Optical constants

Refractive index of Si (Silicon)

Vuye et al. 1993: n,k 0.26–0.83 µm; 350 °C

Data
tabulated nk
Range
0.2638–0.8266 µm
Points
129
State
crystalline
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.2638–0.8266 µm
Refractive index n
4.0713
Extinction coefficient k
0.0128116
Permittivity ε1
16.5754
Permittivity ε2
0.10432
Absorption coefficient α
2739.88 cm⁻¹
Penetration depth δ = λ/(2πk)
7299.59 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-2.6087 µm⁻¹
Group index ng
5.60417
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): Vuye et al. 1993: n,k 0.26–0.83 µm; 350 °C
si = ls.fetch_refractiveindex("main", "Si", "Vuye-350C", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si.range_nm)  # (263.8, 826.6) 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

350 °C; Crysal orientation: <111>

References

G. Vuye, S. Fisson, V. Nguyen Van, Y. Wang, J. Rivory, F. Abelès. Temperature dependence of the dielectric function of silicon using in situ spectroscopic ellipsometry. Thin Solid Films 233, 166-170 (1993)

Cite

G. Vuye et al.. Temperature dependence of the dielectric function of silicon using in situ spectroscopic ellipsometry. Thin Solid Films, 233, 166-170 (1993), doi:10.1016/0040-6090(93)90082-z; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

129 rows as published
Si (Silicon), Vuye et al. 1993: n,k 0.26–0.83 µm; 350 °C: n and k versus wavelength
λ (µm)nk
0.26382.0344.016
0.26522.0774.075
0.26662.1114.143
0.26812.1614.2
0.26952.194.279
0.2712.254.357
0.27252.314.43
0.2742.3814.495
0.27552.4584.571
0.27712.554.657
0.27862.6494.702
0.28022.7554.798
0.28182.8834.859
0.28343.0264.916
0.2853.1634.972
0.28673.3045.001
0.28833.495.056
0.293.6825.078
0.29173.8765.064
0.29354.0985.032
0.29524.3194.952
0.2974.4814.863
0.29884.6564.705
0.30064.7854.572
0.30244.8824.42
0.30434.9694.268
0.30615.0354.12
0.3085.0713.988
0.315.0883.879
0.31195.1053.765
0.31395.1383.652
0.31595.1383.57
0.31795.1463.478
0.325.1463.414
0.3225.1483.346
0.32415.1753.279
0.32635.1773.222
0.32845.1863.163
0.33065.2073.124
0.33285.2133.074
0.33515.2353.035
0.33745.2482.991
0.33975.2722.952
0.3425.3012.913
0.34445.3212.878
0.34685.3582.85
0.34935.3842.808
0.35175.4182.806
0.35425.4652.759
0.35685.5182.747
0.35945.5982.716
0.3625.6652.683
0.36475.7612.655
0.36745.882.603
0.37016.0082.53
0.37296.1382.417
0.37576.2642.291
0.37866.3932.071
0.38156.4681.855
0.38446.4741.606
0.38756.4331.367
0.39056.3571.157
0.39366.2620.966
0.39676.1530.826
0.39996.0280.703
0.40325.9160.6
0.40655.8010.516
0.40995.70.447
0.41335.6010.399
0.41685.5130.354
0.42035.430.315
0.42395.3420.285
0.42755.2670.256
0.43125.1960.238
0.4355.130.207
0.43895.060.193
0.44285.0020.177
0.44684.950.146
0.45094.8940.139
0.4554.8430.129
0.45924.7920.117
0.46354.7450.108
0.46794.6990.104
0.47234.6560.09
0.47694.6150.086
0.48154.5770.074
0.48624.5330.071
0.4914.5010.063
0.49594.4680.056
0.50094.4340.051
0.50614.40.05
0.51134.370.043
0.51664.3420.036
0.5224.3120.035
0.52764.2840.031
0.53334.2580.03
0.53914.2330.026
0.5454.2080.025
0.5514.1860.021
0.55724.1640.02
0.56364.1420.018
0.574.1210.018
0.57674.1030.013
0.58354.0820.014
0.59044.0640.012
0.59754.0480.013
0.60484.02970.011
0.61234.0130.01
0.61993.9940.008
0.62783.9790.007
0.63583.9620.007
0.64413.9470.007
0.65253.9350.008
0.66123.9170.007
0.67023.90270.006
0.67943.89180.006
0.68883.8790.006
0.69853.8670.006
0.70853.8570.005
0.71873.8480.004
0.72933.8360.002
0.74023.8240.0013
0.75143.8160.001
0.7633.8050.0015
0.77493.7960.002
0.78723.7880.0015
0.79993.7780.0015
0.8133.770.0021
0.82663.7570.002

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
—