Optical constants
Refractive index of Si-Ge (Silicon-germanium, SiGe)
Jellison et al. 1993: 47% 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
- 4.45132
- Extinction coefficient k
- 0.0974
- Permittivity ε1
- 19.8048
- Permittivity ε2
- 0.867117
- Absorption coefficient α
- 20829.9 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 960.159 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -4.3 µm⁻¹
- Group index ng
- 6.978
- 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: 47% Si, Si substrate; n,k 0.24–0.84 µm
si_ge = ls.fetch_refractiveindex("other", "Si-Ge", "Jellison-47", 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_587754f3b17a/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-1993-47).
# ... 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
- 0.47
- 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 | 1.638 | 3.233 |
| 0.242 | 1.637 | 3.251 |
| 0.244 | 1.64 | 3.26 |
| 0.246 | 1.658 | 3.348 |
| 0.248 | 1.676 | 3.405 |
| 0.25 | 1.687 | 3.457 |
| 0.252 | 1.717 | 3.51 |
| 0.254 | 1.768 | 3.585 |
| 0.256 | 1.783 | 3.646 |
| 0.258 | 1.826 | 3.719 |
| 0.26 | 1.87 | 3.781 |
| 0.262 | 1.905 | 3.865 |
| 0.264 | 1.954 | 3.943 |
| 0.266 | 2.019 | 4.021 |
| 0.268 | 2.088 | 4.111 |
| 0.27 | 2.155 | 4.198 |
| 0.272 | 2.248 | 4.298 |
| 0.274 | 2.356 | 4.391 |
| 0.276 | 2.478 | 4.481 |
| 0.278 | 2.608 | 4.57 |
| 0.28 | 2.782 | 4.657 |
| 0.282 | 2.975 | 4.73 |
| 0.284 | 3.187 | 4.755 |
| 0.286 | 3.426 | 4.751 |
| 0.288 | 3.673 | 4.689 |
| 0.29 | 3.88 | 4.585 |
| 0.292 | 4.044 | 4.453 |
| 0.294 | 4.171 | 4.31 |
| 0.296 | 4.28 | 4.159 |
| 0.298 | 4.333 | 4.021 |
| 0.3 | 4.384 | 3.897 |
| 0.304 | 4.448 | 3.67 |
| 0.308 | 4.465 | 3.503 |
| 0.312 | 4.477 | 3.364 |
| 0.316 | 4.49 | 3.251 |
| 0.32 | 4.503 | 3.154 |
| 0.324 | 4.522 | 3.069 |
| 0.328 | 4.535 | 2.996 |
| 0.332 | 4.551 | 2.93 |
| 0.336 | 4.57 | 2.875 |
| 0.34 | 4.582 | 2.83 |
| 0.344 | 4.606 | 2.782 |
| 0.348 | 4.623 | 2.744 |
| 0.352 | 4.653 | 2.705 |
| 0.356 | 4.686 | 2.669 |
| 0.36 | 4.717 | 2.638 |
| 0.364 | 4.755 | 2.609 |
| 0.368 | 4.8 | 2.574 |
| 0.372 | 4.847 | 2.532 |
| 0.376 | 4.896 | 2.484 |
| 0.38 | 4.939 | 2.441 |
| 0.384 | 4.984 | 2.388 |
| 0.388 | 5.022 | 2.336 |
| 0.392 | 5.056 | 2.283 |
| 0.396 | 5.088 | 2.234 |
| 0.4 | 5.123 | 2.195 |
| 0.404 | 5.161 | 2.16 |
| 0.408 | 5.209 | 2.124 |
| 0.412 | 5.266 | 2.085 |
| 0.416 | 5.329 | 2.039 |
| 0.42 | 5.4 | 1.982 |
| 0.43 | 5.57 | 1.773 |
| 0.44 | 5.689 | 1.497 |
| 0.45 | 5.707 | 1.168 |
| 0.46 | 5.62 | 0.87 |
| 0.47 | 5.471 | 0.648 |
| 0.48 | 5.314 | 0.498 |
| 0.49 | 5.171 | 0.397 |
| 0.5 | 5.051 | 0.322 |
| 0.51 | 4.951 | 0.266 |
| 0.52 | 4.856 | 0.227 |
| 0.53 | 4.777 | 0.197 |
| 0.54 | 4.702 | 0.173 |
| 0.55 | 4.643 | 0.153 |
| 0.56 | 4.585 | 0.137 |
| 0.57 | 4.536 | 0.122 |
| 0.58 | 4.484 | 0.105 |
| 0.59 | 4.441 | 0.095 |
| 0.6 | 4.401 | 0.084 |
| 0.61 | 4.361 | 0.079 |
| 0.62 | 4.329 | 0.072 |
| 0.63 | 4.289 | 0.067 |
| 0.64 | 4.263 | 0.065 |
| 0.65 | 4.243 | 0.062 |
| 0.66 | 4.217 | 0.056 |
| 0.67 | 4.197 | 0.047 |
| 0.68 | 4.17 | 0.046 |
| 0.69 | 4.144 | 0.044 |
| 0.7 | 4.128 | 0.044 |
| 0.71 | 4.113 | 0.041 |
| 0.72 | 4.093 | 0.04 |
| 0.73 | 4.081 | 0.038 |
| 0.74 | 4.064 | 0.034 |
| 0.75 | 4.05 | 0.032 |
| 0.76 | 4.038 | 0.029 |
| 0.77 | 4.029 | 0.027 |
| 0.78 | 4.011 | 0.025 |
| 0.79 | 4.002 | 0.022 |
| 0.8 | 3.991 | 0.019 |
| 0.81 | 3.974 | 0.024 |
| 0.82 | 3.97 | 0.023 |
| 0.83 | 3.945 | 0.017 |
| 0.84 | 3.935 | 0.03 |
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 = 0.47. 7-μm film grown on Si substrate.