Optical constants
Refractive index of Si-Ge (Silicon-germanium, SiGe)
Jellison et al. 1993: 11% 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
- 5.4044
- Extinction coefficient k
- 0.60092
- Permittivity ε1
- 28.8464
- Permittivity ε2
- 6.49522
- Absorption coefficient α
- 128512 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 155.627 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -11 µm⁻¹
- Group index ng
- 11.868
- 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: 11% Si, Ge substrate; n,k 0.24–0.84 µm
si_ge = ls.fetch_refractiveindex("other", "Si-Ge", "Jellison-11", 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_50b367bdf6b2/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-1993-11).
# ... 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
- 0.11
- 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 | 1.571 | 3.177 |
| 0.242 | 1.564 | 3.216 |
| 0.244 | 1.579 | 3.265 |
| 0.246 | 1.601 | 3.313 |
| 0.248 | 1.613 | 3.368 |
| 0.25 | 1.652 | 3.427 |
| 0.252 | 1.672 | 3.484 |
| 0.254 | 1.705 | 3.546 |
| 0.256 | 1.731 | 3.61 |
| 0.258 | 1.766 | 3.679 |
| 0.26 | 1.809 | 3.75 |
| 0.262 | 1.846 | 3.822 |
| 0.264 | 1.896 | 3.895 |
| 0.266 | 1.948 | 3.979 |
| 0.268 | 2.015 | 4.067 |
| 0.27 | 2.085 | 4.156 |
| 0.272 | 2.17 | 4.258 |
| 0.274 | 2.28 | 4.356 |
| 0.276 | 2.394 | 4.463 |
| 0.278 | 2.537 | 4.567 |
| 0.28 | 2.739 | 4.659 |
| 0.282 | 2.964 | 4.723 |
| 0.284 | 3.211 | 4.723 |
| 0.286 | 3.453 | 4.674 |
| 0.288 | 3.691 | 4.57 |
| 0.29 | 3.866 | 4.434 |
| 0.292 | 3.994 | 4.281 |
| 0.294 | 4.085 | 4.133 |
| 0.296 | 4.165 | 3.988 |
| 0.298 | 4.201 | 3.858 |
| 0.3 | 4.233 | 3.739 |
| 0.304 | 4.274 | 3.538 |
| 0.308 | 4.276 | 3.379 |
| 0.312 | 4.279 | 3.253 |
| 0.316 | 4.284 | 3.144 |
| 0.32 | 4.288 | 3.06 |
| 0.324 | 4.296 | 2.976 |
| 0.328 | 4.296 | 2.906 |
| 0.332 | 4.306 | 2.847 |
| 0.336 | 4.315 | 2.789 |
| 0.34 | 4.317 | 2.741 |
| 0.344 | 4.328 | 2.694 |
| 0.348 | 4.336 | 2.654 |
| 0.352 | 4.353 | 2.614 |
| 0.356 | 4.368 | 2.574 |
| 0.36 | 4.384 | 2.54 |
| 0.364 | 4.402 | 2.505 |
| 0.368 | 4.42 | 2.468 |
| 0.372 | 4.444 | 2.423 |
| 0.376 | 4.458 | 2.379 |
| 0.38 | 4.476 | 2.338 |
| 0.384 | 4.479 | 2.287 |
| 0.388 | 4.487 | 2.241 |
| 0.392 | 4.486 | 2.195 |
| 0.396 | 4.482 | 2.149 |
| 0.4 | 4.468 | 2.115 |
| 0.404 | 4.449 | 2.084 |
| 0.408 | 4.436 | 2.064 |
| 0.412 | 4.423 | 2.049 |
| 0.416 | 4.41 | 2.04 |
| 0.42 | 4.402 | 2.039 |
| 0.43 | 4.395 | 2.058 |
| 0.44 | 4.421 | 2.077 |
| 0.45 | 4.471 | 2.101 |
| 0.46 | 4.537 | 2.125 |
| 0.47 | 4.632 | 2.149 |
| 0.48 | 4.749 | 2.167 |
| 0.49 | 4.902 | 2.165 |
| 0.5 | 5.086 | 2.106 |
| 0.51 | 5.256 | 1.982 |
| 0.52 | 5.362 | 1.837 |
| 0.53 | 5.453 | 1.709 |
| 0.54 | 5.58 | 1.56 |
| 0.55 | 5.687 | 1.326 |
| 0.56 | 5.686 | 1.054 |
| 0.57 | 5.597 | 0.839 |
| 0.58 | 5.488 | 0.683 |
| 0.59 | 5.378 | 0.575 |
| 0.6 | 5.287 | 0.495 |
| 0.61 | 5.2 | 0.434 |
| 0.62 | 5.127 | 0.388 |
| 0.63 | 5.055 | 0.347 |
| 0.64 | 4.995 | 0.318 |
| 0.65 | 4.947 | 0.29 |
| 0.66 | 4.901 | 0.266 |
| 0.67 | 4.857 | 0.245 |
| 0.68 | 4.81 | 0.23 |
| 0.69 | 4.773 | 0.215 |
| 0.7 | 4.741 | 0.203 |
| 0.71 | 4.707 | 0.188 |
| 0.72 | 4.671 | 0.181 |
| 0.73 | 4.647 | 0.168 |
| 0.74 | 4.62 | 0.163 |
| 0.75 | 4.596 | 0.154 |
| 0.76 | 4.579 | 0.144 |
| 0.77 | 4.554 | 0.141 |
| 0.78 | 4.529 | 0.133 |
| 0.79 | 4.516 | 0.125 |
| 0.8 | 4.494 | 0.119 |
| 0.81 | 4.493 | 0.11 |
| 0.82 | 4.466 | 0.112 |
| 0.83 | 4.459 | 0.105 |
| 0.84 | 4.425 | 0.102 |
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 = 0.11. 8-μm film grown on Ge substrate.