Optical constants

Refractive index of HfO₂ (Hafnium dioxide, Hafnia)

Siefke et al. 2026: Thin film; n,k 0.124–0.620 µm

Data: tabulated nk
Range: 0.124–0.6199 µm
Points: 201
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.91078
Extinction coefficient k: 0

Permittivity ε₁: 3.65108
Permittivity ε₂: 0

Absorption coefficient α: 0 cm⁻¹
Penetration depth δ = λ/(2πk): — nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -0.129815 µm⁻¹

Group index n_g: 1.98706
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

# HfO2 (Hafnium dioxide, Hafnia): Siefke et al. 2026: Thin film; n,k 0.124–0.620 µm
hfo2 = ls.fetch_refractiveindex("main", "HfO2", "Siefke", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(hfo2.range_nm)  # (123.984, 619.921) nm
eps = hfo2.eps([277])  # 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_77f21424d918/lightsmith"
hfo2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(hfo2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (hfo2/siefke-2026).

# ... load hfo2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=hfo2)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=619, 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

HfO₂ thin films deposited by plasma-enhanced atomic layer deposition (PEALD)

Conditions

film thickness: 220e-9
substrate: SiO2

References

T. Siefke, K. Gerold, S. Shestaeva, P. Paul, S. Alam, D. Franta, A. Szeghalmi, S. Schröder, S. Kroker. Atomic layer deposition for hafnium oxide-based meta-optics in the ultraviolet spectral range. J. Eur. Opt. Society-Rapid Publ. 22, 33 (2026) (Numerical data kindly provided by Thomas Siefke)

doi:10.1051/jeos/2026036 Atomic layer deposition for hafnium oxide-based meta-optics in the ultraviolet spectral range, Journal of the European Optical Society-Rapid Publications (2026)

Cite

Thomas Siefke et al.. Atomic layer deposition for hafnium oxide-based meta-optics in the ultraviolet spectral range. Journal of the European Optical Society-Rapid Publications, 22, 33 (2026), doi:10.1051/jeos/2026036; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

201 rows as published

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

HfO2 (Hafnium dioxide, Hafnia), Siefke et al. 2026: Thin film; n,k 0.124–0.620 µm: n and k versus wavelength
λ (µm)	n	k
0.1239842	2.3994	1.23641
0.1244821	2.39567	1.20408
0.1249841	2.3915	1.17296
0.1254901	2.38233	1.14697
0.1260002	2.37316	1.12097
0.1265145	2.36399	1.09626
0.127033	2.35324	1.07172
0.1275558	2.3416	1.04885
0.1280828	2.32996	1.03102
0.1286143	2.31832	1.01303
0.1291502	2.30653	0.99395
0.1296906	2.29474	0.97487
0.1302355	2.28294	0.96153
0.130785	2.27052	0.94886
0.1313392	2.25751	0.93592
0.1318981	2.24449	0.92259
0.1324617	2.23147	0.91124
0.1330302	2.21994	0.90287
0.1336037	2.20843	0.89451
0.134182	2.19691	0.88962
0.1347654	2.18539	0.88498
0.1353539	2.17439	0.88044
0.1359476	2.16543	0.8767
0.1365465	2.15647	0.8767
0.1371507	2.14751	0.8767
0.1377602	2.13854	0.87814
0.1383752	2.12958	0.88178
0.1389957	2.12062	0.88542
0.1396218	2.11166	0.89026
0.1402536	2.1071	0.89541
0.1408911	2.10357	0.90057
0.1415345	2.10004	0.90577
0.1421837	2.09652	0.91127
0.1428389	2.09575	0.9178
0.1435002	2.09575	0.92433
0.1441677	2.09653	0.93181
0.1448413	2.10343	0.9395
0.1455214	2.11032	0.9479
0.1462078	2.11722	0.95652
0.1469007	2.12512	0.96477
0.1476002	2.13421	0.9715
0.1483065	2.14331	0.97824
0.1490195	2.15326	0.98111
0.1497394	2.16763	0.98334
0.1504663	2.18199	0.98394
0.1512002	2.19636	0.98394
0.1519414	2.211	0.98348
0.1526899	2.22601	0.98184
0.1534458	2.24102	0.9802
0.1542092	2.25602	0.97951
0.1549802	2.2701	0.9803
0.155759	2.28228	0.97841
0.1565457	2.29605	0.97216
0.1573403	2.31069	0.966
0.1581431	2.32533	0.9607
0.1589541	2.33996	0.9554
0.1597734	2.35325	0.9488
0.1606013	2.36614	0.94174
0.1614378	2.37903	0.93641
0.162283	2.39343	0.93282
0.1631371	2.41324	0.92893
0.1640003	2.43305	0.92494
0.1648726	2.45287	0.91773
0.1657543	2.47268	0.90956
0.1666454	2.49709	0.90066
0.1675462	2.52364	0.89137
0.1684568	2.55019	0.87369
0.1693773	2.57674	0.85258
0.170308	2.60217	0.82735
0.1712489	2.61847	0.80071
0.1722003	2.63476	0.7716
0.1731623	2.65035	0.73837
0.1741351	2.66012	0.70433
0.1751189	2.66989	0.66951
0.1761139	2.67777	0.6327
0.1771203	2.68233	0.5981
0.1781382	2.68689	0.56861
0.1791679	2.68861	0.53909
0.1802096	2.68192	0.50946
0.1812634	2.67524	0.48268
0.1823297	2.66856	0.45924
0.1834086	2.66188	0.4362
0.1845003	2.65599	0.41382
0.1856051	2.6508	0.39083
0.1867232	2.64561	0.36717
0.1878548	2.64042	0.34225
0.1890003	2.63523	0.31652
0.1901598	2.63004	0.29113
0.1913336	2.62485	0.26757
0.192522	2.61374	0.244
0.1937253	2.59768	0.22065
0.1949437	2.58162	0.1976
0.1961775	2.56556	0.17454
0.1974271	2.5495	0.15349
0.1986926	2.53344	0.13802
0.1999745	2.51738	0.12255
0.201273	2.50132	0.10792
0.2025886	2.48526	0.09453
0.2039214	2.46921	0.08113
0.2052718	2.45315	0.07079
0.2066403	2.43719	0.06176
0.2080272	2.42305	0.05381
0.2094328	2.4089	0.04728
0.2108575	2.39476	0.04075
0.2123017	2.38061	0.03422
0.2137658	2.36647	0.02945
0.2152503	2.35233	0.02511
0.2167556	2.33818	0.02076
0.218282	2.32404	0.01641
0.2198301	2.30989	0.01206
0.2214003	2.29575	0.00772
0.2229932	2.2816	0.00337
0.224609	2.26867	0.0
0.2262485	2.25967	0.0
0.2279121	2.25066	0.0
0.2296004	2.24165	0.0
0.2313138	2.23264	0.0
0.233053	2.22363	0.0
0.2348185	2.21462	0.0
0.2366111	2.20561	0.0
0.2384311	2.1966	0.0
0.2402794	2.18759	0.0
0.2421566	2.17858	0.0
0.2440634	2.16957	0.0
0.2460004	2.16056	0.0
0.2479684	2.1524	0.0
0.2499681	2.14637	0.0
0.2520004	2.14034	0.0
0.254066	2.13432	0.0
0.2561657	2.12829	0.0
0.2583004	2.12227	0.0
0.260471	2.11624	0.0
0.2626784	2.11021	0.0
0.2649235	2.10419	0.0
0.2672073	2.09816	0.0
0.2695309	2.09213	0.0
0.2718952	2.08611	0.0
0.2743013	2.08042	0.0
0.2767504	2.07575	0.0
0.2792437	2.07108	0.0
0.2817823	2.06641	0.0
0.2843674	2.06174	0.0
0.2870004	2.05707	0.0
0.2896827	2.0524	0.0
0.2924155	2.04773	0.0
0.2952005	2.04306	0.0
0.2980389	2.03839	0.0
0.3009325	2.03372	0.0
0.3038828	2.02905	0.0
0.3068916	2.02439	0.0
0.3099605	2.01986	0.0
0.3130914	2.01721	0.0
0.3162862	2.01456	0.0
0.3195469	2.01191	0.0
0.3228755	2.00925	0.0
0.3262742	2.0066	0.0
0.3297452	2.00395	0.0
0.3332908	2.0013	0.0
0.3369136	1.99864	0.0
0.3406159	1.99599	0.0
0.3444005	1.99334	0.0
0.3482702	1.99069	0.0
0.3522278	1.98796	0.0
0.3562764	1.9849	0.0
0.3604192	1.98184	0.0
0.3646594	1.97878	0.0
0.3690006	1.97571	0.0
0.3734464	1.97265	0.0
0.3780006	1.96959	0.0
0.3826673	1.96653	0.0
0.3874506	1.96347	0.0
0.392355	1.96041	0.0
0.3973852	1.95734	0.0
0.4025461	1.95428	0.0
0.4078427	1.95122	0.0
0.4132806	1.94816	0.0
0.4188655	1.94613	0.0
0.4246034	1.94437	0.0
0.4305007	1.94261	0.0
0.4365641	1.94085	0.0
0.4428007	1.9391	0.0
0.4492181	1.93734	0.0
0.4558242	1.93558	0.0
0.4626276	1.93383	0.0
0.4696371	1.93207	0.0
0.4768623	1.93031	0.0
0.4843133	1.92855	0.0
0.4920008	1.9268	0.0
0.4999363	1.92504	0.0
0.5081319	1.92328	0.0
0.5166008	1.92153	0.0
0.5253567	1.91993	0.0
0.5344146	1.91846	0.0
0.5437903	1.917	0.0
0.5535009	1.91553	0.0
0.5635645	1.91407	0.0
0.5740009	1.91261	0.0
0.5848311	1.91114	0.0
0.5960779	1.90968	0.0
0.6077657	1.90821	0.0
0.619921	1.90675	0.0

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: —

HfO₂ (Hafnium dioxide, Hafnia): all datasets

Thin film

About HfO2 (Hafnium dioxide, Hafnia)

Hafnium dioxide (HfO₂) is a high-index, low-absorption material used extensively in optical applications. It is especially valuable for making thin-film dielectric coatings for mirrors, anti-reflective coatings, and beam splitters. Due to its excellent thermal stability and resistance to chemical corrosion, it is well-suited for harsh environments. Additionally, its high refractive index makes it an attractive material for planar waveguides and other integrated optics components. Beyond its optical uses, hafnium dioxide is also a key material in the fabrication of advanced gate dielectrics in field-effect transistors, contributing to the miniaturization and performance improvement of electronic devices.

More about HfO2 (Hafnium dioxide, Hafnia) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/HfO2/nk/Siefke.yml
ID: ds_77f21424d918
API: /v1/datasets/ds_77f21424d918

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