Optical constants

Refractive index of HfO2 (Hafnium dioxide, Hafnia)

Franta et al. 2015: n,k 0.115–125 µm

Data
tabulated nk
Range
0.1148–125.1 µm
Points
2431
State
amorphous
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.1148–125.1 µm
Refractive index n
2.0938
Extinction coefficient k
1.35444e-31
Permittivity ε1
4.38402
Permittivity ε2
5.67185e-31
Absorption coefficient α
2.89659e-26 cm⁻¹
Penetration depth δ = λ/(2πk)
6.90468e+32 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-0.151499 µm⁻¹
Group index ng
2.18282
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

# HfO2 (Hafnium dioxide, Hafnia): Franta et al. 2015: n,k 0.115–125 µm
hfo2 = ls.fetch_refractiveindex("main", "HfO2", "Franta", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(hfo2.range_nm)  # (114.773, 125124) nm
eps = hfo2.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

Film HfO2; Deposited by e-beam evaporation on c-Si; 112.7 nm thick film with an amorphous (very fine polycrystalline) structure; Heterogenous data processing combining ellipsometric and spectrophotometric measurements; Room temperature.

Conditions

film thickness
112.7e-9
substrate
c-Si

References

D. Franta, D. Nečas, I. Ohlídal. Universal dispersion model for characterization of optical thin films over wide spectral range: Application to hafnia. Appl. Opt. 54, 9108–9119 (2015) (Numerical data kindly provided by Daniel Franta)
  • doi:10.1364/ao.54.009108 Universal dispersion model for characterization of optical thin films over a wide spectral range: application to hafnia, Applied Optics (2015)

Cite

Daniel Franta, David Nečas and Ivan Ohlídal. Universal dispersion model for characterization of optical thin films over a wide spectral range: application to hafnia. Applied Optics, 54, 9108 (2015), doi:10.1364/ao.54.009108; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

2431 rows as published
HfO2 (Hafnium dioxide, Hafnia), Franta et al. 2015: n,k 0.115–125 µm: n and k versus wavelength
λ (µm)nk
0.1147731.8255739710021.544939697738
0.1151041.8349177609991.540707017397
0.1154361.8441501250321.536395315341
0.1157681.8532699604261.532007489752
0.1161021.8622762351441.527546463335
0.1164371.8711679881381.523015181516
0.1167721.8799443296221.518416610678
0.1171091.8886044412941.513753736415
0.1174461.8971475764911.509029561829
0.1177851.9055730602861.504247105852
0.1181241.9138802895381.499409401619
0.1184651.9220687328851.494519494878
0.1188061.9301379306941.489580442441
0.1191491.9380874949761.484595310694
0.1194921.9459171092531.479567174145
0.1198371.9536265283991.474499114032
0.1201821.9612155784491.469394216985
0.1205291.9686841563921.464255573737
0.1208761.9760322299341.4590862779
0.1212241.9832598372551.453889424793
0.1215741.9903670867561.448668110332
0.1219241.9973541568011.443425429982
0.1222762.0042212954591.438164477759
0.1226282.0109688202561.432888345302
0.1229822.0175971179421.427600121
0.1233362.0241066442611.422302889175
0.1236922.0304979237671.41699972933
0.1240482.0367715496451.411693715449
0.1244062.0429281835841.406387915352
0.1247642.0489685556791.401085390105
0.1251242.0548934643841.395789193483
0.1254842.0607037765161.390502371484
0.1258462.066400427311.385227961882
0.1262092.0719844205441.379968993834
0.1265732.0774568287281.374728487523
0.1269372.082818793371.369509453834
0.1273032.0880715253221.364314894074
0.127672.0932163052091.359147799709
0.1280382.0982544839531.354011152134
0.1284072.1031874833951.348907922456
0.1287772.1080167970191.343841071295
0.1291492.1127439907911.338813548591
0.1295212.1173707041061.333828293409
0.1298942.1218986508641.328888233746
0.1302692.1263296206731.323996286312
0.1306442.130665480181.319155356307
0.1310212.1349081745511.31436833715
0.1313982.1390597290881.309638110183
0.1317772.1431222510071.304967544317
0.1321572.1470979313651.300359495623
0.1325382.1509890471541.295816806852
0.132922.1547979635631.291342306868
0.1333032.1585271364171.286938809988
0.1336872.1621791147891.282609115213
0.1340732.1657565438011.27835600533
0.1344592.1692621676121.274182245873
0.1348472.17269883261.270090583934
0.1352352.1760694907371.266083746785
0.1356252.1793772031681.262164440311
0.1360162.1826251439931.258335347231
0.1364082.1858166042461.254599125066
0.1368012.1889549960931.250958403859
0.1371962.1920438572211.2474157836
0.1375912.1950868554421.243973831333
0.1379882.1980877934971.24063507793
0.1383852.201050614061.23740201448
0.1387842.2039794049311.234277088276
0.1391842.2068784044231.231262698368
0.1395852.2097520069241.228361190632
0.1399882.2126047686221.225574852328
0.1403912.2154414133891.222905906104
0.1407962.2182668387911.220356503402
0.1412022.2210861222241.217928717227
0.1416092.2239045271261.215624534227
0.1420172.2267275092671.213445846034
0.1424262.2295607230551.21139443983
0.1428372.2324100278411.209471988063
0.1432482.2352814941661.207680037283
0.1436612.2381814099171.206019996027
0.1440752.2411162863111.204493121701
0.1444912.2440928636671.203100506408
0.1449072.2471181168831.201843061653
0.1453252.2501992605351.200721501881
0.1457442.2533437535231.199736326777
0.1461642.2565593031381.198887802287
0.1465852.2598538684721.198175940297
0.1470082.2632356630211.197600476919
0.1474312.2667131563591.197160849345
0.1478562.2702950747371.196856171228
0.1482822.2739904004391.196685206546
0.148712.277808369721.196646341931
0.1491392.2817584691361.196737557458
0.1495682.2858504300661.196956395864
0.152.2900942211811.197299930236
0.1504322.2945000386531.197764730183
0.1508652.2990782938211.198346826543
0.15132.3038395980531.199041674693
0.1517362.3087947445211.199844116564
0.1521742.3139546865841.200748341487
0.1526122.3193305124531.201747846028
0.1530522.3249334158371.202835393016
0.1534932.3307746622031.204002969991
0.1539362.3368655503291.205241747377
0.154382.34321736881.206542036706
0.1548252.3498413470971.20789324929
0.1552712.3567486009441.209283855797
0.1557182.3639500716031.210701347254
0.1561672.3714564587961.212132198066
0.1566172.3792781470051.213561831722
0.1570692.3874251249051.21497458992
0.1575222.3959068977651.216353705961
0.1579762.4047323927081.217681283291
0.1584312.41390985681.218938280205
0.1588882.4234467480441.220104501772
0.1593462.4333496194721.221158600133
0.1598052.443623996661.2220780844
0.1602652.4542742491591.222839341414
0.1607272.4653034564911.223417668715
0.1611912.4767132696081.223787321053
0.1616552.4885037688761.223921571805
0.1621212.5006733199411.223792790631
0.1625892.5132184290651.223372538634
0.1630572.5261335998091.222631682185
0.1635272.5394111932251.221540526446
0.1639982.5530412941.22006896938
0.1644712.5670115852841.218186676809
0.1649452.5813072351931.215863278735
0.1654212.5959107982071.21306858675
0.1658982.6108021349011.209772831885
0.1663762.625958353521.205946921746
0.1668552.6413537770331.201562715176
0.1673362.6569599392051.196593312044
0.1678192.6727456130881.191013355109
0.1683022.6886768750771.184799340187
0.1687872.7047172072221.177929930196
0.1692742.7208276399441.170386267966
0.1697622.7369669365991.162152282163
0.1702512.753091820451.153214980151
0.1707422.7691572436481.143564721285
0.1712342.7851166967121.133195463974
0.1717282.800922555821.122104979829
0.1722222.8165264640381.110295028506
0.1727192.8318797413791.097771487324
0.1732172.8469338174841.084544430485
0.1737162.861640679661.070628153698
0.1742172.8759533282141.056041141218
0.1747192.8898262303661.040805973678
0.1752232.9032157636941.024949176631
0.1757282.9160806400351.008501011283
0.1762342.9283823010030.9914952105302
0.1767422.9400852769110.9739686649305
0.1772512.9511575017610.955961064656
0.1777622.9615705781210.9375145046745
0.1782752.9712999870990.9186730613698
0.1787892.9803252401510.8994823494683
0.1793042.9886299710690.8799890684785
0.1798212.9962019681560.8602405478679
0.1803393.0030331481390.8402842998975
0.1808593.0091194748520.8201675884393
0.181383.014460826990.7999370212635
0.1819033.0190608202740.7796381722367
0.1824273.0229265901970.7593152386928
0.1829533.0260685420470.7390107379734
0.183483.02850007520.7187652458487
0.1840093.0302372886810.6986171782727
0.184543.0312986748440.6786026167538
0.1850723.0317048076080.6587551765527
0.1856053.0314780311550.6391059160045
0.186143.0306421543760.619683284496
0.1866773.0292221555870.6005131060357
0.1872153.0272439013150.5816185949205
0.1877543.0247338821470.5630203997321
0.1882953.0217189679330.5447366717594
0.1888383.0182261838960.5267831539424
0.1893833.0142825085810.5091732865253
0.1899283.0099146940060.491918325798
0.1904763.0051491078830.4750274725462
0.1910253.0000115973730.4585080071304
0.1915752.9945273735090.4423654284334
0.1921282.988720915160.4266035942551
0.1926812.982615891230.4112248610681
0.1932372.9762350996560.3962302213788
0.1937942.9696004217130.3816194372508
0.1943522.9627327900710.3673911688361
0.1949132.9556521691190.3535430970246
0.1954742.9483775460490.3400720395608
0.1960382.9409269313190.3269740601813
0.1966032.9333173671380.3142445705094
0.197172.9255649427610.3018784245946
0.1977382.9176848154450.2898700061114
0.1983082.909691236040.2782133083379
0.1988792.9015975782840.2669020071145
0.1994532.8934163709780.25592952705
0.2000282.8851593323110.2452891012877
0.2006042.8768374056940.2349738251788
0.2011822.868460796560.2249767042327
0.2017622.8600390096530.2152906967234
0.2023442.8515808863990.2059087513358
0.2029272.843094642050.1968238402339
0.2035122.8345879022890.1880289879204
0.2040992.826067739110.1795172962493
0.2046872.8175407057710.1712819659344
0.2052772.8090128706930.1633163148808
0.2058682.8004898502030.1556137936462
0.2064622.7919768400460.1481679983208
0.2070572.7834786456330.1409726810925
0.2076542.7749997109790.1340217587461
0.2082522.7665441463510.1273093193247
0.2088532.7581157546210.1208296271627
0.2094552.749718056360.1145771264812
0.2100582.7413543136930.1085464437213
0.2106642.7330275529790.1027323887715
0.2112712.7247405863470.09712995523365
0.211882.7164960321650.09173431985444
0.2124912.7082963344920.08654084123894
0.2131032.7001437815850.08154505794901
0.2137172.692040523530.07674268607884
0.2143332.6839885890750.07212961638949
0.2149512.6759899017470.0677019110753
0.2155712.6680462953180.06345580022607
0.2161922.6601595287330.0593876780419
0.2168152.652331300570.05549409884997
0.217442.6445632631420.05177177296683
0.2180672.6368570363450.04821756244409
0.2186962.6292142213730.04482847673021
0.2193262.6216364144330.04160166827694
0.2199582.6141252206030.03853442811505
0.2205922.606682268020.0356241814205
0.2212282.5993092226040.03286848308941
0.2218662.5920078035690.03026501333761
0.2225052.5847798000230.02781157333833
0.2231462.5776270890750.02550608091007
0.223792.5705516559260.02334656626464
0.2244352.5635556166230.02133116782434
0.2250822.5566412443520.01945812811543
0.225732.5498110005060.01772578974359
0.2263812.5430675722150.01613259145458
0.2270332.5364139188360.01467706427994
0.2276882.5298533310940.01335782776219
0.2283442.5233895086040.01217358624508
0.2290022.5170266650670.01112312519897
0.2296622.5107696770090.01020530752446
0.2303242.5046243051580.009419069725543
0.2309882.4985975466880.008763417735856
0.2316542.492698250340.008237421925818
0.2323222.486938354580.007840210068212
0.2329912.4813361146490.00757095388294
0.2336632.4759345197220.007423284210032
0.2343362.4707578586470.007308533793683
0.2350122.4657471612770.007196316583597
0.2356892.460877527330.007086826349679
0.2363692.4561337634970.006980253383246
0.237052.451504797960.00687680512433
0.2377332.4469819019680.006776714862
0.2384182.4425578744980.006680247204617
0.2391062.4382265983420.006587702050292
0.2397952.433982772040.006499417534474
0.2404862.4298217365120.006415772056123
0.2411792.4257393575050.006337185338289
0.2418742.4217319431960.006264118413946
0.2425722.4177961851010.006197072399135
0.2432712.413929115010.006136585907172
0.2439722.4101280732290.006083230964118
0.2446752.4063906849270.006037607304338
0.245382.4027148422580.006000334954748
0.2460882.3990986905450.00597204505644
0.2467972.3955406171580.005953368921819
0.2475082.3920392419940.005944925383133
0.2482222.3885934086280.005947306552589
0.2489372.3852021753760.005961062183153
0.2496552.3818648055980.005986682890201
0.2503742.3785807566850.006024582564496
0.2510962.3753496672930.006075080373475
0.251822.372171342460.006138382807256
0.2525462.3690457363870.006214566274779
0.2532742.3659729327330.006303560791032
0.2540042.3629531224480.00640513531546
0.2547362.3599865792250.006518885302164
0.255472.3570736328290.006644223002668
0.2562062.3542146406340.006780371020929
0.2569452.3514099578240.006926359557988
0.2576852.3486599068160.007081027701055
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0.259922.3407396363060.007582782328935
0.2606692.3382096219070.007757026139841
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0.2659742.3219894354860.008870083268087
0.2667412.3198713695590.008988928659425
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0.2682812.3157669717170.009177514684118
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0.272172.3061605625790.009302765649306
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0.2737412.3025236189290.009200101632565
0.274532.3007382794080.009115916362927
0.2753212.2989715418470.009010562875579
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0.2769112.2954841407410.008739947498162
0.2777092.2937590058450.008576995558428
0.2785092.2920435731610.008397447456759
0.2793122.2903360912660.008202858341098
0.2801172.288635026820.00799489346087
0.2809252.2869390714750.007775298984597
0.2817342.2852471445630.007545872860515
0.2825462.283558391740.0073084363419
0.2833612.2818721798550.007064806742839
0.2841782.2801880883880.006816771922133
0.2849972.2785058978520.006566066916098
0.2858182.276825575610.006314353058229
0.2866422.2751472595860.006063199838115
0.2874682.2734712403570.00581406966643
0.2882972.2717979421170.005568305629962
0.2891282.2701279029790.005327122242619
0.2899612.2684617550850.005091599127197
0.2907972.2668002049120.004862677499809
0.2916352.265144014170.004641159275292
0.2924762.2634939815960.004427708568414
0.2933192.2618509259280.004222855332402
0.2941642.2602156702650.004027000853204
0.2950122.2585890279850.003840424804554
0.2958622.2569717903250.003663293564625
0.2967152.255364715690.003495669498962
0.297572.2537685206970.003337520925418
0.2984282.2521838729410.003188732493864
0.2992882.250611385410.003049115735228
0.3001512.2490516124760.002918419559822
0.3010162.2475050473280.002796340512734
0.3018842.2459721207340.002682532623168
0.3027542.244453200980.00257661671412
0.3036272.2429485948360.002478189067687
0.3045022.2414585494030.002386829368991
0.3053792.2399832546760.002302107877525
0.306262.2385228466960.002223591798205
0.3071422.2370774111370.00215085084532
0.3080282.2356469872080.002083462010591
0.3089162.2342315717530.002021013561747
0.3098062.2328311234460.001963108310299
0.3106992.2314455669870.001909366196689
0.3115952.2300747972340.001859426247968
0.3124932.2287186831850.001812947967648
0.3133932.2273770717950.001769612219849
0.3142972.226049791550.001729121670419
0.3152032.22473665580.001691200846755
0.3161112.2234374658120.001655595875813
0.3170222.2221520135550.001622073956554
0.3179362.2208800841850.001590422619073
0.3188532.2196214582650.001560448818186
0.3197722.2183759137060.001531977904398
0.3206932.2171432274460.001504852510258
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Showing 2,000 of 2431 rows. Download the CSV for all of them.

Optical transmission calculator

Free-standing sample in vacuum, normal incidence
Method
Transmittance T
—
Reflectance R
—

Fresnel reflection calculator

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