herzinger_1998

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation”, J. Appl. Phys. 83, 3323-3336 (1998)

Source record · Catalogue · Review register

DOI: 10.1063/1.367101

Source kind: measurement

Recorded technique: Variable-angle spectroscopic ellipsometry, 0.75-6.5 eV, with a J. A. Woollam VASE rotating-analyzer ellipsometer with an auto-retarder input unit (Delta measured over 360 deg; psi within 0.02 deg of 45 deg and Delta within 0.2 deg of 0 deg in a straight-through test), polarizer tracking psi, zone averaging over polarizer and retarder positions (p. 2). Six thermal oxides on <100> Si wafers (lightly boron doped, 14-22 Ohm cm, 125 mm CMOS wafers; nominal 10.5, 14.5, 35, 50, 100 and 350 nm, grown at Motorola in dry O2 with low HCl, pure O2 or steam at 900-1050 deg C) at 40 and 75 deg, and one sample with a native oxide over 2 years old at 70 and 79 deg. All seven analysed together (multi-sample) by Levenberg-Marquardt fits of psi and Delta weighted by their regression errors (Eq. 2), with oxide, interface and substrate models of increasing complexity (fit classes a-c, Tables II-IV; 54 fits). The final fit, #c4(iv), has 77 parameters: Si described by a Kramers-Kronig consistent parametric model (Gaussian-broadened critical points built from polynomial sections, 58 parameters; details ‘not discussed here’, Ref. 25, unpublished), thermal SiO2 by a Sellmeier form, and a transparent interface layer about 1 nm thick (p. 5, p. 11).

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 0 formulas.

Curation notes

Pdf pages 1-14 (J. Appl. Phys. pp. 3323-3336). Identity: the library’s record is VALIDATED_WITH_WARNINGS (a repository copy of the publisher’s pdf); title, authors, journal, volume and pages agree with the first page. No datasets: the paper prints no silicon optical constants as numbers.

WHAT IS AND IS NOT PRINTED. The silicon result, Si-final (0.75-6.5 eV, fit #c4(iv)), is shown only in figures: Fig. 4 (epsilon_1 and epsilon_2 against Si-Aspnes and Si-Jellison, 0-7 eV), Fig. 10 (n extrapolated to low energy against Palik’s tables) and Fig. 11 (k near the gap against Hulthen, McFarlane, Dash, Aspnes and Jellison). ‘Tabulated values for Si-final are available electronically through the Physics Auxiliary Publication Service’ (p. 5; no document number is printed); the deposit is not in the library, and the parametric model’s parameters are not printed. The figures are not digitised: the values are published as numbers in the deposit, which is to be sought (TC-699). Temperature not stated. Tables II-IV give the fit quality xi_0 of the 54 multi-sample fits; Tables V-VI the oxide (and interface) thicknesses of samples 1-6 fitted at 1.5-5.3 eV with Si-Aspnes, Si-Jellison or Si-final (no optical data; not extracted).

THERMAL SiO2 AND INTERFACE (pp. 4-5; not recorded as formulas: optmat has no thermal oxide material, and SiO2 is silica glass). The form is n^2 = offset + a lambda^2/ (lambda^2 - b^2) - c lambda^2 (Eq. 4, lambda in um), checked on the page image: Glass-Sellmeier, a fit to Palik’s glass tables (Philipp’s chapter: Malitson’s and Brixner’s prism data below 5.8 eV, Kramers-Kronig of reflectance above) over 0.75-6.5 eV, offset 1.4923, a 0.61497, b 0.115 um, c 0.01059 um^-2, ‘agreement to within 0.001 (0.07 %)’; SiO2-final (thermal oxide, fit #c4(iv)), offset 1.3000, a 0.81996, b 0.10396 um, c 0.01082 (unit not printed), n = 1.4655 at 546.1 nm against 1.4602 for Glass-Palik and Aspnes’s thermal-oxide 1.4631; Native-Jellison, offset 1, a 2.0, b 0.09227 um, c 0 (jellison_1992’s Eq. 4); Interface-final, offset 3.5, a 0.69417, b 0.115 um, c 0.010591 um^-2, n = 2.04 at 546.1 nm. CHECKS (2026-10-14): SiO2-final gives 1.46546 at 546.1 nm (printed 1.4655), Glass-Sellmeier 1.46036 (Palik 1.4602). The interface’s a = 0.69417 contradicts the text (‘interfacial Sellmeier models used the a, b, and c parameters used to describe glass ... only the offset parameter was adjustable’) and its printed index: with a = 0.61497 (Glass-Sellmeier’s) n(546.1 nm) = 2.035, rounding to the printed 2.04; with 0.69417, 2.055. So 0.69417 is presumably a transposition of 0.61497. The thermal oxide is ‘approximately 0.4 % higher in index than published values for bulk glasseous SiO2’ (abstract), independent of the interface model (within 0.00035 for interface offsets 2, 3.5 and 5, p. 11).

FINDINGS ON SILICON (pp. 11-14). The interface’s index and thickness correlate with the silicon epsilon_2 peak for offsets above 3.5 (Fig. 9); offset = 3.5 was chosen by judgement, not by the fit (‘there is no mathematically objective approach to selecting the proper offset’, p. 12): so Si-final’s E2 peak height carries this choice. Single-layer oxide fits (Table V, 1.5-5.3 eV) with Si-Aspnes give oxide thicknesses 0.18 nm lower on average than with Si-Jellison or Si-final (which agree within 0.03 nm): ‘fully expected if the Si-Aspnes optical constants internally retained the effect of 0.18 nm of oxide’ (p. 13), consistent with Aspnes’s later NH4F-prepared surfaces (Yasuda and Aspnes, Appl. Opt. 33, 7435 (1994): 0.2 nm of SiO2-equivalent overlayer, p. 14). Si-final’s extrapolated n matches Palik’s tables below 0.5 eV (Fig. 10), and its k near the gap lies on McFarlane’s, ‘probably coincidental’ (Fig. 11, p. 12). The paper cites Aspnes and Studna’s Si as ‘Phys. Rev. B 27, 7466 (1983)’ (Ref. 1), as jellison_1992 does, not aspnes_1983’s 985.

COMPARISON. No refractiveindex.info page holds this paper’s silicon (data/external/refractiveindex_info/main/Si/nk has no Herzinger file).

Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets

No datasets are recorded.

Formulas

No formulas are recorded.

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.