Optical constants

Refractive index of Si (Silicon)

Franta et al. 2017: n,k 0.0310–310 µm; 50 K

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

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.031–310 µm
Refractive index n
3.91186
Extinction coefficient k
0.0139598
Permittivity ε1
15.3024
Permittivity ε2
0.109217
Absorption coefficient α
2985.43 cm⁻¹
Penetration depth δ = λ/(2πk)
6699.21 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-2.34482 µm⁻¹
Group index ng
5.28967
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 (Silicon): Franta et al. 2017: n,k 0.0310–310 µm; 50 K
si = ls.fetch_refractiveindex("main", "Si", "Franta-50K", 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.

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 50 K."

Conditions

temperature
50 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
Si (Silicon), Franta et al. 2017: n,k 0.0310–310 µm; 50 K: n and k versus wavelength
λ (µm)nk
0.03099630.9170084920210.0111691777718
0.03106780.9165702023350.0112525792202
0.03113940.9161298283380.0113366128527
0.03121120.9156873616090.0114212834554
0.03128310.9152427913460.0115065958785
0.03135520.9147961031290.011592555053
0.03142750.914347289110.0116791658628
0.03150.9138963410780.0117664332309
0.03157260.9134432407240.0118543622462
0.03164530.9129879831060.0119429578614
0.03171830.9125305558010.0120322251618
0.03179140.9120709450610.0121221692875
0.03186470.9116091440520.0122127953235
0.03193820.9111451371370.0123041085089
0.03201180.9106789158430.0123961140242
0.03208560.9102104678520.012488817139
0.03215950.9097397806880.0125822231628
0.03223370.9092668690880.0126763370644
0.0323080.9087917218630.012771164203
0.03238250.9083141238080.0128667128659
0.03245710.9078341826890.0129629868595
0.03253190.9073524706940.0130599832905
0.03260690.9068680870420.0131577204068
0.03268210.9063811378270.0132562021804
0.03275740.9058925906650.0133554198679
0.03283290.9054012534450.0134553963998
0.03290860.9049070623160.0135561384035
0.03298450.9044113624660.013657631296
0.03306050.9039125887570.0137599041813
0.03313670.9034121223480.0138629417483
0.03321310.9029085213110.0139667717115
0.03328970.9024029306660.0140713821962
0.03336640.9018948113580.0141767872634
0.03344340.9013842398610.0142829915264
0.03352050.9008712994860.0143899994862
0.03359770.9003559919270.0144978169509
0.03367520.8998379545530.0146064556764
0.03375280.8993174905350.0147159167493
0.03383060.8987943821550.0148262097256
0.03390860.8982692447150.0149373304612
0.03398680.8977456104230.0150492256206
0.03406510.8971997773660.0151623002195
0.03414360.896685035160.0152756606209
0.03422240.89614883910.0153902015537
0.03430120.8955906989620.015505945567
0.03438030.8950636258660.01562198186
0.03445960.8945186829020.0157391635914
0.0345390.8939649614630.0158573423528
0.03461860.8934222556190.0159761732614
0.03469840.8928653541750.0160961113427
0.03477840.8923104870690.0162168731865
0.03485860.8917593200050.0163384327544
0.0349390.8911978801480.0164610518725
0.03501950.8906302216080.016584665078
0.03510020.8900797873050.0167088405649
0.03518110.8894971025590.0168345122599
0.03526220.8889328286640.0169607339206
0.03534350.8883629432010.0170879646232
0.0354250.8877950605050.0172160648798
0.03550670.8872089341270.0173454351323
0.03558850.8866271943280.0174756436508
0.03567060.8860444627730.0176068008549
0.03575280.8854539910440.0177390480872
0.03583520.8848696331320.0178721150176
0.03591780.884275677170.0180063242833
0.03600060.8836786831370.0181415517298
0.03608360.8830712693860.018277957449
0.03616680.8824816006420.0184149648155
0.03625020.8818778547780.0185532400762
0.03633370.8812632047650.0186927290119
0.03641750.8806488593310.0188332034899
0.03650140.8800369051190.0189746242909
0.03658560.8794167140540.019117227126
0.03666990.8788030765410.0192606981944
0.03675440.8781819867510.0194053494406
0.03683920.8775499871180.0195512679386
0.03692410.8769298761350.0196979536013
0.03700920.8762871055170.0198461883539
0.03709450.8756598394020.019995119469
0.037180.8750198808890.0201453935181
0.03726580.8743866450640.0202965731509
0.03735170.8737372973350.0204491950917
0.03743780.8730883254110.0206028857561
0.03752410.8724445247060.0207575370566
0.03761060.8717813260440.0209137415744
0.03769730.8711310747270.0210707347102
0.03778420.8704697091410.0212291018281
0.03787130.8698122638840.0213884862222
0.03795860.86913981890.0215493609201
0.03804610.8684683546080.0217113419835
0.03813380.8678005677330.0218743672206
0.03822170.8671241917480.0220387524844
0.03830980.8664497829920.0222042390645
0.03839810.8657587206780.0223713132901
0.03848660.8650691619250.0225395192372
0.03857540.8643880352090.0227086804187
0.03866430.8636896034680.022879479595
0.03875340.8629917199970.0230514578025
0.03884270.8622945454460.0232246169083
0.03893230.8615902449450.0233991757726
0.0390220.8608916870810.0235747933905
0.0391120.8601811671940.0237519612953
0.03920210.8594594988040.0239306716656
0.03929250.8587433942860.0241104696855
0.03938310.8580259495570.0242915535873
0.03947390.8572973532780.0244742110658
0.03956490.8565715144440.0246580563698
0.03965610.8558368003120.0248434318971
0.03974750.8551014855350.0250301086051
0.03983910.8543593978870.0252182758616
0.0399310.8536179921530.0254077235442
0.0400230.8528762504670.0255984884636
0.04011530.8521218544470.0257909504638
0.04020780.8513708391490.0259846365415
0.04030040.8506152018370.0261797972183
0.04039340.8498547116280.0263764500327
0.04048650.8490813834580.0265748555054
0.04057980.8483200397330.0267742471712
0.04067330.8475478431230.0269753492193
0.04076710.8467685885740.0271780553754
0.04086110.8459848397450.0273822952469
0.04095530.8452011414030.0275879310554
0.04104970.8444189499390.0277949217141
0.04114430.8436239070190.0280037494547
0.04123920.8428300700880.0282139613634
0.04133420.8420327147310.0284257228155
0.04142950.8412258728790.0286392468847
0.0415250.8404122055730.0288544572996
0.04162070.8396081864920.0290707965496
0.04171670.8387890718960.0292891270892
0.04181290.837961297750.0295092425486
0.04190920.837142059270.0297305469516
0.04200590.8363199075150.0299534495974
0.04210270.8354824748070.030178406741
0.04219980.8346465955510.0304048260841
0.0422970.8338034124730.0306330385282
0.04239450.83295872160.0308628430732
0.04249230.8321109479420.0310943069178
0.04259020.8312581635680.0313275125565
0.04268840.8303949166710.0315626789162
0.04278680.8295386727570.0317991535434
0.04288540.8286715330140.0320376284662
0.04298430.8277986049740.0322779221513
0.04308340.8269199734380.0325200439197
0.04318270.8260398198630.0327638405451
0.04328230.8251568074780.0330093739159
0.0433820.8242715568470.0332566287594
0.0434820.8233754135530.0335059663697
0.04358230.8224753872380.0337571172319
0.04368270.821562696780.0340104557678
0.04378340.8206646629130.0342648615643
0.04388440.8197482848150.0345217153999
0.04398550.8188341892260.0347801677459
0.04408690.8179122417320.0350406570139
0.04418860.8169835882250.0353031490509
0.04429040.8160511016860.0355675328099
0.04439250.8151230594670.0358334553988
0.04449490.8141768553310.0361019207658
0.04459740.8132330954540.0363720347072
0.04470020.8122776627330.0366444378581
0.04480330.8113223014750.0369186160079
0.04490660.8103626491150.0371947758595
0.04501010.8093966676360.0374730233624
0.04511380.8084218964420.0377534874892
0.04521780.8074480554760.0380357274841
0.04532210.8064689682450.0383200420988
0.04542660.8054828528440.0386065295591
0.04553130.8044899658580.0388951925375
0.04563620.8034978533020.0391856778408
0.04574140.8024964685970.0394784849505
0.04584690.801487703820.0397735380435
0.04595260.8004761024610.0400706254068
0.04605850.7994518882660.0403702505386
0.04616470.7984380794230.0406712636682
0.04627110.7974071694140.0409750703627
0.04637780.7963800993370.0412806140586
0.04648470.7953419570130.0415886751972
0.04659180.7942856645030.0418996481444
0.04669920.793243064220.0422118694367
0.04680690.7921863701110.0425268173416
0.04691480.7911300298920.0428437349775
0.0470230.7900578331910.0431635130635
0.04713130.7889861732810.0434852764777
0.047240.7879065742940.0438095012506
0.04734890.7868244295340.0441359019445
0.0474580.7857289408110.0444650987732
0.04756750.7846389603990.0447960407272
0.04767710.7835379447110.0451296775908
0.0477870.7824308513010.0454657432381
0.04789720.781312501360.0458045557194
0.04800760.7801929267190.0461455442522
0.04811830.7790633517290.0464892393982
0.04822920.7779359681880.0468349279116
0.04834040.7768036999790.0471830408686
0.04845180.7756522963370.0475344641067
0.04856350.7745071261210.0478876649609
0.04867540.773347706310.0482439154746
0.04878760.7721823901820.0486027180473
0.04890010.771011202140.0489640854406
0.04901280.7698354899050.0493279455673
0.04912580.7686554461930.0496942979092
0.04923910.7674631569390.0500636702729
0.04935260.7662669739520.0504355383776
0.04946640.765062511380.0508102042904
0.04958040.7638525840540.051187497976
0.04969470.7626362007340.0515675000178
0.04980920.7614127556740.0519502670937
0.04992410.7601871377450.0523354791029
0.05003910.7589453949230.0527241126465
0.05015450.7577027998030.0531151306909
0.05027010.7564521491110.0535090475534
0.0503860.7551874435120.0539063099348
0.05050220.7539270911450.054305622108
0.05061860.752651756670.0547083837741
0.05073530.7513701512430.0551139882713
0.05085220.750079132480.0555226833403
0.05096940.7487901899840.0559336322232
0.05108690.7474881874710.0563479739851
0.05120470.7461725170120.056765783941
0.05132270.7448518839810.0571864243627
0.05144110.7435278022120.0576097904293
0.05155960.7421951335530.05803629308
0.05167850.7408532539550.0584660016917
0.05179760.7395038730120.0588988016783
0.0519170.7381460525090.0593347863644
0.05203670.7367817620330.0597738159966
0.05215670.7354049647970.0602164005384
0.05227690.734023215290.0606619450931
0.05239740.7326295903260.0611110394072
0.05251820.7312277890210.0615634003745
0.05263930.7298223469750.0620186624151
0.05276060.7284059002530.0624774662499
0.05288220.7269800969150.0629396958733
0.05300420.7255421019470.0634056219115
0.05312630.7241021595160.0638743706948
0.05324880.7226471037570.0643471192903
0.05337160.7211876312240.0648229438992
0.05349460.7197190278240.0653022830812
0.05361790.7182332614710.065785895357
0.05374150.7167479640050.0662721943462
0.05386540.7152433637590.0667630235765
0.05398960.7137373453460.0672567480482
0.0541140.7122200219070.0677543110944
0.05423880.710692492040.0682556366275
0.05436380.7091523809490.06876098157
0.05448910.7076021790540.0692701356238
0.05461470.7060462165990.0697826976211
0.05474060.7044691164410.0703002166854
0.05486680.7028880651590.0708210202401
0.05499330.7013031015420.0713451140189
0.05512010.699698540210.071874118605
0.05524710.6980860766480.072406877134
0.05537450.6964648139290.0729435051418
0.05550220.6948283337090.0734847058525
0.05563010.6931805004780.0740301110932
0.05575830.6915211407310.0745797725727
0.05588690.6898532785710.075133394825
0.05601570.6881727308280.0756914624485
0.05614480.6864833468030.0762535861783
0.05627430.6847736395480.0768210807007
0.0564040.6830557024350.0773926405649
0.0565340.681322256180.0779691236086
0.05666430.6795823089170.0785495386926
0.0567950.6778252460680.0791351446562
0.05692590.6760519176450.0797259223296
0.05705710.6742707484530.080321004394
0.05718870.672475465330.0809211766423
0.05732050.6706656751610.0815265350489
0.05745260.6688412284460.0821371487668
0.05758510.6670026549080.0827530042642
0.05771780.6651489096690.0833742835378
0.05785090.663278451070.0840012377617
0.05798420.6613962238430.0846332971982
0.05811790.6595000558440.0852707870757
0.05825190.6575838441630.0859145586062
0.05838620.6556588482090.0865632052251
0.05852070.6537120779730.0872184946462
0.05865570.6517509421970.0878795180637
0.05879090.6497770275470.0885461195961
0.05892640.6477783814080.0892200001644
0.05906220.6457686916240.0898993632307
0.05919840.6437364027980.0905858850609
0.05933490.641689594910.0912785208642
0.05947160.639623248980.0919780626361
0.05960870.6375366137710.0926847162382
0.05974610.6354334989540.093398025956
0.05988390.6333082625390.0941189207983
0.06002190.6311614033380.0948474497972
0.06016030.6289978609990.0955829915292
0.0602990.6268115653190.0963265921644
0.0604380.6246016057170.097078549413
0.06057730.6223675082620.0978391140617
0.06071690.6201140276590.0986077282222
0.06085690.6178347573310.0993856186563
0.06099720.6155304702490.100172921304
0.06113780.613200051450.100970115201
0.06127870.6108421606160.101777772618
0.061420.6084587323850.102595982238
0.06156160.606047573290.103425592286
0.06170350.603604397170.104267915718
0.06184580.6011328020590.105123025535
0.06198830.5986286046870.10599246334
0.06213120.5960864191590.106878165816
0.06227440.5935174532750.107779271722
0.0624180.5909086037280.108699478173
0.06256190.5882621740750.109639950521
0.06270610.5855782854630.110602486378
0.06285070.5828552087490.111589503107
0.06299560.5800930555790.112603368755
0.06314080.5772877436270.113647586314
0.06328630.5744399132250.114725088423
0.06343220.5715525507490.115838663688
0.06357840.5686179454570.116993606799
0.0637250.5656447780190.118192220461
0.06387190.5626305230750.119439395414
0.06401910.5595768517850.12073944358
0.06416670.5564805490860.122097979713
0.06431460.5533557933020.123516987396
0.06446290.550191854980.125004025257
0.06461150.5469998604090.126561824414
0.06476050.5437852379110.128194239317
0.06490970.5405500426890.129905699392
0.06505940.537303119480.131698681583
0.06520940.5340472514820.133576639145
0.06535970.5307933639660.135540400733
0.06551030.5275466722150.137591443426
0.06566140.5243148390960.139729750868
0.06581270.5211077109810.141953705613
0.06596440.5179318701970.144261441261
0.06611650.5147943589370.146649800825
0.06626890.5117060851870.149113274476
0.06642170.5086765361970.151645415669
0.06657480.5056988981820.154243420093
0.06672830.5027908315070.156896000053
0.06688210.4999557855890.159594932727
0.06703630.4971893681040.162333571117
0.06719080.494504110870.165098981762
0.06734570.491892680450.16788401698
0.06750090.4893559478820.17067841992
0.06765660.4868924172260.17347245757
0.06781250.4844998946950.176256579957
0.06796880.4821686573330.179024161098
0.06812550.4799026962050.181763907078
0.06828260.4776841286790.184473249113
0.068440.475511962310.187144043305
0.06859780.473377357470.189771986925
0.06875590.4712734326540.19235300534
0.06891440.4691861465260.194887043626
0.06907320.4671140130920.197370043295
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3.022113.405440852562.11937553296e-15
3.029073.405371197362.08571422626e-15
3.036063.405301870162.05265511528e-15
3.043063.405232862632.02018638151e-15
3.050073.405164182451.98829645211e-15
3.05713.405095818131.95697400262e-15
3.064153.405027773351.92620794928e-15
3.071213.404960050571.89598743446e-15
3.078293.404892645651.86630183944e-15
3.085393.404825552141.8371407639e-15
3.09253.404758771121.80849402872e-15

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Optical transmission calculator

Free-standing sample in vacuum, normal incidence
Method
Transmittance T
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Reflectance R
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Fresnel reflection calculator

Direction
Rp
—
Rs
—
R = (Rp+Rs)/2
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Phase φp
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Phase φs
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Brewster angle θB
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Critical angle θC
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