Optical constants
Refractive index of Si-Ge (Silicon-germanium, SiGe)
Jellison et al. 1993: 85% Si, Si 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
- 4.082
- Extinction coefficient k
- 0.02148
- Permittivity ε1
- 16.6623
- Permittivity ε2
- 0.175363
- Absorption coefficient α
- 4593.7 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 4353.79 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -2.5 µm⁻¹
- Group index ng
- 5.551
- 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: 85% Si, Si substrate; n,k 0.24–0.84 µm
si_ge = ls.fetch_refractiveindex("other", "Si-Ge", "Jellison-85", 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_d57193623194/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-1993-85).
# ... 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
- 0.85
- thickness
- 7 μm
- substrate
- Si
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 | 1.649 | 3.404 |
| 0.242 | 1.659 | 3.446 |
| 0.244 | 1.664 | 3.491 |
| 0.246 | 1.672 | 3.542 |
| 0.248 | 1.683 | 3.596 |
| 0.25 | 1.712 | 3.657 |
| 0.252 | 1.74 | 3.724 |
| 0.254 | 1.756 | 3.818 |
| 0.256 | 1.787 | 3.879 |
| 0.258 | 1.823 | 3.964 |
| 0.26 | 1.864 | 4.06 |
| 0.262 | 1.918 | 4.164 |
| 0.264 | 1.966 | 4.255 |
| 0.266 | 2.037 | 4.367 |
| 0.268 | 2.119 | 4.487 |
| 0.27 | 2.213 | 4.602 |
| 0.272 | 2.334 | 4.731 |
| 0.274 | 2.496 | 4.856 |
| 0.276 | 2.654 | 4.969 |
| 0.278 | 2.843 | 5.063 |
| 0.28 | 3.066 | 5.149 |
| 0.282 | 3.302 | 5.212 |
| 0.284 | 3.561 | 5.236 |
| 0.286 | 3.84 | 5.221 |
| 0.288 | 4.161 | 5.145 |
| 0.29 | 4.422 | 4.989 |
| 0.292 | 4.622 | 4.794 |
| 0.294 | 4.758 | 4.587 |
| 0.296 | 4.871 | 4.383 |
| 0.298 | 4.917 | 4.198 |
| 0.3 | 4.95 | 4.038 |
| 0.304 | 4.98 | 3.777 |
| 0.308 | 4.977 | 3.582 |
| 0.312 | 4.976 | 3.432 |
| 0.316 | 4.988 | 3.314 |
| 0.32 | 5.002 | 3.212 |
| 0.324 | 5.028 | 3.122 |
| 0.328 | 5.053 | 3.043 |
| 0.332 | 5.085 | 2.977 |
| 0.336 | 5.126 | 2.914 |
| 0.34 | 5.161 | 2.864 |
| 0.344 | 5.207 | 2.811 |
| 0.348 | 5.26 | 2.777 |
| 0.352 | 5.331 | 2.738 |
| 0.356 | 5.422 | 2.7 |
| 0.36 | 5.538 | 2.655 |
| 0.364 | 5.67 | 2.598 |
| 0.368 | 5.828 | 2.503 |
| 0.372 | 5.997 | 2.349 |
| 0.376 | 6.146 | 2.14 |
| 0.38 | 6.234 | 1.874 |
| 0.384 | 6.255 | 1.597 |
| 0.388 | 6.226 | 1.355 |
| 0.392 | 6.157 | 1.135 |
| 0.396 | 6.063 | 0.941 |
| 0.4 | 5.954 | 0.783 |
| 0.404 | 5.842 | 0.651 |
| 0.408 | 5.725 | 0.547 |
| 0.412 | 5.611 | 0.467 |
| 0.416 | 5.512 | 0.403 |
| 0.42 | 5.418 | 0.351 |
| 0.43 | 5.186 | 0.255 |
| 0.44 | 5.029 | 0.206 |
| 0.45 | 4.893 | 0.165 |
| 0.46 | 4.772 | 0.142 |
| 0.47 | 4.681 | 0.122 |
| 0.48 | 4.595 | 0.098 |
| 0.49 | 4.516 | 0.083 |
| 0.5 | 4.452 | 0.07 |
| 0.51 | 4.39 | 0.053 |
| 0.52 | 4.332 | 0.044 |
| 0.53 | 4.279 | 0.038 |
| 0.54 | 4.239 | 0.039 |
| 0.55 | 4.209 | 0.034 |
| 0.56 | 4.17 | 0.027 |
| 0.57 | 4.136 | 0.027 |
| 0.58 | 4.101 | 0.023 |
| 0.59 | 4.076 | 0.021 |
| 0.6 | 4.045 | 0.018 |
| 0.61 | 4.021 | 0.02 |
| 0.62 | 4.004 | 0.013 |
| 0.63 | 3.977 | 0.016 |
| 0.64 | 3.969 | 0.01 |
| 0.65 | 3.941 | 0.004 |
| 0.66 | 3.921 | 0.004 |
| 0.67 | 3.904 | 0.003 |
| 0.68 | 3.891 | 0.007 |
| 0.69 | 3.876 | 0.0 |
| 0.7 | 3.857 | 0.003 |
| 0.71 | 3.846 | 0.009 |
| 0.72 | 3.832 | 0.013 |
| 0.73 | 3.831 | 0.009 |
| 0.74 | 3.816 | 0.009 |
| 0.75 | 3.803 | 0.01 |
| 0.76 | 3.793 | 0.011 |
| 0.77 | 3.784 | 0.009 |
| 0.78 | 3.779 | 0.01 |
| 0.79 | 3.772 | 0.008 |
| 0.8 | 3.764 | 0.01 |
| 0.81 | 3.759 | 0.008 |
| 0.82 | 3.753 | 0.009 |
| 0.83 | 3.752 | 0.007 |
| 0.84 | 3.75 | 0.004 |
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 = 0.85. 7-μm film grown on Si substrate.