Optical constants

Refractive index of Si (Silicon)

Pierce and Spicer 1972: n,k 0.0103–2.07 µm

Data
tabulated nk
Range
0.1033–2.066 µm
Points
46
State
amorphous
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.1033–2.066 µm
Refractive index n
4.30458
Extinction coefficient k
0.59238
Permittivity ε1
18.1785
Permittivity ε2
5.0999
Absorption coefficient α
126686 cm⁻¹
Penetration depth δ = λ/(2πk)
157.871 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-2.30906 µm⁻¹
Group index ng
5.66139
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): Pierce and Spicer 1972: n,k 0.0103–2.07 µm
si = ls.fetch_refractiveindex("main", "Si", "Pierce", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si.range_nm)  # (103.3, 2066) 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

Amorphous silicon (α-Si or a-Si). 60-nm film.

References

1) D. T. Pierce and W. E. Spicer. Electronic structure of amorphous Si from photoemission and optical studies. Phys. Rev. B 5, 3017-3029 (1972)
2) Handbook of Optical Constants of Solids, Edward D. Palik, ed. Academic Press, Boston, 1985
* Ref. 2 provides numerical values for the graphical data reported in Ref. 1

Cite

D. T. Pierce and W. E. Spicer. Electronic Structure of Amorphous Si from Photoemission and Optical Studies. Physical Review B, 5, 3017-3029 (1972), doi:10.1103/physrevb.5.3017; 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), Pierce and Spicer 1972: n,k 0.0103–2.07 µm: n and k versus wavelength
λ (µm)nk
0.10330.3270.726
0.10780.3630.847
0.11270.3920.946
0.11810.4231.04
0.1240.4591.14
0.13050.4971.24
0.13780.5431.35
0.14590.5971.47
0.1550.661.6
0.16530.7351.74
0.17710.8321.89
0.19070.9512.07
0.20661.112.28
0.22541.352.51
0.2481.692.76
0.25831.862.85
0.26952.072.93
0.28182.32.99
0.29522.563.04
0.312.873.06
0.32633.213.0
0.34443.552.88
0.35433.732.79
0.36473.92.66
0.38754.172.38
0.41334.382.02
0.44284.471.64
0.47694.491.28
0.4964.471.12
0.51664.460.969
0.56364.360.69
0.61994.230.461
0.65264.170.363
0.68884.090.271
0.72934.010.199
0.77493.930.136
0.82663.860.0812
0.88563.770.0401
0.95383.680.0
1.0333.610.0
1.1273.570.0
1.243.540.0
1.3783.50.0
1.553.480.0
1.7713.450.0
2.0663.440.0

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
—