Optical constants

Refractive index of Si (Silicon)

Schinke et al. 2015: n,k 0.25–1.45 µm

Data
tabulated nk
Range
0.25–1.45 µm
Points
121
Temperature
295 K
State
crystalline
Licence
CC0-1.0
Lightsmith
bundled

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.25–1.45 µm
Refractive index n
3.95952
Extinction coefficient k
0.0205128
Permittivity ε1
15.6774
Permittivity ε2
0.162442
Absorption coefficient α
4386.85 cm⁻¹
Penetration depth δ = λ/(2πk)
4559.08 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-2.3 µm⁻¹
Group index ng
5.311
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): Schinke et al. 2015: n,k 0.25–1.45 µm
si = ls.LibraryMaterial(name="Si", dataset="Schinke")
print(si.range_nm)  # (250, 1450) nm
eps = si.eps([633])  # complex permittivity

Ships with the library: works offline.

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

Relative uncertainties of the absorption coefficient: 0.4% at 0.250 µm, 11% at 0.6 µm, 1.4% at 1 µm, 12% at 1.2 µm and 180% at 1.45 µm. Temperature: 295 K.

Conditions

temperature
295 K

References

1) C. Schinke, P. C. Peest, J. Schmidt, R. Brendel, K. Bothe, M. R. Vogt, I. Kröger, S. Winter, A. Schirmacher, S. Lim, H. T. Nguyen, D. MacDonald. Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon. AIP Advances 5, 67168 (2015)
2) M. R. Vogt. Development of physical models for the simulation of optical properties of solar cell modules. PhD. Thesis (2015)
  • doi:10.1063/1.4923379 Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon, AIP Advances (2015)

Cite

Carsten Schinke et al.. Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon. AIP Advances, 5, 067168 (2015), doi:10.1063/1.4923379; M. R. Vogt. Development of physical models for the simulation of optical properties of solar cell modules. PhD. Thesis (2015); Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

121 rows as published
Si (Silicon), Schinke et al. 2015: n,k 0.25–1.45 µm: n and k versus wavelength
λ (µm)nk
0.251.6373.5889
0.261.7373.9932
0.272.034.5958
0.282.845.1961
0.294.1855.3124
0.35.0494.29
0.315.0913.6239
0.325.0853.2824
0.335.1353.0935
0.345.2452.9573
0.355.4232.9078
0.365.9142.9135
0.376.822.1403
0.386.5870.98399
0.396.0250.50308
0.45.6230.32627
0.415.3410.24127
0.425.110.17694
0.434.9320.13766
0.444.790.11201
0.454.6730.095362
0.464.5720.079105
0.474.4850.07024
0.484.4120.059817
0.494.3490.05381
0.54.2890.048542
0.514.2350.043831
0.524.1870.039531
0.534.1450.034804
0.544.1030.029896
0.554.0730.028038
0.564.0380.026551
0.574.0060.023746
0.583.9770.021896
0.593.9540.020076
0.63.9310.018521
0.613.9080.017257
0.623.8880.016809
0.633.8690.016268
0.643.8510.014693
0.653.8350.014447
0.663.8170.013608
0.673.8050.012807
0.683.7910.012045
0.693.7760.011317
0.73.7650.010623
0.713.7530.009961
0.723.7410.0093335
0.733.730.0087312
0.743.7190.0081618
0.753.7120.0076156
0.763.7010.0070942
0.773.6930.0066054
0.783.6840.0061338
0.793.6770.0056888
0.83.6690.0052655
0.813.6620.004864
0.823.6550.0044836
0.833.6460.0041235
0.843.6410.0037828
0.853.6360.0034605
0.863.6280.0031563
0.873.6220.0028697
0.883.6170.0026001
0.893.6130.0023464
0.93.610.0021092
0.913.6040.0018864
0.923.5980.0016787
0.933.5970.0014757
0.943.590.0013061
0.953.5840.0011393
0.963.5840.00098243
0.973.5780.0008406
0.983.5820.00071334
0.993.5790.00059638
1.03.5750.0004902
1.013.5720.00039616
1.023.5680.00031437
1.033.5650.00024048
1.043.5620.00017959
1.053.5590.00013043
1.063.5569.245e-05
1.073.5536.782e-05
1.083.5495.2168e-05
1.093.5473.977e-05
1.13.5453.0217e-05
1.113.5422.2913e-05
1.123.541.7068e-05
1.133.5371.2382e-05
1.143.5348.621e-06
1.153.5335.6876e-06
1.163.533.4275e-06
1.173.5271.7653e-06
1.183.5265.5561e-07
1.193.5242.3153e-07
1.23.5221.3904e-07
1.213.528.0863e-08
1.223.5184.794e-08
1.233.5172.7132e-08
1.243.5151.4318e-08
1.253.5135.8798e-09
1.263.5122.3352e-09
1.273.5091.2714e-09
1.283.5097.5284e-10
1.293.5064.4799e-10
1.33.5052.7228e-10
1.313.5031.5856e-10
1.323.5028.7196e-11
1.333.5014.2039e-11
1.343.51.8128e-11
1.353.4991.0428e-11
1.363.4976.2911e-12
1.373.4963.903e-12
1.383.4962.6367e-12
1.393.4961.7377e-12
1.43.4931.0428e-12
1.413.4926.0422e-13
1.423.4924.2895e-13
1.433.492.0381e-13
1.443.4881.3785e-13
1.453.4871.0901e-13

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
—