franta_2025#
D. Franta, J. Vohánka, J. Dvořák, P. Franta, I. Ohlídal, P. Klapetek, J. Březina and D. Škoda, “Wide spectral range optical characterization of tantalum pentoxide (Ta2O5) films by the universal dispersion model”, Opt. Mater. Express 15, 903 (2025)
Source record · Catalogue · Review register
DOI: 10.1364/ome.550708
Source kind: fit
Recorded technique: Multi-sample, multi-instrument characterization of five Ta2O5 films (e-beam evaporation of crystalline Ta2O5 with an advanced plasma source, Buhler SYRUSpro 1110, substrates at 120 C, 3e-4 mbar, 20 sccm O2, 0.3 nm/s; nominal 25, 60, 85, 130, 250 nm) on float-zone c-Si: Horiba UVISEL and Woollam IR-VASE ellipsometry; McPherson VUVAS 1000 (VUV reflectance), Perkin Elmer Lambda 1050+ (relative reflectance and NIR transmittance), Bruker Vertex 80v and 70v (IR and far-IR); 25 cm-1 (400 um) to 10.7 eV (116 nm). Universal dispersion model; a homogeneous-layer (HL) model and a three-phase inhomogeneous-layer (IHL) model (pp. 904-907).
Materials in structured entries: Nb2O5, Ta2O5
Dataset quantities: band_gap, refractive_index
Contents: 4 datasets; 1 formula.
Curation notes#
Journal pages 903-918 = PDF pages 1-16. Identity checked against the first page. The films are polycrystalline with very fine grains (‘very fine polycrystalline (amorphous) material’, p. 915; AFM grain scale 3.2-5.8 nm, p. 910), assumed isotropic.
WHAT IS PRINTED. ‘The equations describing the dispersion model are given in Supplement 1’ and ‘the values of the dispersion parameters can be found in Supplement 1’ (pp. 908, 911); ‘Optical constants and UDM parameter file (parfile) are available on [58]’ (newAD2 site, p. 917). Supplement 1 (figshare doi 10.6084/m9.figshare.28349450) is not in the library, and no newAD2 parameter file of Ta2O5 was obtained: the model cannot be implemented from the paper.
UDM TERMS USED (p. 908; the forms are those of the 2017-2018 papers, not of franta_2015/franta_2015b). Electron excitations: ‘contributions combining the Tauc’s law with the Lorentz model’ (similar to Ferlauto’s Cody-Lorentz model; refs. [24, 36]: Nb2O5, Optical Materials 157, 116133 (2024), and Thin Solid Films 631, 12 (2017), neither in the library) plus an Urbach tail; parameters E_g (common to all contributions), E_ex,j and B_ex,j (peak energy and width of structure j), E_q (‘tuning the steepness of the Tauc’s law’ above E_g), E_u, and one strength per contribution; two contributions for the HL model and phases a and b of the IHL model, three for phase c. This E_q parameter does not exist in the 2015 UDM (TC-387). Phonons: nine symmetric Gaussian peaks for Ta2O5 plus 11 (HL) or 13 (IHL) peaks for water and organic contamination (p. 908), ‘the one-dimensional Dawson function’ (franta_2015b Eqs. (41)-(46)). Native oxide: UDM with fixed parameters from refs. [42-44]; substrate: the temperature-dependent ADM of franta_2017 and later papers (p. 909).
STRUCTURAL MODEL. Profile function Eq. (3), p. 906 (Eq. (4), p. 907): p(z) = sum_{i=1}^{N_p - 1} [erf((z - h_i)/w_i) - erf(-h_i/w_i)]/[1 - erf(-h_i/w_i)]; Eq. (4): each dispersion parameter interpolated linearly between phases a, b, c by p(z); fitted h_1 = 16.0(4) nm, w_1 = 1.0(2) nm, h_2 = 206(2) nm, w_2 = 30(2) nm (p. 911); Rayleigh-Rice roughness. Table 1 (p. 909): thicknesses (HL 22.32-262.62 nm, IHL 24.88-263.40 nm), substrate thicknesses, roughness (optics and two AFMs). Table 2 (p. 912): chi of the fits per instrument (all data: HL 0.9392, IHL 0.8307). Not extracted.
COMPARISONS (p. 915-916; not extracted): Rodriguez-de Marcos et al. (ref. [49], Opt. Materials Express 6, 3622 (2016); the library copy is rodriguez_de_marcos_2016) show stronger sub-gap absorption and lower peaks at 5.5 and 12 eV (thin 53 nm layers, roughness neglected); Bright et al. (ref. [50]) differ in the phonon region (Palik’s c-Si and a Lorentz model); Franke et al. (ref. [48], J. Appl. Phys. 88, 5166 (2000)) described the edge by two gaps ‘E_g1 = 4.7 eV and E_g2 = 5.4 eV’, which the authors call incorrect for an amorphous material (not recorded as band gaps).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
franta_2025/band_gap#
{
"id": "band_gap",
"material": "Ta2O5",
"table": "text",
"quantity": "band_gap",
"unit": "eV",
"abscissa": "none",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"kind": "tauc",
"form": "film"
}
}
1 inline points in the source record.
p. 916: ‘From our dispersion model, the band gap was determined at the value of 4.1099(7) eV’ (least-squares uncertainty in concise notation); p. 904: ‘E_g = 4.11 eV’ for the homogeneous-layer model. The UDM’s E_g, the onset of the Tauc-law absorption.
franta_2025/n_2eV#
{
"id": "n_2eV",
"material": "Ta2O5",
"table": "text",
"quantity": "refractive_index",
"abscissa_unit": "eV",
"use": "primary",
"parameters": {
"form": "film"
}
}
1 inline points in the source record.
p. 904: the Ta2O5 layers have ‘a lower refractive index in the transparent region (E_g = 4.11 eV, n = 2.125 at 2 eV)’ than Nb2O5, with the homogeneous-layer model. The profile of n at 632.991 nm (1.9587 eV) in the IHL model is Fig. 4 only.
franta_2025/band_gap_Nb2O5#
{
"id": "band_gap_Nb2O5",
"material": "Nb2O5",
"table": "text",
"quantity": "band_gap",
"unit": "eV",
"abscissa": "none",
"use": "reproduced",
"reproduced_from": [
"D. Franta, B. Hroncová, J. Dvořák, et al., \"Wide spectral range optical characterization of niobium pentoxide (Nb2O5) films by universal dispersion model\", Opt. Mater. 157, 116133 (2024)"
],
"parameters": {
"kind": "tauc",
"form": "film"
}
}
1 inline points in the source record.
p. 904: ‘Nb2O5 layers (E_g = 3.48 eV, n = 2.331 at 2 eV)’, from the group’s Nb2O5 paper (ref. [24]).
franta_2025/n_2eV_Nb2O5#
{
"id": "n_2eV_Nb2O5",
"material": "Nb2O5",
"table": "text",
"quantity": "refractive_index",
"abscissa_unit": "eV",
"use": "reproduced",
"reproduced_from": [
"D. Franta, B. Hroncová, J. Dvořák, et al., \"Wide spectral range optical characterization of niobium pentoxide (Nb2O5) films by universal dispersion model\", Opt. Mater. 157, 116133 (2024)"
],
"parameters": {
"form": "film"
}
}
1 inline points in the source record.
p. 904 (quoted with band_gap_Nb2O5).
Formulas#
franta_2025/profile_function#
{
"id": "profile_function",
"material": "Ta2O5",
"equation": "Eqs. (3)-(4), pp. 906-907; values p. 911",
"printed": "p(z) = \\sum_{i=1}^{N_p - 1} [erf((z - h_i)/w_i) - erf(-h_i/w_i)]/[1 - erf(-h_i/w_i)]",
"variable": "z: distance from the bottom interface (nm); N_p = 3 phases",
"coefficients": {
"h1": "16.0",
"h1_sigma": "0.4",
"w1": "1.0",
"w1_sigma": "0.2",
"h2": "206",
"h2_sigma": "2",
"w2": "30",
"w2_sigma": "2"
},
"check": "Values in concise notation as printed (16.0(4) etc.); no printed quantity to reproduce from them alone (the phase parameters are in Supplement 1)."
}
Each dispersion parameter p_j(z) = p_j^a [1 - p] + p_j^b p for p in [0, 1], p_j^b [2 - p] + p_j^c [p - 1] for p in [1, 2] (Eq. (4)). Structural, not optical; recorded because the IHL optical constants depend on it.
Corrections#
No dataset errata are recorded in this source record.
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.