Optical constants

Refractive index of Si (Silicon)

Aspnes and Studna 1983: n,k 0.21–0.83 µm

Data
tabulated nk
Range
0.2066–0.8266 µm
Points
46
State
crystalline
Licence
CC0-1.0
Lightsmith
bundled

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.2066–0.8266 µm
Refractive index n
3.97663
Extinction coefficient k
0.030209
Permittivity ε1
15.8126
Permittivity ε2
0.240259
Absorption coefficient α
6460.47 cm⁻¹
Penetration depth δ = λ/(2πk)
3095.75 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-2.72388 µm⁻¹
Group index ng
5.57718
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): Aspnes and Studna 1983: n,k 0.21–0.83 µm
si = ls.LibraryMaterial(name="Si", dataset="Aspnes-Studna")
print(si.range_nm)  # (206.6, 826.6) 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

Crystal orientation: <111>; Doping: 2.3×1014 cm-3, n; Room temperature

References

D. E. Aspnes and A. A. Studna. Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV. Phys. Rev. B 27, 985-1009 (1983)
  • doi:10.1103/physrevb.27.985 Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV, Physical Review B (1983)

Cite

D. E. Aspnes and A. A. Studna. Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV. Physical Review B, 27, 985-1009 (1983), doi:10.1103/physrevb.27.985; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

46 rows as published
Si (Silicon), Aspnes and Studna 1983: n,k 0.21–0.83 µm: n and k versus wavelength
λ (µm)nk
0.20661.012.909
0.21011.0832.982
0.21381.1333.045
0.21751.1863.12
0.22141.2473.206
0.22541.343.302
0.22961.4713.366
0.23391.5793.353
0.23841.5893.354
0.24311.5713.429
0.2481.573.565
0.2531.5973.749
0.25831.6583.979
0.26381.7644.278
0.26951.9884.678
0.27552.4525.082
0.28183.125.344
0.28834.0875.395
0.29524.8884.639
0.30245.023.979
0.315.013.586
0.31795.0163.346
0.32635.0653.182
0.33515.1563.058
0.34445.2962.987
0.35425.613.014
0.36476.5222.705
0.37576.7091.32
0.38756.0620.63
0.39995.570.387
0.41335.2220.269
0.42754.9610.203
0.44284.7530.163
0.45924.5830.13
0.47694.4420.09
0.49594.320.073
0.51664.2150.06
0.53914.1230.048
0.56364.0420.032
0.59043.9690.03
0.61993.9060.022
0.65253.8470.016
0.68883.7960.013
0.72933.7520.01
0.77493.7140.008
0.82663.6730.005

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
—