Optical constants
Refractive index of Si-Ge (Silicon-germanium, SiGe)
Jellison et al. 1993: 20% Si, Ge substrate; n,k 0.24–0.84 µm
- Data
- tabulated nk
- Range
- 0.24–0.84 µm
- Points
- 103
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 5.1152
- Extinction coefficient k
- 0.38648
- Permittivity ε1
- 26.0159
- Permittivity ε2
- 3.95384
- Absorption coefficient α
- 82652.3 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 241.977 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -8 µm⁻¹
- Group index ng
- 9.816
- 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-Ge (Silicon-germanium, SiGe): Jellison et al. 1993: 20% Si, Ge substrate; n,k 0.24–0.84 µm
si_ge = ls.fetch_refractiveindex("other", "Si-Ge", "Jellison-20", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si_ge.range_nm) # (240, 840) nm
eps = si_ge.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_fc6c30f63a49/lightsmith"
si_ge = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(si_ge.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (si-ge/jellison-1993-20).
# ... load si_ge as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=si_ge)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=840, 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
- x
- 0.20
- thickness
- 8 μm
- substrate
- Ge
References
- doi:10.1016/0925-3467(93)90035-y Optical functions of silicon-germanium alloys determined using spectroscopic ellipsometry, Optical Materials (1993)
Cite
G.E. Jellison, T.E. Haynes and H.H. Burke. Optical functions of silicon-germanium alloys determined using spectroscopic ellipsometry. Optical Materials, 2, 105-117 (1993), doi:10.1016/0925-3467(93)90035-y; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
103 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.24 | 1.624 | 3.109 |
| 0.242 | 1.627 | 3.138 |
| 0.244 | 1.655 | 3.189 |
| 0.246 | 1.675 | 3.248 |
| 0.248 | 1.688 | 3.29 |
| 0.25 | 1.708 | 3.353 |
| 0.252 | 1.739 | 3.413 |
| 0.254 | 1.772 | 3.481 |
| 0.256 | 1.788 | 3.539 |
| 0.258 | 1.829 | 3.613 |
| 0.26 | 1.862 | 3.68 |
| 0.262 | 1.916 | 3.76 |
| 0.264 | 1.958 | 3.833 |
| 0.266 | 2.017 | 3.92 |
| 0.268 | 2.081 | 4.001 |
| 0.27 | 2.148 | 4.087 |
| 0.272 | 2.233 | 4.179 |
| 0.274 | 2.343 | 4.278 |
| 0.276 | 2.457 | 4.385 |
| 0.278 | 2.599 | 4.477 |
| 0.28 | 2.773 | 4.564 |
| 0.282 | 2.987 | 4.619 |
| 0.284 | 3.215 | 4.632 |
| 0.286 | 3.448 | 4.596 |
| 0.288 | 3.685 | 4.511 |
| 0.29 | 3.864 | 4.385 |
| 0.292 | 4.002 | 4.248 |
| 0.294 | 4.098 | 4.107 |
| 0.296 | 4.194 | 3.963 |
| 0.298 | 4.234 | 3.836 |
| 0.3 | 4.273 | 3.722 |
| 0.304 | 4.322 | 3.515 |
| 0.308 | 4.333 | 3.355 |
| 0.312 | 4.333 | 3.231 |
| 0.316 | 4.345 | 3.117 |
| 0.32 | 4.35 | 3.027 |
| 0.324 | 4.357 | 2.944 |
| 0.328 | 4.358 | 2.869 |
| 0.332 | 4.37 | 2.808 |
| 0.336 | 4.382 | 2.749 |
| 0.34 | 4.385 | 2.703 |
| 0.344 | 4.399 | 2.657 |
| 0.348 | 4.405 | 2.615 |
| 0.352 | 4.424 | 2.573 |
| 0.356 | 4.443 | 2.535 |
| 0.36 | 4.46 | 2.499 |
| 0.364 | 4.479 | 2.465 |
| 0.368 | 4.5 | 2.426 |
| 0.372 | 4.526 | 2.384 |
| 0.376 | 4.55 | 2.334 |
| 0.38 | 4.559 | 2.291 |
| 0.384 | 4.572 | 2.243 |
| 0.388 | 4.581 | 2.195 |
| 0.392 | 4.581 | 2.149 |
| 0.396 | 4.578 | 2.103 |
| 0.4 | 4.656 | 2.066 |
| 0.404 | 4.554 | 2.041 |
| 0.408 | 4.542 | 2.023 |
| 0.412 | 4.534 | 2.01 |
| 0.416 | 4.53 | 2.0 |
| 0.42 | 4.531 | 1.997 |
| 0.43 | 4.544 | 2.01 |
| 0.44 | 4.589 | 2.02 |
| 0.45 | 4.661 | 2.031 |
| 0.46 | 4.761 | 2.032 |
| 0.47 | 4.883 | 2.027 |
| 0.48 | 5.046 | 1.982 |
| 0.49 | 5.207 | 1.878 |
| 0.5 | 5.325 | 1.732 |
| 0.51 | 5.42 | 1.593 |
| 0.52 | 5.53 | 1.434 |
| 0.53 | 5.615 | 1.204 |
| 0.54 | 5.591 | 0.941 |
| 0.55 | 5.498 | 0.742 |
| 0.56 | 5.384 | 0.599 |
| 0.57 | 5.283 | 0.502 |
| 0.58 | 5.176 | 0.426 |
| 0.59 | 5.096 | 0.374 |
| 0.6 | 5.027 | 0.327 |
| 0.61 | 4.963 | 0.29 |
| 0.62 | 4.907 | 0.258 |
| 0.63 | 4.845 | 0.23 |
| 0.64 | 4.799 | 0.213 |
| 0.65 | 4.752 | 0.194 |
| 0.66 | 4.712 | 0.18 |
| 0.67 | 4.677 | 0.167 |
| 0.68 | 4.642 | 0.16 |
| 0.69 | 4.613 | 0.151 |
| 0.7 | 4.587 | 0.142 |
| 0.71 | 4.561 | 0.131 |
| 0.72 | 4.533 | 0.121 |
| 0.73 | 4.515 | 0.115 |
| 0.74 | 4.5 | 0.106 |
| 0.75 | 4.48 | 0.094 |
| 0.76 | 4.46 | 0.084 |
| 0.77 | 4.438 | 0.074 |
| 0.78 | 4.42 | 0.067 |
| 0.79 | 4.404 | 0.059 |
| 0.8 | 4.389 | 0.051 |
| 0.81 | 4.378 | 0.04 |
| 0.82 | 4.352 | 0.038 |
| 0.83 | 4.343 | 0.03 |
| 0.84 | 4.294 | 0.021 |
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
- —
SixGe1-x, x = 0.20. 8-μm film grown on Ge substrate.