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
- 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.
import lightsmith as ls
# Si (Silicon): Schinke et al. 2015: n,k 0.25–1.45 µm
si = ls.fetch_refractiveindex("main", "Si", "Schinke", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si.range_nm) # (250, 1450) 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_d4dd934e5b5f/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/schinke-2015).
# ... 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=1000, 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
Conditions
- temperature
- 295 K
References
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| λ (µm) | n | k |
|---|---|---|
| 0.25 | 1.637 | 3.5889 |
| 0.26 | 1.737 | 3.9932 |
| 0.27 | 2.03 | 4.5958 |
| 0.28 | 2.84 | 5.1961 |
| 0.29 | 4.185 | 5.3124 |
| 0.3 | 5.049 | 4.29 |
| 0.31 | 5.091 | 3.6239 |
| 0.32 | 5.085 | 3.2824 |
| 0.33 | 5.135 | 3.0935 |
| 0.34 | 5.245 | 2.9573 |
| 0.35 | 5.423 | 2.9078 |
| 0.36 | 5.914 | 2.9135 |
| 0.37 | 6.82 | 2.1403 |
| 0.38 | 6.587 | 0.98399 |
| 0.39 | 6.025 | 0.50308 |
| 0.4 | 5.623 | 0.32627 |
| 0.41 | 5.341 | 0.24127 |
| 0.42 | 5.11 | 0.17694 |
| 0.43 | 4.932 | 0.13766 |
| 0.44 | 4.79 | 0.11201 |
| 0.45 | 4.673 | 0.095362 |
| 0.46 | 4.572 | 0.079105 |
| 0.47 | 4.485 | 0.07024 |
| 0.48 | 4.412 | 0.059817 |
| 0.49 | 4.349 | 0.05381 |
| 0.5 | 4.289 | 0.048542 |
| 0.51 | 4.235 | 0.043831 |
| 0.52 | 4.187 | 0.039531 |
| 0.53 | 4.145 | 0.034804 |
| 0.54 | 4.103 | 0.029896 |
| 0.55 | 4.073 | 0.028038 |
| 0.56 | 4.038 | 0.026551 |
| 0.57 | 4.006 | 0.023746 |
| 0.58 | 3.977 | 0.021896 |
| 0.59 | 3.954 | 0.020076 |
| 0.6 | 3.931 | 0.018521 |
| 0.61 | 3.908 | 0.017257 |
| 0.62 | 3.888 | 0.016809 |
| 0.63 | 3.869 | 0.016268 |
| 0.64 | 3.851 | 0.014693 |
| 0.65 | 3.835 | 0.014447 |
| 0.66 | 3.817 | 0.013608 |
| 0.67 | 3.805 | 0.012807 |
| 0.68 | 3.791 | 0.012045 |
| 0.69 | 3.776 | 0.011317 |
| 0.7 | 3.765 | 0.010623 |
| 0.71 | 3.753 | 0.009961 |
| 0.72 | 3.741 | 0.0093335 |
| 0.73 | 3.73 | 0.0087312 |
| 0.74 | 3.719 | 0.0081618 |
| 0.75 | 3.712 | 0.0076156 |
| 0.76 | 3.701 | 0.0070942 |
| 0.77 | 3.693 | 0.0066054 |
| 0.78 | 3.684 | 0.0061338 |
| 0.79 | 3.677 | 0.0056888 |
| 0.8 | 3.669 | 0.0052655 |
| 0.81 | 3.662 | 0.004864 |
| 0.82 | 3.655 | 0.0044836 |
| 0.83 | 3.646 | 0.0041235 |
| 0.84 | 3.641 | 0.0037828 |
| 0.85 | 3.636 | 0.0034605 |
| 0.86 | 3.628 | 0.0031563 |
| 0.87 | 3.622 | 0.0028697 |
| 0.88 | 3.617 | 0.0026001 |
| 0.89 | 3.613 | 0.0023464 |
| 0.9 | 3.61 | 0.0021092 |
| 0.91 | 3.604 | 0.0018864 |
| 0.92 | 3.598 | 0.0016787 |
| 0.93 | 3.597 | 0.0014757 |
| 0.94 | 3.59 | 0.0013061 |
| 0.95 | 3.584 | 0.0011393 |
| 0.96 | 3.584 | 0.00098243 |
| 0.97 | 3.578 | 0.0008406 |
| 0.98 | 3.582 | 0.00071334 |
| 0.99 | 3.579 | 0.00059638 |
| 1.0 | 3.575 | 0.0004902 |
| 1.01 | 3.572 | 0.00039616 |
| 1.02 | 3.568 | 0.00031437 |
| 1.03 | 3.565 | 0.00024048 |
| 1.04 | 3.562 | 0.00017959 |
| 1.05 | 3.559 | 0.00013043 |
| 1.06 | 3.556 | 9.245e-05 |
| 1.07 | 3.553 | 6.782e-05 |
| 1.08 | 3.549 | 5.2168e-05 |
| 1.09 | 3.547 | 3.977e-05 |
| 1.1 | 3.545 | 3.0217e-05 |
| 1.11 | 3.542 | 2.2913e-05 |
| 1.12 | 3.54 | 1.7068e-05 |
| 1.13 | 3.537 | 1.2382e-05 |
| 1.14 | 3.534 | 8.621e-06 |
| 1.15 | 3.533 | 5.6876e-06 |
| 1.16 | 3.53 | 3.4275e-06 |
| 1.17 | 3.527 | 1.7653e-06 |
| 1.18 | 3.526 | 5.5561e-07 |
| 1.19 | 3.524 | 2.3153e-07 |
| 1.2 | 3.522 | 1.3904e-07 |
| 1.21 | 3.52 | 8.0863e-08 |
| 1.22 | 3.518 | 4.794e-08 |
| 1.23 | 3.517 | 2.7132e-08 |
| 1.24 | 3.515 | 1.4318e-08 |
| 1.25 | 3.513 | 5.8798e-09 |
| 1.26 | 3.512 | 2.3352e-09 |
| 1.27 | 3.509 | 1.2714e-09 |
| 1.28 | 3.509 | 7.5284e-10 |
| 1.29 | 3.506 | 4.4799e-10 |
| 1.3 | 3.505 | 2.7228e-10 |
| 1.31 | 3.503 | 1.5856e-10 |
| 1.32 | 3.502 | 8.7196e-11 |
| 1.33 | 3.501 | 4.2039e-11 |
| 1.34 | 3.5 | 1.8128e-11 |
| 1.35 | 3.499 | 1.0428e-11 |
| 1.36 | 3.497 | 6.2911e-12 |
| 1.37 | 3.496 | 3.903e-12 |
| 1.38 | 3.496 | 2.6367e-12 |
| 1.39 | 3.496 | 1.7377e-12 |
| 1.4 | 3.493 | 1.0428e-12 |
| 1.41 | 3.492 | 6.0422e-13 |
| 1.42 | 3.492 | 4.2895e-13 |
| 1.43 | 3.49 | 2.0381e-13 |
| 1.44 | 3.488 | 1.3785e-13 |
| 1.45 | 3.487 | 1.0901e-13 |
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
- —
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.