Optical constants

Refractive index of Si (Silicon)

Franta et al. 2017: n,k 0.0310–310 µm; 500 K

Data: tabulated nk
Range: 0.031–310 µm
Points: 4001
Temperature: 500 K
State: crystalline
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 4.04693
Extinction coefficient k: 0.0419461

Permittivity ε₁: 16.3759
Permittivity ε₂: 0.339506

Absorption coefficient α: 8970.56 cm⁻¹
Penetration depth δ = λ/(2πk): 2229.51 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -2.66476 µm⁻¹

Group index n_g: 5.61274
Group velocity dispersion: — fs²/mm

Dispersion parameter D: — ps/(nm·km)
Photon energy: 2.11001 eV

ε = (n + ik)², α = 4πk/λ, n_g = 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 (Silicon): Franta et al. 2017: n,k 0.0310–310 µm; 500 K
si = ls.fetch_refractiveindex("main", "Si", "Franta-500K", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si.range_nm)  # (30.9963, 309963) nm
eps = si.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_fc25934786ac/lightsmith"
si = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(si.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (si/franta-2017-500k).

# ... load si as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=si)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=1000, 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"]).

Materials guide Open a sphere of it in Studio Quick start Ask the community

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

Float zone c-Si; Heterogenous data processing combining ellipsometric and spectrophotometric measurements with refractive index determined in B. J. Frey, D. B. Leviton, T. J. Madison. Temperature-dependent refractive index of silicon and germanium, Proc. SPIE 6273, 62732J (2006). Numerical procedures updated in D. Franta, P. Franta, J. Vohánka, M. Čermák, I. Ohlídal. Determination of thicknesses and temperatures of crystalline silicon wafers from optical measurements in the far infrared region, J. Appl. Phys. 123, 185707 (2018). Temperature 500 K."

Conditions

temperature: 500 K

References

D. Franta, A. Dubroka, C. Wang, A. Giglia, J. Vohánka, P. Franta, I. Ohlídal. Temperature-dependent dispersion model of float zone crystalline silicon, Appl. Surf. Sci. 421, 405-419 (2017) (Numerical data kindly provided by Daniel Franta)

Cite

D. Franta, A. Dubroka, C. Wang, A. Giglia, J. Vohánka, P. Franta, I. Ohlídal. Temperature-dependent dispersion model of float zone crystalline silicon, Appl. Surf. Sci. 421, 405-419 (2017) (Numerical data kindly provided by Daniel Franta); Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

4001 rows as published

CSV comma separated TXT tab separated YAML n, k Full database record original YAML All quantities CSV JSON metadata

Si (Silicon), Franta et al. 2017: n,k 0.0310–310 µm; 500 K: n and k versus wavelength
λ (µm)	n	k
0.0309963	0.916581643785	0.00979912098418
0.0310678	0.916137053745	0.0098726002544
0.0311394	0.915690301321	0.0099466439326
0.0312112	0.915241365969	0.0100212565746
0.0312831	0.91479023933	0.0100964426405
0.0313552	0.914336911197	0.0101722066456
0.0314275	0.91388136908	0.0102485531664
0.0315	0.913423600552	0.0103254868158
0.0315726	0.912963593328	0.0104030122415
0.0316453	0.912501336574	0.0104811341122
0.0317183	0.912036816899	0.010559857163
0.0317914	0.911570021945	0.0106391861553
0.0318647	0.911100940107	0.0107191258794
0.0319382	0.910629558588	0.0107996811782
0.0320118	0.910155865807	0.010880856919
0.0320856	0.909679880001	0.0109626576481
0.0321595	0.909201597855	0.0110450882013
0.0322337	0.908720850671	0.0111281554755
0.032308	0.908237774745	0.011211862704
0.0323825	0.907752298001	0.0112962156948
0.0324571	0.907264470425	0.0113812187888
0.0325319	0.906774962963	0.0114668684903
0.0326069	0.906279452568	0.0115532247283
0.0326821	0.905785565645	0.0116401956841
0.0327574	0.905289590461	0.0117278333089
0.0328329	0.904788005736	0.0118161886377
0.0329086	0.904287168475	0.011905184179
0.0329845	0.903780649014	0.0119949094883
0.0330605	0.903271992727	0.0120853234467
0.0331367	0.902762308908	0.0121764163103
0.0332131	0.902249765115	0.0122682178861
0.0332897	0.901736218364	0.012360708246
0.0333664	0.901218496396	0.0124539361758
0.0334434	0.900695300412	0.0125479258164
0.0335205	0.900171920807	0.0126426094039
0.0335977	0.899651837153	0.0127379424525
0.0336752	0.899123006076	0.0128341004744
0.0337528	0.898593949524	0.0129309686451
0.0338306	0.898057234952	0.0130286596816
0.0339086	0.89752107321	0.0131270610463
0.0339868	0.896985293882	0.0132261799378
0.0340651	0.896440220743	0.0133261649681
0.0341436	0.895896650423	0.0134268626448
0.0342224	0.895352486655	0.0135283090752
0.0343012	0.894800445675	0.0136306204401
0.0343803	0.894249909929	0.0137336606257
0.0344596	0.893696054627	0.0138375088536
0.034539	0.893140360276	0.0139421483813
0.0346186	0.892578640258	0.0140476509466
0.0346984	0.892009167835	0.0141540514565
0.0347784	0.891417578203	0.0142615879785
0.0348586	0.890872566334	0.0143691664683
0.034939	0.890305490008	0.01447789006
0.0350195	0.889710589842	0.0145878672653
0.0351002	0.889176345563	0.0146976520713
0.0351811	0.888590776047	0.014809091506
0.0352622	0.887979999366	0.0149217731099
0.0353435	0.887430502039	0.0150342475755
0.035425	0.886800169185	0.0151489223972
0.0355067	0.886183892383	0.0152642029003
0.0355885	0.885636443279	0.0153791375965
0.0356706	0.885038987645	0.0154957832961
0.0357528	0.884447286272	0.0156131827817
0.0358352	0.883785852895	0.015732682878
0.0359178	0.883224508628	0.0158512722086
0.0360006	0.882593158363	0.0159719902395
0.0360836	0.88199385378	0.0160930120186
0.0361668	0.881407578713	0.016214678795
0.0362502	0.880768885865	0.0163382044332
0.0363337	0.880143469758	0.016462390233
0.0364175	0.879519019814	0.0165874681996
0.0365014	0.878862314552	0.0167140756632
0.0365856	0.878245198594	0.0168408563088
0.0366699	0.87758079981	0.0169694770854
0.0367544	0.876958337303	0.0170982273865
0.0368392	0.876318595889	0.0172282572012
0.0369241	0.875674187709	0.0173593311335
0.0370092	0.875017485796	0.0174916101895
0.0370945	0.874382060761	0.0176244301271
0.03718	0.873715635488	0.0177588490913
0.0372658	0.873112869967	0.0178929491354
0.0373517	0.87237782325	0.0180307533339
0.0374378	0.871731412997	0.018167732702
0.0375241	0.871077525236	0.0183058674342
0.0376106	0.870418227105	0.0184451241099
0.0376973	0.869714555474	0.0185863447397
0.0377842	0.869047110137	0.0187278228973
0.0378713	0.868363895195	0.0188706755933
0.0379586	0.86771049766	0.0190139191361
0.0380461	0.866994066254	0.0191595955915
0.0381338	0.866282205991	0.0193062402946
0.0382217	0.865584313382	0.0194536464153
0.0383098	0.864920352236	0.0196013605105
0.0383981	0.864182125215	0.019751842859
0.0384866	0.863480648511	0.01990258454
0.0385754	0.862767691727	0.02005469228
0.0386643	0.862071421349	0.0202075196123
0.0387534	0.861333754409	0.0203624367598
0.0388427	0.860606239652	0.0205182467176
0.0389323	0.8598842567	0.0206750616747
0.039022	0.859159021757	0.0208330984811
0.039112	0.858437643943	0.0209921925436
0.0392021	0.857690666071	0.0211530752227
0.0392925	0.856961968784	0.0213146785151
0.0393831	0.856193272056	0.0214784601991
0.0394739	0.855465099367	0.021642416149
0.0395649	0.854716639689	0.0218080793572
0.0396561	0.853964801166	0.0219750354021
0.0397475	0.853182840383	0.0221439881672
0.0398391	0.852435032101	0.0223132828746
0.039931	0.85163227219	0.0224852567838
0.040023	0.850860275886	0.0226576724471
0.0401153	0.850109592158	0.0228307705643
0.0402078	0.849332564793	0.0230058351024
0.0403004	0.848551019302	0.0231822958823
0.0403934	0.847751410108	0.0233605372393
0.0404865	0.846981891456	0.0235392416447
0.0405798	0.846151676316	0.0237209405367
0.0406733	0.845360657863	0.0239028614284
0.0407671	0.844553043646	0.0240865750978
0.0408611	0.843747404719	0.0242715676884
0.0409553	0.842939281754	0.0244579753393
0.0410497	0.842099697078	0.0246466562468
0.0411443	0.841314333433	0.0248351132013
0.0412392	0.840460609066	0.0250269631443
0.0413342	0.839622213226	0.0252197536307
0.0414295	0.838809353478	0.0254131720105
0.041525	0.837966867105	0.0256088924836
0.0416207	0.837124602891	0.0258060269445
0.0417167	0.836267136161	0.0260050634896
0.0418129	0.835410198837	0.0262055296729
0.0419092	0.834558595533	0.0264072818036
0.0420059	0.833686441283	0.0266111504741
0.0421027	0.83282667506	0.026816101081
0.0421998	0.831966015843	0.0270225634712
0.042297	0.831063497799	0.027231889559
0.0423945	0.830198833639	0.0274414895212
0.0424923	0.829316408143	0.0276531940972
0.0425902	0.828420896625	0.0278668705849
0.0426884	0.827524515979	0.0280821251467
0.0427868	0.826617487207	0.0282993025705
0.0428854	0.825710991042	0.0285180356117
0.0429843	0.824811007691	0.02873812477
0.0430834	0.823879200476	0.028960920954
0.0431827	0.822971440911	0.0291844818586
0.0432823	0.822060732161	0.0294097602942
0.043382	0.821104738195	0.0296382965462
0.043482	0.820184700634	0.0298671851977
0.0435823	0.819249699485	0.0300982719545
0.0436827	0.818305417939	0.0303313703787
0.0437834	0.817343427371	0.0305668145705
0.0438844	0.816366763705	0.0308045175408
0.0439855	0.8154329261	0.0310423151029
0.0440869	0.814449921989	0.0312837070832
0.0441886	0.813489867687	0.0315259591115
0.0442904	0.812527780242	0.0317700343549
0.0443925	0.811537314497	0.032016984278
0.0444949	0.810536369874	0.032266136567
0.0445974	0.809563236818	0.0325159748012
0.0447002	0.808548460454	0.032769294043
0.0448033	0.807551255729	0.0330237285796
0.0449066	0.806548002318	0.0332802441527
0.0450101	0.805524894919	0.0335394327024
0.0451138	0.804524773774	0.0337995272739
0.0452178	0.803392128762	0.0340671054238
0.0453221	0.802365825763	0.0343321111636
0.0454266	0.801333972773	0.0345992630378
0.0455313	0.800360385807	0.0348657980669
0.0456362	0.799036420874	0.0351496261156
0.0457414	0.798035348924	0.0354213019822
0.0458469	0.797220823028	0.035686555428
0.0459526	0.795837285691	0.0359793094671
0.0460585	0.794849303486	0.0362562892639
0.0461647	0.793981830657	0.0365296751824
0.0462711	0.792570168339	0.0368301960726
0.0463778	0.791474154715	0.0371182525929
0.0464847	0.790357880431	0.0374093433969
0.0465918	0.789460906243	0.0376920655525
0.0466992	0.788177472021	0.0379953366808
0.0468069	0.787001101742	0.0382956770786
0.0469148	0.785971332477	0.0385910121457
0.047023	0.785089804764	0.0388810780872
0.0471313	0.783871620777	0.0391899228383
0.04724	0.782575115343	0.0395049900534
0.0473489	0.781716750915	0.0398000954642
0.047458	0.780486845605	0.0401162528356
0.0475675	0.779044770145	0.040445740813
0.0476771	0.778101899087	0.0407516145356
0.047787	0.776659940542	0.0410859438031
0.0478972	0.775515363617	0.0414069661901
0.0480076	0.774611769281	0.0417172921232
0.0481183	0.773648829143	0.0420329068293
0.0482292	0.772097205788	0.0423829417196
0.0483404	0.771028699851	0.0427089574164
0.0484518	0.76936839149	0.0430703338442
0.0485635	0.768303644085	0.0434009612728
0.0486754	0.766992663798	0.0437479056288
0.0487876	0.7659784004	0.0440803191844
0.0489001	0.764504268881	0.0444416965555
0.0490128	0.763137320405	0.0447995474273
0.0491258	0.762037175388	0.0451442446487
0.0492391	0.760838841575	0.0454971852336
0.0493526	0.759771031553	0.0458447411444
0.0494664	0.758249561315	0.0462222949651
0.0495804	0.757174136039	0.0465752992467
0.0496947	0.755785204712	0.0469501621055
0.0498092	0.754435902568	0.0473253098726
0.0499241	0.75313108968	0.0477003772618
0.0500391	0.751538914891	0.0480965256103
0.0501545	0.750438111781	0.0484640011851
0.0502701	0.749129761754	0.0488474860826
0.050386	0.747663337594	0.0492441247684
0.0505022	0.746736774013	0.049607837376
0.0506186	0.745176422101	0.050016363115
0.0507353	0.743485054367	0.050436898706
0.0508522	0.742394702638	0.0508195886983
0.0509694	0.741169944733	0.0512141017983
0.0510869	0.739340225372	0.0516535648096
0.0512047	0.737976279067	0.0520637442699
0.0513227	0.736444044623	0.0524888514327
0.0514411	0.735432169299	0.0528797081069
0.0515596	0.733949821642	0.0533072085713
0.0516785	0.732240692183	0.0537545023742
0.0517976	0.730682634977	0.0541941035547
0.051917	0.729399736925	0.054616394411
0.0520367	0.728006525757	0.0550499355356
0.0521567	0.726514835241	0.0554940827072
0.0522769	0.724889876864	0.055951764804
0.0523974	0.72328138848	0.0564116421752
0.0525182	0.722148560519	0.0568375308733
0.0526393	0.720654002265	0.0572949239531
0.0527606	0.718812779472	0.0577834939477
0.0528822	0.717261264912	0.0582524576201
0.0530042	0.715722340237	0.0587238427833
0.0531263	0.713973705629	0.059216067711
0.0532488	0.712575646231	0.0596827523135
0.0533716	0.711017779143	0.0601662093912
0.0534946	0.709560401689	0.06064461643
0.0536179	0.707862867199	0.0611471456634
0.0537415	0.705965816795	0.06167092851
0.0538654	0.704550473461	0.0621564204025
0.0539896	0.703051028023	0.0626527695575
0.054114	0.70128645155	0.0631765225482
0.0542388	0.699810373826	0.0636780602197
0.0543638	0.697777519468	0.0642343325086
0.0544891	0.696419828368	0.0647324376623
0.0546147	0.694257147458	0.0653095218272
0.0547406	0.693102527116	0.0657957723216
0.0548668	0.691202731528	0.0663564933687
0.0549933	0.689300620453	0.0669219149291
0.0551201	0.687548361359	0.067477136886
0.0552471	0.686160545427	0.0680004361193
0.0553745	0.684324995024	0.0685720624144
0.0555022	0.682442303742	0.0691529067485
0.0556301	0.680597438355	0.0697344508721
0.0557583	0.678730651241	0.0703227842301
0.0558869	0.677130470202	0.0708877925538
0.0560157	0.675172693491	0.0714946682576
0.0561448	0.673278122091	0.0720996439402
0.0562743	0.671413078634	0.0727061693148
0.056404	0.669398352688	0.0733337943249
0.056534	0.667911412013	0.0739080801974
0.0566643	0.665857242076	0.074549692973
0.056795	0.663829405557	0.0751935987305
0.0569259	0.661840762094	0.0758382566546
0.0570571	0.660053121138	0.0764647974322
0.0571887	0.657758055127	0.0771555176768
0.0573205	0.655941573812	0.0777956889347
0.0574526	0.654043773297	0.0784506031961
0.0575851	0.652205629151	0.0791035548663
0.0577178	0.649953612248	0.0798124465268
0.0578509	0.647632075403	0.0805363618676
0.0579842	0.645797204172	0.0812056837953
0.0581179	0.643789479321	0.0819022313611
0.0582519	0.64143294349	0.0826494731144
0.0583862	0.639452217541	0.0833546141481
0.0585207	0.63720508098	0.0841006764677
0.0586557	0.63524064845	0.0848156374705
0.0587909	0.63310775385	0.0855591615026
0.0589264	0.630725904461	0.0863431343569
0.0590622	0.628532930686	0.0871082100509
0.0591984	0.626217665238	0.0878971355127
0.0593349	0.624199308061	0.0886510473596
0.0594716	0.621661387133	0.0894858843714
0.0596087	0.619581757135	0.0902620502669
0.0597461	0.617447171062	0.0910528371556
0.0598839	0.614943018287	0.0919055950594
0.0600219	0.612615880502	0.0927398063296
0.0601603	0.610241306041	0.0935889432335
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1.64934	3.51114401661	3.51324412618e-07
1.65314	3.51087046065	3.49169826754e-07
1.65695	3.51059839459	3.47053004935e-07
1.66077	3.51032764261	3.44973362083e-07
1.6646	3.51005820032	3.42930301671e-07
1.66844	3.50979009244	3.40923243247e-07
1.67228	3.50952348624	3.38951604291e-07
1.67614	3.50925805236	3.37014862654e-07
1.68	3.5089939459	3.35112461987e-07
1.68388	3.50873104469	3.33243887821e-07
1.68776	3.50846955829	3.3140860168e-07
1.69165	3.50820953675	3.29606094194e-07
1.69555	3.50795056679	3.27835908973e-07
1.69946	3.50769289738	3.26097543237e-07
1.70337	3.50743672192	3.24390502778e-07
1.7073	3.50718159279	3.22714373e-07
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1.71518	3.50667525454	3.19452967188e-07
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2.51947	3.47789805703	3.05295546647e-07
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2.54865	3.47734299996	3.10744868945e-07
2.55452	3.4772336503	3.11874663037e-07
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2.57816	3.4768012153	3.16528421607e-07
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2.97379	3.4710464952	4.18816892407e-07
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2.98751	3.47088750639	4.23162806543e-07
2.9944	3.47080848829	4.2536305333e-07
3.0013	3.47072983939	4.27581617925e-07
3.00822	3.47065162203	4.29818591955e-07
3.01516	3.47057377164	4.32074083409e-07
3.02211	3.47049628845	4.34348193163e-07
3.02907	3.47041918766	4.36641021267e-07
3.03606	3.47034235626	4.38952684519e-07
3.04306	3.47026581857	4.41283283708e-07
3.05007	3.47018985402	4.43632887695e-07
3.0571	3.47011416395	4.46001639668e-07
3.06415	3.47003881662	4.4838963714e-07
3.07121	3.46996379021	4.50796990114e-07
3.07829	3.46988919869	4.5322379178e-07
3.08539	3.4698148451	4.55670176506e-07
3.0925	3.4697408452	4.58136239175e-07

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Optical transmission calculator

Free-standing sample in vacuum, normal incidence

Transmittance T: —
Reflectance R: —

Fresnel reflection calculator

R_p: —
R_s: —
R = (R_p+R_s)/2: —
Phase φ_p: —
Phase φ_s: —
Brewster angle θ_B: —
Critical angle θ_C: —

Plot