Optical constants
Refractive index of Si-Ge (Silicon-germanium, SiGe)
Jellison et al. 1993: 48% 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
- 4.40424
- Extinction coefficient k
- 0.08396
- Permittivity ε1
- 19.3903
- Permittivity ε2
- 0.73956
- Absorption coefficient α
- 17955.6 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 1113.86 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -5.1 µm⁻¹
- Group index ng
- 7.401
- 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: 48% Si, Ge substrate; n,k 0.24–0.84 µm
si_ge = ls.fetch_refractiveindex("other", "Si-Ge", "Jellison-48", 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_dde5a9207b3e/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-1993-48).
# ... 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
- 0.48
- thickness
- 4 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 | 1.754 | 3.266 |
| 0.242 | 1.724 | 3.318 |
| 0.244 | 1.704 | 3.343 |
| 0.246 | 1.712 | 3.382 |
| 0.248 | 1.728 | 3.447 |
| 0.25 | 1.752 | 3.505 |
| 0.252 | 1.79 | 3.564 |
| 0.254 | 1.827 | 3.637 |
| 0.256 | 1.861 | 3.71 |
| 0.258 | 1.91 | 3.766 |
| 0.26 | 1.953 | 3.85 |
| 0.262 | 2.007 | 3.912 |
| 0.264 | 2.07 | 3.989 |
| 0.266 | 2.132 | 4.078 |
| 0.268 | 2.212 | 4.168 |
| 0.27 | 2.297 | 4.258 |
| 0.272 | 2.399 | 4.343 |
| 0.274 | 2.51 | 4.427 |
| 0.276 | 2.647 | 4.522 |
| 0.278 | 2.806 | 4.596 |
| 0.28 | 2.99 | 4.675 |
| 0.282 | 3.206 | 4.719 |
| 0.284 | 3.436 | 4.721 |
| 0.286 | 3.68 | 4.679 |
| 0.288 | 3.896 | 4.584 |
| 0.29 | 4.097 | 4.452 |
| 0.292 | 4.237 | 4.304 |
| 0.294 | 4.357 | 4.14 |
| 0.296 | 4.425 | 3.99 |
| 0.298 | 4.484 | 3.845 |
| 0.3 | 4.508 | 3.721 |
| 0.304 | 4.54 | 3.502 |
| 0.308 | 4.553 | 3.327 |
| 0.312 | 4.554 | 3.191 |
| 0.316 | 4.556 | 3.08 |
| 0.32 | 4.561 | 2.985 |
| 0.324 | 4.568 | 2.907 |
| 0.328 | 4.575 | 2.833 |
| 0.332 | 4.582 | 2.767 |
| 0.336 | 4.591 | 2.712 |
| 0.34 | 4.602 | 2.661 |
| 0.344 | 4.62 | 2.613 |
| 0.348 | 4.635 | 2.571 |
| 0.352 | 4.654 | 2.532 |
| 0.356 | 4.683 | 2.494 |
| 0.36 | 4.712 | 2.457 |
| 0.364 | 4.746 | 2.417 |
| 0.368 | 4.787 | 2.375 |
| 0.372 | 4.826 | 2.329 |
| 0.376 | 4.859 | 2.272 |
| 0.38 | 4.886 | 2.21 |
| 0.384 | 4.905 | 2.155 |
| 0.388 | 4.922 | 2.102 |
| 0.392 | 4.939 | 2.046 |
| 0.396 | 4.951 | 1.997 |
| 0.4 | 4.959 | 1.961 |
| 0.404 | 4.974 | 1.928 |
| 0.408 | 4.995 | 1.9 |
| 0.412 | 5.021 | 1.875 |
| 0.416 | 5.055 | 1.849 |
| 0.42 | 5.097 | 1.821 |
| 0.43 | 5.225 | 1.719 |
| 0.44 | 5.355 | 1.562 |
| 0.45 | 5.466 | 1.345 |
| 0.46 | 5.517 | 1.064 |
| 0.47 | 5.448 | 0.779 |
| 0.48 | 5.311 | 0.575 |
| 0.49 | 5.162 | 0.436 |
| 0.5 | 5.04 | 0.345 |
| 0.51 | 4.936 | 0.28 |
| 0.52 | 4.836 | 0.226 |
| 0.53 | 4.748 | 0.191 |
| 0.54 | 4.673 | 0.171 |
| 0.55 | 4.611 | 0.151 |
| 0.56 | 4.56 | 0.126 |
| 0.57 | 4.502 | 0.098 |
| 0.58 | 4.443 | 0.087 |
| 0.59 | 4.392 | 0.083 |
| 0.6 | 4.346 | 0.08 |
| 0.61 | 4.312 | 0.081 |
| 0.62 | 4.288 | 0.078 |
| 0.63 | 4.254 | 0.071 |
| 0.64 | 4.228 | 0.061 |
| 0.65 | 4.206 | 0.057 |
| 0.66 | 4.183 | 0.053 |
| 0.67 | 4.161 | 0.045 |
| 0.68 | 4.144 | 0.033 |
| 0.69 | 4.116 | 0.023 |
| 0.7 | 4.085 | 0.024 |
| 0.71 | 4.068 | 0.028 |
| 0.72 | 4.05 | 0.028 |
| 0.73 | 4.036 | 0.028 |
| 0.74 | 4.021 | 0.023 |
| 0.75 | 4.004 | 0.02 |
| 0.76 | 3.985 | 0.019 |
| 0.77 | 3.971 | 0.02 |
| 0.78 | 3.957 | 0.027 |
| 0.79 | 3.952 | 0.032 |
| 0.8 | 3.955 | 0.027 |
| 0.81 | 3.95 | 0.021 |
| 0.82 | 3.95 | 0.016 |
| 0.83 | 3.923 | 0.016 |
| 0.84 | 3.883 | 0.025 |
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. 4-μm film grown on Ge substrate.