Optical constants
Refractive index of Si-Ge (Silicon-germanium, SiGe)
Jellison et al. 1993: 98% 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
- 3.98428
- Extinction coefficient k
- 0.021
- Permittivity ε1
- 15.874
- Permittivity ε2
- 0.16734
- Absorption coefficient α
- 4491.04 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 4453.31 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -2.2 µm⁻¹
- Group index ng
- 5.277
- 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: 98% Si, Si substrate; n,k 0.24–0.84 µm
si_ge = ls.fetch_refractiveindex("other", "Si-Ge", "Jellison-98", 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_bd9fedd8cae0/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-1993-98).
# ... 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
- 0.98
- thickness
- 8 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 | 1.62 | 3.404 |
| 0.242 | 1.619 | 3.434 |
| 0.244 | 1.641 | 3.464 |
| 0.246 | 1.635 | 3.538 |
| 0.248 | 1.643 | 3.596 |
| 0.25 | 1.668 | 3.65 |
| 0.252 | 1.687 | 3.727 |
| 0.254 | 1.711 | 3.816 |
| 0.256 | 1.723 | 3.884 |
| 0.258 | 1.758 | 3.98 |
| 0.26 | 1.796 | 4.077 |
| 0.262 | 1.843 | 4.187 |
| 0.264 | 1.886 | 4.3 |
| 0.266 | 1.97 | 4.423 |
| 0.268 | 2.06 | 4.551 |
| 0.27 | 2.165 | 4.676 |
| 0.272 | 2.299 | 4.808 |
| 0.274 | 2.47 | 4.935 |
| 0.276 | 2.652 | 5.04 |
| 0.278 | 2.849 | 5.126 |
| 0.28 | 3.076 | 5.196 |
| 0.282 | 3.308 | 5.234 |
| 0.284 | 3.559 | 5.251 |
| 0.286 | 3.815 | 5.234 |
| 0.288 | 4.106 | 5.177 |
| 0.29 | 4.362 | 5.059 |
| 0.292 | 4.593 | 4.89 |
| 0.294 | 4.754 | 4.694 |
| 0.296 | 4.88 | 4.486 |
| 0.298 | 4.95 | 4.295 |
| 0.3 | 4.987 | 4.127 |
| 0.304 | 5.032 | 3.846 |
| 0.308 | 5.031 | 3.644 |
| 0.312 | 5.028 | 3.49 |
| 0.316 | 5.038 | 3.369 |
| 0.32 | 5.055 | 3.269 |
| 0.324 | 5.084 | 3.19 |
| 0.328 | 5.118 | 3.117 |
| 0.332 | 5.153 | 3.058 |
| 0.336 | 5.206 | 3.006 |
| 0.34 | 5.257 | 2.978 |
| 0.344 | 5.34 | 2.95 |
| 0.348 | 5.441 | 2.925 |
| 0.352 | 5.582 | 2.882 |
| 0.356 | 5.752 | 2.82 |
| 0.36 | 5.937 | 2.741 |
| 0.364 | 6.164 | 2.608 |
| 0.368 | 6.415 | 2.377 |
| 0.372 | 6.622 | 2.019 |
| 0.376 | 6.68 | 1.582 |
| 0.38 | 6.572 | 1.171 |
| 0.384 | 6.375 | 0.863 |
| 0.388 | 6.184 | 0.663 |
| 0.392 | 5.992 | 0.526 |
| 0.396 | 5.827 | 0.429 |
| 0.4 | 5.678 | 0.359 |
| 0.404 | 5.544 | 0.308 |
| 0.408 | 5.426 | 0.267 |
| 0.412 | 5.325 | 0.234 |
| 0.416 | 5.236 | 0.208 |
| 0.42 | 5.152 | 0.187 |
| 0.43 | 4.964 | 0.147 |
| 0.44 | 4.834 | 0.119 |
| 0.45 | 4.712 | 0.098 |
| 0.46 | 4.611 | 0.083 |
| 0.47 | 4.522 | 0.07 |
| 0.48 | 4.443 | 0.064 |
| 0.49 | 4.371 | 0.057 |
| 0.5 | 4.317 | 0.049 |
| 0.51 | 4.262 | 0.042 |
| 0.52 | 4.214 | 0.038 |
| 0.53 | 4.172 | 0.033 |
| 0.54 | 4.13 | 0.031 |
| 0.55 | 4.095 | 0.029 |
| 0.56 | 4.063 | 0.029 |
| 0.57 | 4.037 | 0.024 |
| 0.58 | 4.001 | 0.021 |
| 0.59 | 3.979 | 0.021 |
| 0.6 | 3.957 | 0.021 |
| 0.61 | 3.935 | 0.017 |
| 0.62 | 3.918 | 0.016 |
| 0.63 | 3.892 | 0.014 |
| 0.64 | 3.873 | 0.014 |
| 0.65 | 3.858 | 0.014 |
| 0.66 | 3.84 | 0.011 |
| 0.67 | 3.831 | 0.013 |
| 0.68 | 3.814 | 0.013 |
| 0.69 | 3.8 | 0.013 |
| 0.7 | 3.789 | 0.011 |
| 0.71 | 3.777 | 0.009 |
| 0.72 | 3.76 | 0.014 |
| 0.73 | 3.753 | 0.008 |
| 0.74 | 3.744 | 0.011 |
| 0.75 | 3.734 | 0.008 |
| 0.76 | 3.725 | 0.009 |
| 0.77 | 3.716 | 0.009 |
| 0.78 | 3.705 | 0.009 |
| 0.79 | 3.702 | 0.006 |
| 0.8 | 3.697 | 0.004 |
| 0.81 | 3.69 | 0.003 |
| 0.82 | 3.683 | 0.003 |
| 0.83 | 3.697 | 0.002 |
| 0.84 | 3.671 | 0.003 |
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 = 0.98. 8-μm film grown on Si substrate.