Optical constants
Refractive index of Si-Ge (Silicon-germanium, SiGe)
Jellison et al. 1993: 28% 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
- 4.91892
- Extinction coefficient k
- 0.29488
- Permittivity ε1
- 24.1088
- Permittivity ε2
- 2.90098
- Absorption coefficient α
- 63062.8 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 317.144 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -5.8 µm⁻¹
- Group index ng
- 8.327
- 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: 28% Si, Ge substrate; n,k 0.24–0.84 µm
si_ge = ls.fetch_refractiveindex("other", "Si-Ge", "Jellison-28", 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_e7b314453e78/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-1993-28).
# ... 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
- 0.28
- 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 | 1.655 | 3.144 |
| 0.242 | 1.634 | 3.176 |
| 0.244 | 1.636 | 3.221 |
| 0.246 | 1.661 | 3.27 |
| 0.248 | 1.674 | 3.333 |
| 0.25 | 1.691 | 3.385 |
| 0.252 | 1.724 | 3.451 |
| 0.254 | 1.766 | 3.515 |
| 0.256 | 1.783 | 3.573 |
| 0.258 | 1.821 | 3.638 |
| 0.26 | 1.866 | 3.715 |
| 0.262 | 1.906 | 3.792 |
| 0.264 | 1.953 | 3.864 |
| 0.266 | 2.008 | 3.945 |
| 0.268 | 2.081 | 4.031 |
| 0.27 | 2.145 | 4.115 |
| 0.272 | 2.237 | 4.212 |
| 0.274 | 2.348 | 4.307 |
| 0.276 | 2.459 | 4.398 |
| 0.278 | 2.601 | 4.482 |
| 0.28 | 2.773 | 4.571 |
| 0.282 | 2.975 | 4.631 |
| 0.284 | 3.201 | 4.65 |
| 0.286 | 3.425 | 4.623 |
| 0.288 | 3.67 | 4.546 |
| 0.29 | 3.846 | 4.432 |
| 0.292 | 3.996 | 4.298 |
| 0.294 | 4.103 | 4.155 |
| 0.296 | 4.201 | 4.009 |
| 0.298 | 4.245 | 3.887 |
| 0.3 | 4.286 | 3.767 |
| 0.304 | 4.347 | 3.556 |
| 0.308 | 4.359 | 3.394 |
| 0.312 | 4.366 | 3.26 |
| 0.316 | 4.382 | 3.147 |
| 0.32 | 4.386 | 3.056 |
| 0.324 | 4.398 | 2.973 |
| 0.328 | 4.4 | 2.897 |
| 0.332 | 4.408 | 2.831 |
| 0.336 | 4.426 | 2.774 |
| 0.34 | 4.432 | 2.725 |
| 0.344 | 4.445 | 2.679 |
| 0.348 | 4.457 | 2.637 |
| 0.352 | 4.478 | 2.593 |
| 0.356 | 4.498 | 2.554 |
| 0.36 | 4.517 | 2.52 |
| 0.364 | 4.542 | 2.484 |
| 0.368 | 4.57 | 2.441 |
| 0.372 | 4.596 | 2.398 |
| 0.376 | 4.622 | 2.347 |
| 0.38 | 4.639 | 2.302 |
| 0.384 | 4.656 | 2.25 |
| 0.388 | 4.668 | 2.201 |
| 0.392 | 4.673 | 2.151 |
| 0.396 | 4.672 | 2.105 |
| 0.4 | 4.665 | 2.069 |
| 0.404 | 4.658 | 2.041 |
| 0.408 | 4.651 | 2.022 |
| 0.412 | 4.652 | 2.006 |
| 0.416 | 4.655 | 1.996 |
| 0.42 | 4.661 | 1.988 |
| 0.43 | 4.701 | 1.983 |
| 0.44 | 4.769 | 1.974 |
| 0.45 | 4.867 | 1.949 |
| 0.46 | 4.99 | 1.906 |
| 0.47 | 5.128 | 1.827 |
| 0.48 | 5.25 | 1.693 |
| 0.49 | 5.334 | 1.545 |
| 0.5 | 5.421 | 1.395 |
| 0.51 | 5.497 | 1.181 |
| 0.52 | 5.485 | 0.949 |
| 0.53 | 5.418 | 0.759 |
| 0.54 | 5.315 | 0.615 |
| 0.55 | 5.213 | 0.511 |
| 0.56 | 5.122 | 0.434 |
| 0.57 | 5.039 | 0.378 |
| 0.58 | 4.963 | 0.323 |
| 0.59 | 4.905 | 0.286 |
| 0.6 | 4.844 | 0.253 |
| 0.61 | 4.789 | 0.226 |
| 0.62 | 4.746 | 0.202 |
| 0.63 | 4.694 | 0.18 |
| 0.64 | 4.655 | 0.162 |
| 0.65 | 4.617 | 0.142 |
| 0.66 | 4.581 | 0.128 |
| 0.67 | 4.549 | 0.114 |
| 0.68 | 4.519 | 0.105 |
| 0.69 | 4.492 | 0.092 |
| 0.7 | 4.461 | 0.079 |
| 0.71 | 4.437 | 0.069 |
| 0.72 | 4.411 | 0.057 |
| 0.73 | 4.381 | 0.056 |
| 0.74 | 4.333 | 0.052 |
| 0.75 | 4.315 | 0.053 |
| 0.76 | 4.307 | 0.052 |
| 0.77 | 4.29 | 0.046 |
| 0.78 | 4.268 | 0.042 |
| 0.79 | 4.258 | 0.042 |
| 0.8 | 4.248 | 0.042 |
| 0.81 | 4.24 | 0.037 |
| 0.82 | 4.219 | 0.032 |
| 0.83 | 4.216 | 0.03 |
| 0.84 | 4.166 | 0.037 |
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 = 0.28. 8-μm film grown on Ge substrate.