A Sensitive and Versatile Thickness Determination Method Based on Non-Inflection Terahertz Property Fitting
Open accessAbstract
The accuracy of thin-film characterization in terahertz spectroscopy is mainly set by the thickness uncertainty. Physical thickness measurement has limited accuracy for thin-film samples thinner than a few hundreds of micrometers and is sometimes even impossible. The temporal resolution of time-domain terahertz spectrometers is not sufficient to resolve such thin films. Previously reported numerical methods mainly only work for materials with low dispersion and absorption. Here, we propose a novel method for thickness determination by fitting a non-inflection offset exponential function to the material optical properties. Theoretical analysis predicts the best fitting to only be achieved when the correct thickness is given. Transmission measurements on a thin-film polymer, water, and a lactose pallet verify the theory and show the accurate thickness determination and property characterization on materials which are either achromatic or dispersive, transparent or absorptive, featureless or resonant. The measurements demonstrate the best versatility and sensitivity compared to the state-of-art. The method could be widely adapted to various types of research and industrial applications.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The layer of air modifies the refractive index shape by introducing inflection.
“Because the layer of air modifies the refractive index shape by introducing inflection (see Fig. 3), its thickness is determined by the method developed in Ref. [16].”
From Methods for fast and accurate material properties estimate with terahertz time-domain spectroscopy in transmission and reflection with optically thick materials (2024) · cites this paper as [16]
The Method section (page not provided) says that using an incorrect sample thickness produces Fabry–Perot oscillations and inflection points in the extracted refractive index, which the proposed fitting method uses to determine thickness. It does not establish that a layer of air specifically introduces those inflections. (LLM, conf=0.84)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
The citation lists haven’t been fetched yet
References 27 · Cited by 18
Research works printed but not linked: 22
- [1]Fujiwara H. Spectroscopic Ellipsometry Principles and Applications John Wiley & Sons Chichester, UK 2007 9780470016084
- [2]Dorney T.D. Baraniuk R.G. Mittleman D.M. Material parameter estimation with terahertz time-domain spectroscopy Opt. Soc. Am. 2001 18 1562 1571 10.1364/JOSAA.18.001562 11444549 · DOI · Paper page
- [4]Kindt J.T. Schmuttenmaer C.A. Far-Infrared Dielectric Properties of Polar Liquids Probed by Femtosecond Terahertz Pulse Spectroscopy J. Phys. Chem. 1996 100 10373 10379 10.1021/jp960141g · DOI
- [5]Grischkowsky D. Keiding S. van Exter M. Fattinger C. Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors J. Opt. Soc. Am. B 1990 7 2006 2015 10.1364/JOSAB.7.002006 · DOI · Paper page
- [7]Naftaly M. Miles R.E. Terahertz Time-Domain Spectroscopy for Material Characterization Proc. IEEE 2007 95 1658 1665 10.1109/JPROC.2007.898835 · DOI · Paper page
- [8]Cunningham P.D. Valdes N.N. Vallejo F.A. Hayden L.M. Polishak B. Zhou X.H. Luo J. Jen A.K.Y. Williams J.C. Twieg R.J. Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials J. Appl. Phys. 2011 109 043505 10.1063/1.3549120 · DOI
- [9]Pupeza I. Wilk R. Koch M. Highly accurate optical material parameter determination with THz time-domain spectroscopy Opt. Express 2007 15 4335 10.1364/OE.15.004335 19532679 · DOI · Paper page
- [10]Duvillaret L. Garet F. Coutaz J.-L. Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy Appl. Opt. 1999 38 409 415 10.1364/AO.38.000409 18305628 · DOI · Paper page
- [12]Fastampa R. Pilozzi L. Missori M. Cancellation of Fabry-Perot interference effects in terahertz time-domain spectroscopy of optically thin samples Phys. Rev. A 2017 95 1 6 10.1103/PhysRevA.95.063831 · DOI
- [13]Taschin A. Bartolini P. Tasseva J. Torre R. THz time-domain spectroscopic investigations of thin films Meas. J. Int. Meas. Confed. 2018 118 282 288 10.1016/j.measurement.2017.05.074 · DOI
- [14]Yang F. Liu L.P. Song M.J. Zhang F. Fast Determination of Optical Constants and Sample Thickness of Thin Liquid Samples in Terahertz Time-Domain Spectroscopy J. Appl. Spectrosc. 2018 85 891 896 10.1007/s10812-018-0735-0 · DOI
- [15]Rønne C. Thrane L. Åstrand P.O. Wallqvist A. Mikkelsen K.V. Keiding S.R. Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation J. Chem. Phys. 1997 107 5319 5331 10.1063/1.474242 · DOI
- [16]Chen X. Parrott E.P.J. Huang Z. Chan H. Pickwell-MacPherson E. Robust and Accurate Terahertz Time-Domain Spectroscopic Ellipsometry Photonics Res. 2018 6 768 775 10.1364/PRJ.6.000768 · DOI
- [17]He Y. Liu K. Au C. Sun Q. Parrott E.P.J. Pickwell-MacPherson E. Determination of terahertz permittivity of dehydrated biological samples Phys. Med. Biol. 2017 62 8882 8893 10.1088/1361-6560/aa8ebe 28944763 · DOI
- [18]Markelz A.G. Roitberg A. Heilweil E.J. Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz Chem. Phys. Lett. 2000 320 42 48 10.1016/S0009-2614(00)00227-X · DOI
- [19]Liu Z. Huang C.-Y. Liu H. Zhang X. Lee C. Resonance enhancement of terahertz metamaterials by liquid crystals/indium tin oxide interfaces Opt. Express 2013 21 6519 6525 10.1364/OE.21.006519 23482222 · DOI
- [20]Son H. Choi D.-H. Park G.-S. Improved thickness estimation of liquid water using Kramers–Kronig relations for determination of precise optical parameters in terahertz transmission spectroscopy Opt. Express 2017 25 4509 10.1364/OE.25.004509 28241653 · DOI
- [22]Soltani A. Jahn D. Duschek L. Castro-Camus E. Koch M. Withayachumnankul W. Attenuated total reflection terahertz time-domain spectroscopy: uncertainty analysis and reduction scheme IEEE Trans. Terahertz Sci. Technol. 2015 6 1 8 10.1109/TTHZ.2015.2505909 · DOI
- [23]Yada H. Nagai M. Tanaka K. Origin of the fast relaxation component of water and heavy water revealed by terahertz time-domain attenuated total reflection spectroscopy Chem. Phys. Lett. 2008 464 166 170 10.1016/j.cplett.2008.09.015 · DOI
- [24]Nagai M. Yada H. Arikawa T. Tanaka K. Terahertz time-domain attenuated total reflection spectroscopy in water and biological solution Int. J. Infrared Millimeter Waves 2006 27 505 515 10.1007/s10762-006-9098-3 · DOI
- [25]Fischer B. Hoffmann M. Helm H. Modjesch G. Jepsen P.U. Chemical recognition in terahertz time-domain spectroscopy and imaging Semicond. Sci. Technol. 2005 20 S246 10.1088/0268-1242/20/7/015 · DOI · Paper page
- [27]Brown E.R. Fedor J.E.B.M. Korter T.M. On the strong and narrow absorption signature in lactose at 0.53 THz Appl. Phys. Lett. 2011 90 061908 10.1063/1.2437107 · DOI · Paper page
- Authors
- Chen, X., & Pickwell-MacPherson, E.
- Affiliations
- Chinese University of Hong Kong (HK)
- Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 999077, China
- ORCID
- Chen, Xuequan
- Venue
- Sensors
- Publisher
- MDPI AG
- Published
- 2019-09-23
- Volume
- 19
- Issue
- 19
- Pages
- 4118
- ISSN
- 1424-8220 (ISSN-L)
- PMC
- PMC6806189
- OpenAlex
- W2973491333
- Cited by
- 18
- References
- 27
- Citations by year
- 2026: 1 · 2024: 4 · 2023: 3 · 2022: 3 · 2021: 2 · 2020: 5
- FWCI
- 0.90
- Type
- journal article
- Language
- en
- Open access
- gold
- dx.doi.org
- Licence
- Locations
- Sensors (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- Research Grants Council, University Grants Committee (14206717, 14201415)
- Innovation and Technology Commission - Hong Kong (ITS/371/16)
- Royal Society (Wolfson Merit Award (EPM))
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Terahertz technology and applications
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Microwave and Dielectric Measurement Techniques
- Physical Sciences › Engineering › Mechanics of Materials › Thermography and Photoacoustic Techniques
- Keywords
- thin film thickness measurement, terahertz spectroscopy, dispersive materials, absorbing materials, polymer thin films, water, lactose
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
