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Cited by 38Terahertz technology and applicationsMicrowave and Dielectric Measurement TechniquesSuperconducting and THz Device Technology

Highly sensitive terahertz measurement of layer thickness using a two-cylinder waveguide sensor

Open access
Theuer, M., Beigang, R., Grischkowsky, D.·2010·Applied Physics Letters
DOI 10.1063/1.3481080
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Abstract

We report on the layer thickness determination on dielectrically coated metal cylinders using terahertz (THz) time-domain spectroscopy. A considerable sensitivity increase of up to a factor of 150 is obtained for layers down to 2.5 μm thickness by introducing an experimental geometry based on a two-cylinder waveguide sensor. The layer attached on one metal cylinder is guided in contact with the second metal cylinder in the THz beam waist. This approach uses concepts of adiabatic THz wave compression and the advantages of THz waveguides. The results are compared to measurements on free-standing layers.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper introduces a two-cylinder waveguide sensor for THz time-domain measurement of dielectric layer thickness on metal cylinders, using adiabatic THz wave compression and in-plane propagation through a subwavelength gap. It reports up to a 150× sensitivity increase over single-pass transmission for a 2.5 µm PET layer, with sensitivity dropping to 66× for 24.5 µm and 32× for a 50 µm gap.

Key findings

  • The two-cylinder sensor increased measured pulse delay per micron: sensitivity increase reached up to a factor of 150 for a 2.5 µm coating with cylinders in contact, dropping to 66 for a 24.5 µm coating. With a 50 µm gap, the pulse-delay factor was 74.1 fs/µm, corresponding to a sensitivity increase by a factor of 32.
  • For free-standing thick PE cling wrap (12.5 µm, n_PE = 1.52), the measured pulse-delay factor was 2.1 fs/µm versus 1.7 fs/µm for theory, indicating the film was 15.1 µm thick, within manufacturing specifications. For thin PET Mylar layers (2.5/3.5 µm, n_PET = 1.7), theory gave 2.3 fs/µm, while measured up-run and down-run factors were 3.5 and 3.1 fs/µm; the total reference drift was 0.014 ps, corresponding to 6.0 µm, giving a relative error above 200% for the down-run 2.5 µm sample.
  • With cylinders in contact, theory for g = 0 µm predicted larger delays than observed, especially for thin layers; an averaged tiny gap of g = 2 µm, in the order of surface roughness, showed good agreement with measurements. A 50 µm gap gave nearly linear delay versus coating thickness and good agreement with theory.
  • The authors conclude that detection of layers below 1 µm is feasible with the two-cylinder waveguide sensor, and that the technique’s limit is no longer long-term thermal stability but the accuracy of the gap and sample mount.

Methods

  • THz time-domain spectroscopy (THz-TDS) was used with the beam waist centered between two parabolic mirrors. Free-standing films were measured in single-pass transmission. The two-cylinder sensor wrapped the film on one 63 mm diameter metal cylinder, with an opposing 63 mm cylinder in direct contact or separated by spacer-defined gaps, placed in the THz beam waist; the wave was compressed from a ~9 mm diameter spot at 1 THz to a subwavelength line focus of less than 10 µm, with in-plane propagation through the gap.
  • Samples were Mylar PET films of 2.5 or 3.5 µm thickness (n_PET = 1.7) and PE cling wrap of 12.5 µm thickness (n_PE = 1.52), including stacks. Pulse delay was determined from zero crossings, with linear fits and theoretical curves based on Eq. (1) and a partially filled parallel-plate waveguide model.
  • Sensitivity was computed as the ratio of the measured stretched delay of the two-cylinder waveguide sensor to the theoretical single-pass delay.

Limitations

  • The paper states that thermal drift was the largest influence: the reference zero delay drifted by approximately 20 fs/h, and long-term stability limited reliable investigation of sub-10 µm thin film samples within one measurement series. For layers below 10 µm, systematic error increased considerably; during a measurement time of approximately three hours, the total reference drift was 0.014 ps, corresponding to a layer thickness of 6.0 µm, giving a relative error above 200% for the down-run 2.5 µm sample. The paper notes this drift can be subtracted.
  • The paper states that residual gaps from machining accuracy and surface roughness reduce the filling factor and delay, requiring a calibration curve for the actual gap and sample. The limit of the technique is defined by the accuracy of the gap and sample mount, not thermal stability.
  • Evident from the text: validation was limited to PET and PE films on 63 mm metal cylinders; no other materials, cylinder geometries, or industrial environments were tested in this paper.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1063/1.3481080

Cites

17 of 17 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 19 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    Using a two-cylinder waveguide sensor geometry, sensitivity increased by as much as a factor of 150 for layers as thin as 2.5 μm.

    “A considerable sensitivity increase of up to a factor of 150 is obtained for layers down to 2.5 m thickness by introducing an experimental geometry based on a two-cylinder waveguide sensor.”
    Quote in the paperSubstantial claim
  • Findingown data

    Layer thickness on metal cylinders with dielectric coatings was measured using terahertz time-domain spectroscopy.

    “We report on the layer thickness determination on dielectrically coated metal cylinders using terahertz ͑THz͒ time-domain spectroscopy.”
    Quote in the paperSubstantial claim
  • Findingnone given

    Additional contact pressure and independent mounts reduce this gap considerably.

    “Additional contact pressure and independent mounts decrease this gap considerably.”
    Quote in the paperNot a substantial claim
  • Findingown data

    For free-standing samples, measured delay and theoretical values agree rather well for thick layers within experimental accuracy.

    “Within the experimental accuracy, the measured delay and the theoretical values correspond rather well for thick layers.”
    Quote in the paperNot a substantial claim
  • Findingreasoning

    The reference zero delay of the system drifts by about 20 fs per hour.

    “The reference zero delay of our system drifts by approximately 20 fs/h.”
    Quote in the paperSubstantial claim
  • The quote only partly states this claim. 4
  • May combine two claims. 18
  • Classified as probably not a substantial claim. 8

  • The quote only partly states this claim.

    Findingreasoning

    For the down-run measured 2.5 μm layer sample, the relative error exceeds 200%.

    “So for the down-run measured 2.5 m layer sample, this gives a relative error above 200%.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Measured pulse-delay factor 2.1 fs/μm versus theoretical 1.7 fs/μm indicates the PE cling wrap was 15.1 μm thick instead of the expected 12.5 μm.

    “The different pulse-delay factors of 2.1 fs/ m for the measurement and 1.7 fs/ m for theory indicate that the film was 15.1 m thick, instead of the expected 12.5 m.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Subtracting the linear thermal drift with measurement time from the data points achieves consistency and makes up-run and down-run data overlap.

    “However, it is possible to subtract the linear ͑with measurement time͒ thermal drift from the data points to achieve consistency and then the up-run and down-run data will overlap.”
    Quote in the paperNot a substantial claim
    • Rests on an assumption: The thermal drift of the reference zero is linear with measurement time.

  • The quote only partly states this claim.

    Findingown data

    The total reference drift for the decreasing-thickness series was 0.014 ps, corresponding to a layer thickness of 6.0 μm.

    “The total reference drift for the series according to the linear fit for decreasing layer thicknesses was 0.014 ps corresponding to a layer thickness of 6.0 m.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    For thin PET layers, both increasing and decreasing thickness series show linear delay versus thickness but deviate largely from theory.

    “Although both series show a linear behavior of delay versus layer thickness, the deviation from theory is rather large.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The theoretical pulse-delay factor for thin PET layers is 2.3 fs/μm, while measured up-run and down-run factors are 3.5 and 3.1 fs/μm.

    “The theoretical pulse-delay factor is 2.3 fs/ m, while for the measured up-run the factor is 3.5 and 3.1 fs/ m for the down-run.”
    Quote in the paperNot a substantial claim

  • The quote only partly states this claim.

    Findingown data

    For layers below 10 μm, systematic error increases considerably.

    “The systematic error increases considerably for layers below 10 m as seen in the inset.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    For in-contact pressed cylinders and the corresponding g=2 μm theory curve, values match for thin layers, while thick layers show a transition into saturation.

    “For the in-contact pressed cylinders and the corresponding theory curve ͑g=2 m͒, the values match for thin layers, while for thick layers a transition into saturation can be observed.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The delay can be modeled by simple formulas for partially filled parallel-plate waveguides.

  • May combine two claims.

    Findingown data

    The sensitivity increase ratio of measured stretched delay to theoretical single-pass delay reaches up to 150 for a 2.5 μm coating with cylinders in contact, dropping to 66 for a 24.5 μm coating.

    “The sensitivity increase given by the ratio of measured stretched delay of the two-cylinder waveguide sensor to the theoretical single-pass delay reaches up to 150 for the 2.5 m coating and the cylinders in contact, dropping to 66 for a 24.5 m coating.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The delay can be modeled by simple formulas for partially filled parallel-plate waveguides.

  • May combine two claims.

    Findingown data

    With a 50 μm gap, the pulse-delay factor is 74.1 fs/μm, corresponding to a sensitivity increase factor of 32.

    “In the case of a 50 m gap, the pulse-delay factor is 74.1 fs/ m which corresponds to a sensitivity increase by a factor of 32.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The delay can be modeled by simple formulas for partially filled parallel-plate waveguides.

  • May combine two claims.

    Findingreasoning

    Although the inherent gap lowers the filling factor and decreases delay, it remains acceptable, gives a much higher delay than single-pass, and stays constant during measurements.

    “Although the inherent gap reduces the filling factor of the waveguide and thereby decreases the delay, it is still acceptable, shows a much higher delay than the single-pass, and remains constant during the measurements.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    With a 50 μm gap, theory predicts nearly linear delay versus coating thickness, in good agreement with measured values.

    “Working with a larger gap ͑g=50 m͒, theory predicts a nearly linear behavior of the delay as a function of coating thickness, which is also in good agreement with the measured values.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The delay can be modeled by simple formulas for partially filled parallel-plate waveguides.

  • May combine two claims.

    Interpretationreasoning

    In this arrangement, the terahertz wave propagates a much longer distance within the film than in the single-pass case, producing a considerably increased delay.

    “In this arrangement the THz wave has a much longer propagation length within the film compared to the single-pass case, thereby giving rise to a considerably increased delay.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Thickness is usually determined by measuring the terahertz pulse delay of a sample.

    “The determination of the thickness is typically carried out by measuring the THz pulse delay of a sample.6”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [6] 2007, Opt. Express source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    Thermal drifts have the largest influence and require frequent reference scans to minimize accumulated error.

    “However, the largest influence is due to thermal drifts, 14 which requires frequent reference scans to minimize the accumulated error.15”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [14] 2008, J. Opt. Soc. Am. B source

      Not checked in the free run.

    • cites [15] 2010, Opt. Commun. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Several methods have been reported to lower the detection threshold for terahertz thin-film sensing, such as difference signals, metamaterial resonance shifts, and metal meshes.

    “Various techniques have been reported to improve the detection threshold for THz thin film sensing, e. g., evaluation of difference signals, 3 resonance changes of metamaterials, 4 or the application of metal meshes to enhance the amplitude reduction of the THz bandpass.5”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [3] 2000, Appl. Phys. Lett. source

      Not checked in the free run.

    • cites [4] 2008, Opt. Express source

      Not checked in the free run.

    • cites [5] 2009, Appl. Phys. Express source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Waveguide geometries using slowly varying metal surfaces have recently drawn interest in the terahertz range.

    “Waveguide geometries based on slowly varying metal surfaces have recently attracted interest in the THz range.[8][9][10][11][12][13]”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [8] 2005, Appl. Phys. Lett. source

      Not checked in the free run.

    • cites [9] 2010, Opt. Express source

      Not checked in the free run.

    • cites [10] 2010, Opt. Express source

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationreasoning

    Increasing the measured delay per micron of sample would enhance THz-TDS sensitivity for thin-film sensing and reduce thermal-drift effects.

    “Therefore, it is desirable to increase the measured delay per micron of sample to enhance the sensitivity of THz-TDS for thin film sensing to minimize the negative influence of thermal drifts, especially if stable measurements are necessary.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The increased delay in thin PET measurements is not entirely due to extra sample thickness; thermal drift of the reference zero was significant during the approximately three-hour measurement.

    “The reason for the increasing delay is not entirely due to extra sample thickness; the thermal drift of the reference zero of the delay was quite significant during the measurement time of approximately three hours.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S1 (asserted), S3 (load-bearing), S4 (based).

    Premisenone given

    Delay lines have mechanical specifications with accuracy between 0.1 and 1 μm.

    “Delay lines, for instance, have mechanical specifications with an accuracy between 0.1 and 1 m.”
    Quote in the paperNot a substantial claim

  • The quote only partly states this claim.

    Interpretationreasoning

    Under optimal conditions, long-term stability limits reliable investigation of sub-10 μm thin-film samples within a single measurement series.

    “long-term stability limits a reliable investigation of sub-10 m thin film samples within one measurement series.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    Over a 1 m propagation distance, this delay drift corresponds to a thermal drift of 0.3°C, typical of an air-conditioned laboratory.

    “With a 1 m propagation distance between optics this delay drift corresponds to a thermal drift of 0.3 ° C, which is a typical temperature oscillation of an airconditioned laboratory.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    The approach combines prior work on terahertz wave compression using metal flares with the sensing capabilities of terahertz surface waveguides.

    “This approach combines our previous work on THz wave compression using metal flares 12 and the sensing capabilities of THz surface waveguides.13”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [12] 2010, Appl. Phys. Lett. source

      Not checked in the free run.

    • cites [13] 2010, Opt. Express source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisenone given

    Systematic errors, in addition to random errors that averaging can reduce, contribute to uncertainty in measured quantities.

    “Besides random errors, which can be reduced by averaging, systematic errors con-tribute to the uncertainty of the measured quantities.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Interpretationnone given

    Commercial metal cylinders provide a reproducible geometry that is easy to align and needs no additional optical components.

    “The geometry of commercial metal cylinders is reproducible, easy to align, and does not require additional optical components.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Terahertz time-domain spectroscopy systems based on femtosecond lasers measure the electric field by sampling the terahertz pulse versus delay.

    “This can be done using THz time-domain spectroscopy ͑THz-TDS͒ systems based on femtosecond lasers.7 The electric field is measured by sampling the THz pulse as a function of delay, typically using a mechanical delay line.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [7] 1990, J. Opt. Soc. Am. B source

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data

    Detection of layers below 1 μm is feasible with the two-cylinder waveguide sensor, as demonstrated by measuring delays below 0.1 ps.

    “Therefore, we believe that detection of layers below 1 m is feasible with the two-cylinder waveguide sensor as demonstrated by our ability to measure delays of less than 0.1 ps shown in Fig. 2.”
    Quote in the paperSubstantial claim
27 of 27

  • The authors state this as an assumption.

    The delay can be modeled by simple formulas for partially filled parallel-plate waveguides.

    “assuming a simple model using formulas known for partially filled parallel-plate waveguides.”

  • The paper relies on this without support.

    The thermal drift of the reference zero is linear with measurement time.

    “However, it is possible to subtract the linear ͑with measurement time͒ thermal drift from the data points to achieve consistency”
2 of 2

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?

  • Any linear translation stage has a limited length resolution and positional accuracy; the actual position can differ from the set point by several micrometers.

    “any linear translation stage has a limited length resolution and positional accuracy. Depending on the implementation, the actual position of the delay can differ from the set point by several micrometers [35, 36].”

    From Terahertz-time domain spectrometer with 90 dB peak dynamic range (2014) · cites this paper as [35]

    The passage labelled Abstract in our copy says delay lines have mechanical accuracy specifications of 0.1–1 µm, supporting the point that positioning accuracy is limited. It does not say that the actual position differs from the set point by several micrometers; its discussion of larger measurement errors attributes them chiefly to thermal drift, not stage positioning. (LLM, conf=0.88)

    Experimental — accuracy not yet measured

  • The system's time resolution of 1.3 fs is an improvement of more than one order of magnitude compared to the 10 fs level inferred from prior work.

    “This is an improvement of more than one order of magnitude, compared to the 10 fs level inferred from [35, 36].”

    From Terahertz-time domain spectrometer with 90 dB peak dynamic range (2014) · cites this paper as [35]

    The cited paper discusses pulse-delay accuracy and reports a reference-zero drift of approximately 20 fs/h (opening passage) and a 0.014 ps drift during a measurement series (Fig. 1 discussion). Neither establishes a 10 fs time-resolution level. Searches for “10 fs” and temporal-resolution accuracy found no passage supporting that inferred benchmark; the citing system’s 1.3 fs result is not attributed to this source. (LLM, conf=0.70)

    Experimental — accuracy not yet measured

Cites

Flagged first, then by citations

Research works printed but not linked: 1

  1. 2010, Armenian J. Phys., 3, 69

Cited by

Sorted by citations

Related

Authors
Theuer, M., Beigang, R., & Grischkowsky, D.
Affiliations
  • Oklahoma State University (US)
  • University of Kaiserslautern (DE)
ORCID
Venue
Applied Physics Letters
Publisher
AIP Publishing
Published
2010-08-16
Volume
97
Issue
7
ISSN
  • 0003-6951 (ISSN-L)
  • 1077-3118
DOI
10.1063/1.3481080
OpenAlex
W1992911170
Semantic Scholar
f6a425a9bee045fb097f62741f23e3d9493aadab
Cited by
38
References
17
Citations by year
2024: 1 · 2023: 1 · 2021: 1 · 2020: 1 · 2019: 1 · 2018: 2 · 2017: 4 · 2016: 4 · 2015: 1 · 2014: 7 · 2013: 3 · 2012: 5
FWCI
3.78
Type
journal article
Language
en
Open access
Locations
  • Applied Physics Letters (publishedVersion)
  • SHAREOK (University of Oklahoma; Oklahoma State University; Central Oklahoma University) (acceptedVersion, other-oa)
  • Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft) (submittedVersion)
  • Fraunhofer-Publica (Fraunhofer-Gesellschaft) (submittedVersion)
  • SHAREOK (University of Oklahoma; Oklahoma State University; Central Oklahoma University) (submittedVersion, other-oa)
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 › Physics and Astronomy › Astronomy and Astrophysics › Superconducting and THz Device Technology
Keywords
terahertz time-domain spectroscopy, layer thickness measurement, sensitivity enhancement, thin film metrology

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