

Daniel Franta, David Nečas, Lenka Zajíčková, Ivan Ohlídal and Jiří Stuchlík. Advanced modeling for optical characterization of amorphous hydrogenated silicon films. Thin Solid Films, 541, 12-16 (2013), doi:10.1016/j.tsf.2013.04.129; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

230 rows as published
Si (Silicon), Franta et al. 2013: n,k 0.138–26.9 µm: n and k versus wavelength
λ (µm)nk
0.1380380.47884571.722429
0.1412540.50581891.778852
0.1445440.5342451.835721
0.1479110.56416341.893278
0.1513560.59567181.951619
0.1548820.6289032.010843
0.1584890.66397572.070984
0.1621810.70106082.132131
0.1659590.74031542.194312
0.1698240.78191142.257546
0.173780.82607112.32189
0.1778280.8730042.387341
0.181970.92295162.453898
0.1862090.97619162.521558
0.1905461.0330032.590268
0.1949841.0937172.659981
0.1995261.1586982.730619
0.2041741.228332.802052
0.208931.3030292.874105
0.2137961.3832442.946547
0.2187761.4694943.019107
0.2238721.5622963.091404
0.2290871.6622133.162968
0.2344231.7698073.233198
0.2398831.885663.301361
0.2454712.0103643.366569
0.2511892.1444153.427717
0.257042.2882373.483499
0.2630272.4421073.532374
0.2691532.6060753.57257
0.2754232.7799363.602098
0.2818382.9629623.618771
0.2884033.1540233.620326
0.2951213.3513253.604526
0.3019953.5524163.569359
0.309033.7542443.51324
0.3162283.9531163.435286
0.3235944.1450553.335484
0.3311314.3259623.214883
0.3388444.492063.075568
0.3467374.6401712.920582
0.3548134.7680152.753684
0.3630784.8744322.578921
0.3715354.9592972.400382
0.3801895.023482.221768
0.3890455.0685882.046192
0.3981075.0967011.876066
0.407385.1101141.713031
0.4168695.111091.558038
0.426585.1016731.411459
0.4365165.0835791.273314
0.4466845.0581481.143356
0.4570885.026391.021329
0.4677354.9890740.9070121
0.478634.9468580.8003134
0.4897794.9003810.7012142
0.5011874.8503220.6097244
0.5128614.7973880.5257952
0.5248074.7422940.4493076
0.5370324.6857180.3800502
0.5495414.6282790.3177529
0.5623414.5705060.262091
0.575444.5128420.2127233
0.5888444.4556680.1693269
0.602564.3993070.1316004
0.6165954.3440490.09927914
0.6309574.2901710.07213833
0.6456544.2379670.04999817
0.6606934.1877980.03272366
0.6760834.1401530.02021864
0.6918314.0959860.01227668
0.7079464.05620.00756899
0.7244364.0205290.004778184
0.741313.9884470.003149738
0.7585783.9594550.002249266
0.7762473.9331380.001818857
0.7943283.9091620.001693012
0.8128313.8872540.001751892
0.8317643.8671860.00189871
0.8511383.848750.002053538
0.8709643.8317520.00215583
0.8912513.816010.00216889
0.9120113.8013580.002081454
0.9332543.7876550.001904373
0.9549933.7747820.001663291
0.9772373.7626530.00138989
1.03.7512010.001114041
1.023293.740380.0008588612
1.047133.7301490.0006385087
1.071523.7204830.00045904
1.096483.7113520.0003199259
1.122023.702730.0002166975
1.148153.694590.0001429917
1.17493.68699.210185e-05
1.202263.6796395.804756e-05
1.230273.6727753.584583e-05
1.258933.6662842.172236e-05
1.288253.6601461.292461e-05
1.318263.6543337.538765e-06
1.348963.6488294.291265e-06
1.380383.6436122.424935e-06
1.412543.6386641.368778e-06
1.445443.6339717.654815e-07
1.479113.6295174.245623e-07
1.513563.6252882.338369e-07
1.548823.6212711.280066e-07
1.584893.6174546.973955e-08
1.621813.6138253.783681e-08
1.659593.6103752.046433e-08
1.698243.6070941.104489e-08
1.73783.6039715.951286e-09
1.778283.6009983.204357e-09
1.81973.5981681.725274e-09
1.862093.5954739.293685e-10
1.905463.5929055.012662e-10
1.949843.5904582.708291e-10
1.995263.5881251.46641e-10
2.041743.58597.961281e-11
2.08933.5837784.336081e-11
2.137963.5817532.370304e-11
2.187763.579821.300743e-11
2.238723.5779747.168816e-12
2.290873.576213.969151e-12
2.344233.5745242.208557e-12
2.398833.5729121.235346e-12
2.454713.571376.946976e-13
2.511893.5698933.928919e-13
2.57043.5684792.235169e-13
2.630273.5671231.279357e-13
2.691533.5658237.368775e-14
2.754233.5645754.270899e-14
2.818383.5633752.491782e-14
2.884033.5622211.463388e-14
2.951213.5611098.652275e-15
3.019953.5600375.150862e-15
3.09033.5593.087434e-15
3.162283.5579981.863659e-15
3.235943.5570241.132849e-15
3.311313.5560786.935201e-16
3.388443.5551544.275759e-16
3.467373.5542492.6549e-16
3.548133.5533591.660353e-16
3.630783.5524781.045754e-16
3.715353.5516016.633906e-17
3.801893.5507184.238417e-17
3.890453.5498222.727207e-17
3.981073.5488971.767338e-17
4.07383.5479261.153438e-17
4.168693.5468788.768435e-18
4.26583.5457064.176726e-14
4.365163.5443262.970432e-10
4.466843.542563.466628e-07
4.570883.5399045.700552e-05
4.677353.5351160.00142311
4.78633.5294480.00744167
4.897793.526390.02295477
5.011873.5503010.03916796
5.128613.5706140.01746651
5.248073.5619610.001934548
5.370323.5548035.732404e-05
5.495413.5515214.973912e-07
5.623413.5495161.379222e-09
5.75443.5480461.326324e-12
5.888443.546864.783685e-16
6.02563.5458429.243948e-20
6.165953.5449321.673838e-20
6.309573.5440911.235754e-20
6.456543.5432969.178386e-21
6.606933.5425296.856087e-21
6.760833.5417795.150149e-21
6.918313.5410343.890199e-21
7.079463.5402872.954766e-21
7.244363.539532.354482e-21
7.41313.5387562.954249e-20
7.585783.5379594.820575e-18
7.762473.537135.260442e-16
7.943283.5362623.714361e-14
8.128313.5353481.739321e-12
8.317643.5343765.52878e-11
8.511383.5333351.220472e-09
8.709643.5322111.911942e-08
8.912513.5309842.16935e-07
9.120113.5296281.818625e-06
9.332543.5281011.147951e-05
9.549933.5263445.557686e-05
9.772373.5242830.0002100332
10.03.5218810.0006304492
10.23293.5192260.001528157
10.47133.5165980.003040935
10.71523.5143860.005043569
10.96483.5128330.007077337
11.22023.5117740.008520432
11.48153.5105910.008920302
11.7493.5084060.00824719
12.02263.5043450.006937142
12.30273.4976750.005813567
12.58933.4878560.006095167
12.88253.47470.009539885
13.18263.4588560.018519
13.48963.4425650.0355738
13.80383.4300520.06223322
14.12543.4268910.09737662
14.45443.4379610.1362383
14.79113.4648780.1713228
15.13563.5046230.19503
15.48823.5504920.2026389
15.84893.5946060.1937397
16.21813.630590.1717028
16.59593.6549310.141939
16.98243.6671430.1100155
17.3783.6689510.08029646
17.78283.6631440.05545612
18.1973.652570.03660543
18.62093.6395820.02389226
19.05463.626090.01712334
19.49843.613990.01589349
19.95263.6053530.01909776
20.41743.6017720.02439979
20.8933.6032190.02865614
21.37963.6076670.02938572
21.87763.6121440.02606043
22.38723.6143780.02006419
22.90873.6137060.01351195
23.44233.6108170.008025806
23.98833.6068930.0042395
24.54713.6029080.002007423
25.11893.5993790.0008588622
25.7043.5964450.0003345584
26.30273.5940480.0001195254
26.91533.5920733.943971e-05

Optical transmission calculator

Free-standing sample in vacuum, normal incidence
Method
Transmittance T
—
Reflectance R
—

Fresnel reflection calculator

Direction
Rp
—
Rs
—
R = (Rp+Rs)/2
—
Phase φp
—
Phase φs
—
Brewster angle θB
—
Critical angle θC
—