Optical constants
Refractive index of Si (Silicon)
Vuye et al. 1993: n,k 0.26–0.83 µm; 300 °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
- Refractive index n
- 4.05812
- Extinction coefficient k
- 0.01
- Permittivity ε1
- 16.4682
- Permittivity ε2
- 0.0811623
- Absorption coefficient α
- 2138.59 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 9351.94 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -2.89855 µm⁻¹
- Group index ng
- 5.7613
- 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; 300 °C
si = ls.fetch_refractiveindex("main", "Si", "Vuye-300C", 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.
import json, urllib.request
import lightsmith as ls
url = "https://materials.lightsmith.dev/v1/datasets/ds_32795a2dac88/lightsmith"
si = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(si.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (si/vuye-1993-300c).
# ... load si as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=si)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=826, num=81),
)
res = ls.solve(sim) # exact Mie for a sphere
print(res.q_ext) # extinction efficiency at each wavelength
Same spec runs with DDA, FDTD, BEM or T-matrix: ls.compare(sim, ["mie", "dda"]).
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
References
- doi:10.1016/0040-6090(93)90082-z Temperature dependence of the dielectric function of silicon using in situ spectroscopic ellipsometry, Thin Solid Films (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| λ (µm) | n | k |
|---|---|---|
| 0.2638 | 1.998 | 4.044 |
| 0.2652 | 2.023 | 4.113 |
| 0.2666 | 2.065 | 4.162 |
| 0.2681 | 2.091 | 4.236 |
| 0.2695 | 2.164 | 4.309 |
| 0.271 | 2.202 | 4.396 |
| 0.2725 | 2.276 | 4.452 |
| 0.274 | 2.354 | 4.543 |
| 0.2755 | 2.441 | 4.632 |
| 0.2771 | 2.526 | 4.692 |
| 0.2786 | 2.65 | 4.784 |
| 0.2802 | 2.764 | 4.849 |
| 0.2818 | 2.872 | 4.908 |
| 0.2834 | 3.011 | 4.985 |
| 0.285 | 3.163 | 5.031 |
| 0.2867 | 3.339 | 5.065 |
| 0.2883 | 3.517 | 5.113 |
| 0.29 | 3.712 | 5.123 |
| 0.2917 | 3.925 | 5.113 |
| 0.2935 | 4.153 | 5.074 |
| 0.2952 | 4.344 | 4.973 |
| 0.297 | 4.54 | 4.851 |
| 0.2988 | 4.704 | 4.723 |
| 0.3006 | 4.83 | 4.555 |
| 0.3024 | 4.937 | 4.393 |
| 0.3043 | 4.999 | 4.234 |
| 0.3061 | 5.033 | 4.089 |
| 0.308 | 5.061 | 3.975 |
| 0.31 | 5.097 | 3.837 |
| 0.3119 | 5.107 | 3.745 |
| 0.3139 | 5.126 | 3.634 |
| 0.3159 | 5.137 | 3.554 |
| 0.3179 | 5.135 | 3.471 |
| 0.32 | 5.156 | 3.413 |
| 0.322 | 5.156 | 3.343 |
| 0.3241 | 5.159 | 3.277 |
| 0.3263 | 5.172 | 3.221 |
| 0.3284 | 5.197 | 3.174 |
| 0.3306 | 5.202 | 3.116 |
| 0.3328 | 5.211 | 3.074 |
| 0.3351 | 5.241 | 3.037 |
| 0.3374 | 5.256 | 3.004 |
| 0.3397 | 5.279 | 2.968 |
| 0.342 | 5.301 | 2.924 |
| 0.3444 | 5.33 | 2.894 |
| 0.3468 | 5.364 | 2.865 |
| 0.3493 | 5.396 | 2.838 |
| 0.3517 | 5.44 | 2.806 |
| 0.3542 | 5.493 | 2.78 |
| 0.3568 | 5.55 | 2.756 |
| 0.3594 | 5.614 | 2.75 |
| 0.362 | 5.696 | 2.719 |
| 0.3647 | 5.808 | 2.683 |
| 0.3674 | 5.939 | 2.626 |
| 0.3701 | 6.086 | 2.544 |
| 0.3729 | 6.24 | 2.414 |
| 0.3757 | 6.383 | 2.239 |
| 0.3786 | 6.494 | 2.002 |
| 0.3815 | 6.538 | 1.739 |
| 0.3844 | 6.516 | 1.485 |
| 0.3875 | 6.461 | 1.256 |
| 0.3905 | 6.363 | 1.043 |
| 0.3936 | 6.239 | 0.882 |
| 0.3967 | 6.114 | 0.755 |
| 0.3999 | 5.99 | 0.641 |
| 0.4032 | 5.87 | 0.54 |
| 0.4065 | 5.766 | 0.477 |
| 0.4099 | 5.661 | 0.413 |
| 0.4133 | 5.559 | 0.366 |
| 0.4168 | 5.47 | 0.319 |
| 0.4203 | 5.385 | 0.291 |
| 0.4239 | 5.309 | 0.257 |
| 0.4275 | 5.233 | 0.236 |
| 0.4312 | 5.162 | 0.212 |
| 0.435 | 5.097 | 0.187 |
| 0.4389 | 5.034 | 0.171 |
| 0.4428 | 4.975 | 0.151 |
| 0.4468 | 4.918 | 0.14 |
| 0.4509 | 4.866 | 0.135 |
| 0.455 | 4.814 | 0.118 |
| 0.4592 | 4.766 | 0.106 |
| 0.4635 | 4.721 | 0.094 |
| 0.4679 | 4.677 | 0.089 |
| 0.4723 | 4.634 | 0.083 |
| 0.4769 | 4.59 | 0.074 |
| 0.4815 | 4.555 | 0.067 |
| 0.4862 | 4.516 | 0.062 |
| 0.491 | 4.48 | 0.056 |
| 0.4959 | 4.447 | 0.049 |
| 0.5009 | 4.415 | 0.044 |
| 0.5061 | 4.383 | 0.042 |
| 0.5113 | 4.352 | 0.035 |
| 0.5166 | 4.325 | 0.032 |
| 0.522 | 4.294 | 0.03 |
| 0.5276 | 4.266 | 0.026 |
| 0.5333 | 4.24 | 0.024 |
| 0.5391 | 4.216 | 0.018 |
| 0.545 | 4.194 | 0.019 |
| 0.551 | 4.17 | 0.016 |
| 0.5572 | 4.149 | 0.016 |
| 0.5636 | 4.129 | 0.014 |
| 0.57 | 4.108 | 0.015 |
| 0.5767 | 4.089 | 0.01 |
| 0.5835 | 4.07 | 0.01 |
| 0.5904 | 4.05 | 0.01 |
| 0.5975 | 4.0343 | 0.011 |
| 0.6048 | 4.0165 | 0.008 |
| 0.6123 | 3.9993 | 0.006 |
| 0.6199 | 3.982 | 0.006 |
| 0.6278 | 3.9664 | 0.005 |
| 0.6358 | 3.9507 | 0.006 |
| 0.6441 | 3.9356 | 0.005 |
| 0.6525 | 3.923 | 0.006 |
| 0.6612 | 3.907 | 0.005 |
| 0.6702 | 3.8935 | 0.003 |
| 0.6794 | 3.8806 | 0.004 |
| 0.6888 | 3.87 | 0.003 |
| 0.6985 | 3.8563 | 0.001 |
| 0.7085 | 3.8449 | 0.002 |
| 0.7187 | 3.8341 | 0.005 |
| 0.7293 | 3.8256 | 0.005 |
| 0.7402 | 3.8141 | 0.002 |
| 0.7514 | 3.8048 | 0.001 |
| 0.763 | 3.793 | 0.0 |
| 0.7749 | 3.784 | 0.007 |
| 0.7872 | 3.773 | 0.003 |
| 0.7999 | 3.764 | 0.001 |
| 0.813 | 3.753 | 0.001 |
| 0.8266 | 3.743 | 0.0 |
Optical transmission calculator
Free-standing sample in vacuum, normal incidence- Transmittance T
- —
- Reflectance R
- —
Fresnel reflection calculator
- Rp
- —
- Rs
- —
- R = (Rp+Rs)/2
- —
- Phase φp
- —
- Phase φs
- —
- Brewster angle θB
- —
- Critical angle θC
- —
300 °C; Crysal orientation: <111>