Optical constants
Refractive index of Si-Ge (Silicon-germanium, SiGe)
Jellison et al. 1993: 65% 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
- 4.28612
- Extinction coefficient k
- 0.06644
- Permittivity ε1
- 18.3664
- Permittivity ε2
- 0.56954
- Absorption coefficient α
- 14208.8 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 1407.58 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -3.8 µm⁻¹
- Group index ng
- 6.519
- 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: 65% Si, Si substrate; n,k 0.24–0.84 µm
si_ge = ls.fetch_refractiveindex("other", "Si-Ge", "Jellison-65", 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_5dc27a570a77/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-1993-65).
# ... 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
- 0.65
- 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 | 1.572 | 3.271 |
| 0.242 | 1.576 | 3.304 |
| 0.244 | 1.601 | 3.351 |
| 0.246 | 1.616 | 3.393 |
| 0.248 | 1.635 | 3.463 |
| 0.25 | 1.655 | 3.51 |
| 0.252 | 1.675 | 3.572 |
| 0.254 | 1.71 | 3.638 |
| 0.256 | 1.737 | 3.705 |
| 0.258 | 1.769 | 3.777 |
| 0.26 | 1.803 | 3.848 |
| 0.262 | 1.856 | 3.934 |
| 0.264 | 1.915 | 4.011 |
| 0.266 | 1.968 | 4.106 |
| 0.268 | 2.03 | 4.188 |
| 0.27 | 2.128 | 4.29 |
| 0.272 | 2.214 | 4.385 |
| 0.274 | 2.323 | 4.486 |
| 0.276 | 2.441 | 4.585 |
| 0.278 | 2.598 | 4.671 |
| 0.28 | 2.778 | 4.762 |
| 0.282 | 2.988 | 4.832 |
| 0.284 | 3.203 | 4.87 |
| 0.286 | 3.466 | 4.862 |
| 0.288 | 3.697 | 4.792 |
| 0.29 | 3.916 | 4.684 |
| 0.292 | 4.093 | 4.542 |
| 0.294 | 4.232 | 4.381 |
| 0.296 | 4.334 | 4.228 |
| 0.298 | 4.398 | 4.086 |
| 0.3 | 4.443 | 3.954 |
| 0.304 | 4.503 | 3.727 |
| 0.308 | 4.523 | 3.552 |
| 0.312 | 4.534 | 3.414 |
| 0.316 | 4.552 | 3.298 |
| 0.32 | 4.57 | 3.2 |
| 0.324 | 4.586 | 3.124 |
| 0.328 | 4.606 | 3.049 |
| 0.332 | 4.63 | 2.981 |
| 0.336 | 4.649 | 2.929 |
| 0.34 | 4.667 | 2.883 |
| 0.344 | 4.703 | 2.831 |
| 0.348 | 4.727 | 2.797 |
| 0.352 | 4.761 | 2.764 |
| 0.356 | 4.809 | 2.727 |
| 0.36 | 4.855 | 2.701 |
| 0.364 | 4.909 | 2.671 |
| 0.368 | 4.974 | 2.635 |
| 0.372 | 5.045 | 2.593 |
| 0.376 | 5.116 | 2.544 |
| 0.38 | 5.19 | 2.487 |
| 0.384 | 5.269 | 2.415 |
| 0.388 | 5.338 | 2.347 |
| 0.392 | 5.401 | 2.277 |
| 0.396 | 5.469 | 2.196 |
| 0.4 | 5.543 | 2.108 |
| 0.404 | 5.619 | 2.002 |
| 0.408 | 5.689 | 1.885 |
| 0.412 | 5.749 | 1.751 |
| 0.416 | 5.794 | 1.605 |
| 0.42 | 5.816 | 1.458 |
| 0.43 | 5.777 | 1.067 |
| 0.44 | 5.633 | 0.77 |
| 0.45 | 5.442 | 0.565 |
| 0.46 | 5.266 | 0.433 |
| 0.47 | 5.117 | 0.346 |
| 0.48 | 4.987 | 0.285 |
| 0.49 | 4.881 | 0.235 |
| 0.5 | 4.79 | 0.196 |
| 0.51 | 4.703 | 0.165 |
| 0.52 | 4.626 | 0.146 |
| 0.53 | 4.565 | 0.126 |
| 0.54 | 4.502 | 0.114 |
| 0.55 | 4.449 | 0.101 |
| 0.56 | 4.4 | 0.09 |
| 0.57 | 4.359 | 0.08 |
| 0.58 | 4.315 | 0.071 |
| 0.59 | 4.277 | 0.065 |
| 0.6 | 4.246 | 0.059 |
| 0.61 | 4.214 | 0.053 |
| 0.62 | 4.181 | 0.046 |
| 0.63 | 4.152 | 0.045 |
| 0.64 | 4.128 | 0.045 |
| 0.65 | 4.106 | 0.043 |
| 0.66 | 4.087 | 0.043 |
| 0.67 | 4.069 | 0.04 |
| 0.68 | 4.052 | 0.036 |
| 0.69 | 4.037 | 0.032 |
| 0.7 | 4.016 | 0.028 |
| 0.71 | 4.002 | 0.026 |
| 0.72 | 3.985 | 0.022 |
| 0.73 | 3.968 | 0.022 |
| 0.74 | 3.953 | 0.021 |
| 0.75 | 3.944 | 0.02 |
| 0.76 | 3.934 | 0.019 |
| 0.77 | 3.922 | 0.016 |
| 0.78 | 3.909 | 0.015 |
| 0.79 | 3.9 | 0.016 |
| 0.8 | 3.89 | 0.014 |
| 0.81 | 3.887 | 0.015 |
| 0.82 | 3.869 | 0.017 |
| 0.83 | 3.865 | 0.016 |
| 0.84 | 3.844 | 0.013 |
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 = 0.65. 8-μm film grown on Si substrate.