Terahertz Time-domain Spectroscopy Data Research Articles

Nondestructive Evaluation of Thermal Barrier Coatings’ Porosity Based on Terahertz Multi-Feature Fusion and a Machine Learning Approach

Thermal barrier coatings (TBCs) play a crucial role in safeguarding aero-engine blades from high-temperature environments and enhancing their performance and durability. Accurate evaluation of TBCs’ porosity is of paramount importance for aerospace material research. However, existing evaluation methods often involve destructive testing or lack precision. In this study, we proposed a novel nondestructive evaluation method for TBCs’ porosity, utilizing terahertz time-domain spectroscopy (THz-TDS) and a machine learning approach. The primary objective was to achieve reliable and precise porosity evaluation without causing damage to the coatings. Multiple feature parameters were extracted from THz-TDS data to characterize porosity variations. Additionally, correlation analysis and p-value testing were employed to assess the significance and correlations among the feature parameters. Subsequently, the dung-beetle-optimizer-algorithm-optimized random forest (DBO-RF) regression model was applied to accurately predict the porosity. Model performance was evaluated using K-fold cross-validation. Experimental results demonstrated the effectiveness of our proposed method, with the DBO-RF model achieving high precision and robustness in porosity prediction. The model evaluation revealed a root-mean-square error of 1.802, mean absolute error of 1.549, mean absolute percentage error of 8.362, and average regression coefficient of 0.912. This study introduces a novel technique that presents a dependable nondestructive testing solution for the evaluation and prediction of TBCs’ porosity, effectively monitoring the service life of TBCs and determining their effectiveness. With its practical applicability in the aerospace industry, this method plays a vital role in the assessment and analysis of TBCs’ performance, driving progress in aerospace material research.

Dopant profiling of ion-implanted GaAs by terahertz time-domain spectroscopy

We investigate terahertz time-domain spectroscopy (THz-TDS) as a non-destructive and non-contact technique for depth profiling of dopants in semiconductors. THz temporal waveforms transmitted through silicon-ion-implanted semi-insulating gallium arsenide substrates, as-implanted or post-annealed by rapid thermal annealing, were analyzed by assuming a multi-layered Gaussian refractive index profile in the ∼sub-micrometer-thick implantation region. The implantation energy and dosages in this work were 200 KeV, 1014, 5 × 1014, and 1015 ions/cm2, respectively. The average values of real (n) and imaginary (κ) parts of refractive indices of an as-implanted sample in the depth range of 0–800 nm are 5.8 and 0.7, respectively, at 0.5 THz and are 6.2 and 0.2, respectively, at 1 THz. On the other hand, the refractive index profile of the post-annealed samples displays a prominent Gaussian-like form, and peak refractive indices (n ∼ 25 and κ ∼ 32.7 at 0.5 THz and n, κ ∼17 at 1 THz) were found to be at the depth of 210 nm. Reconstructed dopant profiles in as-implanted, implanted, and post-annealed substrates were found to be in good agreement with measurements by secondary ion mass spectroscopy as well as simulation by the Monte Carlo method. We were also able to determine accurately the projected range (Rp), straggle (Rs), and concentration of dopants by the analysis of THz-TDS data. The spatial resolution, along the depth direction, of the THz-TDS technique for depth profiling of dopants was estimated to be as small as 8-nm. This work suggests the feasibility of using THz-TDS for nondestructive and non-contact diagnostics for profiling dopants in semiconductors.

Broadband spectroscopy of astrophysical ice analogues

Context. Broadband optical constants of astrophysical ice analogues in the infrared (IR) and terahertz (THz) ranges are required for modeling the dust continuum emission and radiative transfer in dense and cold regions, where thick icy mantles are formed on the surface of dust grains. Such data are still missing from the literature, which can be attributed to the lack of appropriate spectroscopic systems and methods for laboratory studies. Aims. In this paper, the THz time-domain spectroscopy (TDS) and the Fourier-transform IR spectroscopy (FTIR) are combined to study optical constants of CO and CO2 ices in the broad THz-IR spectral range. Methods. The measured ices were grown at cryogenic temperatures by gas deposition on a cold silicon window. We developed a method to quantify the broadband THz-IR optical constants of ices, based on the direct reconstruction of the complex refractive index of ices in the THz range from the TDS data and the use of the Kramers-Kronig relation in the IR range for the reconstruction from the FTIR data. Uncertainties introduced by the Kramers-Kronig relations were eliminated by merging the THz and IR spectra. Finally, the reconstructed THz-IR response was analyzed using classical models of complex dielectric permittivity. Results. The complex refractive index of CO and CO2 ices deposited at the temperature of 28 K was obtained in the range of 0.312.0 THz and fitted using the analytical Lorentz model. Based on the measured dielectric constants, opacities of the astrophysical dust with CO and CO2 icy mantles were computed. Conclusions. The method developed in this work can be used for a model-independent reconstructions of optical constants of various astrophysical ice analogs in a broad THz-IR range. Such data can provide important benchmarks for interpreting broadband observations from existing and future ground-based facilities and space telescopes. The reported results will be useful in modeling sources that exhibit a drastic molecular freeze-out, such as the central regions of prestellar cores and mid-planes of protoplanetary disks, as well as CO and CO2 snow lines in disks.

Artificial neural networks for material parameter extraction in terahertz time-domain spectroscopy.

Terahertz time-domain spectroscopy (THz-TDS) is a proven technique whereby the complex refractive indices of materials can be obtained without requiring the use of the Kramers-Kronig relations, as phase and amplitude information can be extracted from the measurement. However, manual pre-processing of the data is still required and the material parameters require iterative fitting, resulting in complexity, loss of accuracy and inconsistencies between measurements. Alternatively approximations can be used to enable analytical extraction but with a considerable sacrifice of accuracy. We investigate the use of machine learning techniques for interpreting spectroscopic THz-TDS data by training with large data sets of simulated light-matter interactions, resulting in a computationally efficient artificial neural network for material parameter extraction. The trained model improves on the accuracy of analytical methods that need approximations while being easier to implement and faster to run than iterative root-finding methods. We envisage neural networks can alleviate many of the common hurdles involved in analyzing THz-TDS data such as phase unwrapping, time domain windowing, slow computation times, and extraction accuracy at the low frequency range.

Non-destructive evaluation of coatings using terahertz reflection spectroscopy

Terahertz time-domain spectroscopy (THz-TDS) provides a non-contact, non-destructive method for evaluating different materials and their properties. This short review discusses the commonly used numerical models for the non-destructive estimation of thickness, refractive index, surface and interface roughness of paints, thermal barrier coatings, and polymer coatings using THz-TDS in the reflection geometry. To demonstrate the applicability of these models, we used paint layers on metallic substrates and extracted different paraments by fitting the experimental THz-TDS data. We conclude by discussing further steps to improve the efficiency of the fitting procedure used to extract the layer parameters.

Extracting complex refractive indices from THz-TDS data with artificial neural networks

Terahertz time-domain spectroscopy (THz-TDS) benefits from high signal-to-noise ratios (SNR), however extraction of material parameters involves a number of steps which can introduce errors into the final result. We present the use of artificial neural networks (ANN) as the first step to achieve a comprehensive approach for the extraction of the complex refractive index from THz-TDS data. The ANN shows performance superior to approximation methods and has a more straightforward implementation than root finding methods. Deep and convolutional neural networks are demonstrated to accept an entire frequency range at once, providing a tool for fitting where SNR is low, producing a more stable result.

Broadband Super-Resolution Terahertz Time-Domain Spectroscopy Applied to Gas Analysis

Commercially available Terahertz (THz) Time domain spectroscopy (THz-TDS) apparatus are used in multiple application fields from material science to biology, and even in industry to measure the thickness of a paint layers. Its broad spectral coverage is of interest for air quality monitoring and atmospheric composition analysis. However, gas spectroscopy needs high resolution that the usual approach in THz-TDS is unable to provide. In this letter, we introduce the concept of constraint reconstruction for super-resolution spectroscopy based on the modeling of the spectroscopic rotational lines in a sparse spectrum. It is demonstrated for low-molecular weight molecules in gas phase that typically have spectra containing a small number of narrow lines over a broad spectrum. This alternative approach directly reconstructing the spectra achieved a resolution improvement factor of 10 compared to the best available resolution by the standard THz-TDS data treatment.

Nelly: A User-Friendly and Open-Source Implementation of Tree-Based Complex Refractive Index Analysis for Terahertz Spectroscopy.

Terahertz (THz) spectroscopy is a powerful tool for unambiguously extracting complex-valued material properties (e.g., refractive index, conductivity, etc.) from a wide range of samples, with applications ranging from materials science to biology. However, extracting complex refractive indices from THz time-domain spectroscopy data can prove challenging, especially for multilayer samples. These challenges arise from the large number of transmission-reflection paths the THz pulse can take through the sample layers, leading to unwieldy strings of Fresnel coefficients. This issue has often been addressed using various approximations. However, these approximations are only applicable to specific classes of samples and can give erroneous results when misapplied. An alternative to this approach is to programmatically model all possible paths through the sample. The many paths through the sample layers can be modeled as a tree that branches at every point where the paths diverge, i.e., whenever the pulse can either be transmitted or reflected. This tree can then be used to generate expressions relating the unknown refractive index to the observed time domain data. Here, we provide a freely available open-source package implementing this method as both a MATLAB library and a corresponding graphical user interface, which can also be run without a MATLAB license (https://github.com/YaleTHz/nelly). We have tested this method for a range of samples and compared the results to commonly used approximations to demonstrate its accuracy and wide applicability. Our method consistently gives better agreement than common approximations.

THz-TDS parameter extraction: empirical correction terms for the analytical transfer function solution.

Terahertz time-domain spectroscopy (TDS) is capable of determining both real and imaginary refractive indices of a wide range of material samples; however, converting the TDS data into complex refractive indices typically involves iterative algorithms that are computationally slow, involve complex analysis steps, and can sometimes lead to non-convergence issues. To avoid using iterative algorithms, it is possible to solve the transfer function analytically by assuming the material loss is low; however, this leads to errors in the refractive index values. Here we demonstrate how the errors created by solving the transfer function analytically are largely predictable, and present a set of empirically derived equations to diminish the error associated with this analytical solution by an impressive two to three orders of magnitude. We propose these empirical correction terms are well suited for use in industrial applications such as process monitoring where analysis speed and accuracy are of the utmost importance.

Terahertz Conductivity Analysis for Highly Doped Thin-Film Semiconductors

The analysis of terahertz transmission through semiconducting thin films has proven to be an excellent tool for investigating optoelectronic properties of novel materials. Terahertz time-domain spectroscopy (THz-TDS) can provide information about phonon modes of the crystal, as well as the electrical conductivity of the sample. When paired with photoexcitation, optical-pump-THz-probe (OPTP) technique can be used to gain an insight into the transient photoconductivity of the semiconductor, revealing the dynamics and the mobility of photoexcited charge carriers. As the relation between the conductivity of the material and the THz transmission function is generally complicated, simple analytical expressions have been developed to enable straightforward calculations of frequency-dependent conductivity from THz-TDS data in the regime of optically thin samples. Here, we assess the accuracy of these approximated analytical formulas in thin films of highly doped semiconductors, finding significant deviations of the calculated photoconductivity from its actual value in materials with background conductivity comparable to 102Ω− 1cm− 1. We propose an alternative analytical expression, which greatly improves the accuracy of the estimated value of the real photoconductivity, while remaining simple to implement experimentally. Our approximation remains valid in thin films with high dark conductivity of up to 104Ω− 1cm− 1 and provides a very high precision for calculating photoconductivity up to 104Ω− 1cm− 1, and therefore is highly relevant for studies of photoexcited charge-carrier dynamics in electrically doped semiconductors. Using the example of heavily doped thin films of tin-iodide perovskites, we show a simple experimental method of implementing our correction and find that the commonly used expression for photoconductivity could result in an underestimate of charge-carrier mobility by over 50%.

Peak emission of terahertz waves from (110)-oriented ZnTe by interacting phase-matched phonon resonances

We demonstrate the measurement and assignment of phonon resonances responsible for observed peak emission of terahertz (THz) waves from (110)-ZnTe. We show that optical rectification in ZnTe using femtosecond pulses centered at 790 nm involves phase-matched fundamental and difference-phonon resonances at 1.63, 1.95, 2.25, and 2.55 THz, which produce a THz peak at 2.1 THz and damped oscillations for 6 ps after the main THz pulse. Phonon resonances in ZnTe have been measured and assigned by mathematical modeling and terahertz time-domain spectroscopy (THz-TDS) over the range 0.1–3 THz. The refractive index and optical absorption coefficient of ZnTe have also been extracted from the measured THz-TDS data. The results give greater insight into the dynamics of ZnTe for ultrafast optoelectronic systems.

Nitroxoline Molecule: Planar or Not? A Story of Battle between π–π Conjugation and Interatomic Repulsion

The conformational properties of the nitro group in nitroxoline (8-hydroxy-5-nitroquinoline, NXN) were investigated in the gas phase by means of gas electron diffraction (GED) and quantum chemical calculations, and also with solid-state analysis performed using terahertz time-domain spectroscopy (THz-TDS). The results of the GED refinement show that in the equilibrium structure the NO2 group is twisted by angle ϕ = 8 ± 3° with respect to the 8-hydroxyoquinoline plane. This is the result of interatomic repulsion of oxygen in the NO2 group from the closest hydrogen, which overcomes the energy gain from the π-π conjugation of the nitro group and aromatic system of 8-hydroxyoquinoline. The computation of equilibrium geometry using MP2/cc-pVXZ (X = T, Q) shows a large overestimation of the ϕ value, while DFT with the cc-pVTZ basis set performs reasonably well. On the other hand, DFT computations with double-ζ basis sets yield a planar structure of NXN. The refined potential energy surface of the torsion vibration the of nitro group in the condensed phase derived from the THz-TDS data indicates the NXN molecule to be planar. This result stays in good agreement with the previous X-ray structure determination. The strength of the π-system conjugation for the NO2 group and 8-hydroxyoquinoline is discussed using NBO analysis, being further supported by comparison of the refined semiexperimental gas-phase structure of NXN from GED with other nitrocompounds.

THz spectral data analysis and components unmixing based on non-negative matrix factorization methods

In many situations the THz spectroscopic data observed from complex samples represent the integrated result of several interrelated variables or feature components acting together. The actual information contained in the original data might be overlapping and there is a necessity to investigate various approaches for model reduction and data unmixing. The development and use of low-rank approximate nonnegative matrix factorization (NMF) and smooth constraint NMF (CNMF) algorithms for feature components extraction and identification in the fields of terahertz time domain spectroscopy (THz-TDS) data analysis are presented. The evolution and convergence properties of NMF and CNMF methods based on sparseness, independence and smoothness constraints for the resulting nonnegative matrix factors are discussed. For general NMF, its cost function is nonconvex and the result is usually susceptible to initialization and noise corruption, and may fall into local minima and lead to unstable decomposition. To reduce these drawbacks, smoothness constraint is introduced to enhance the performance of NMF. The proposed algorithms are evaluated by several THz-TDS data decomposition experiments including a binary system and a ternary system simulating some applications such as medicine tablet inspection. Results show that CNMF is more capable of finding optimal solutions and more robust for random initialization in contrast to NMF. The investigated method is promising for THz data resolution contributing to unknown mixture identification.

Accurate Characterization of Resonant Samples in the Terahertz Regime Through a Technique Combining Time-Domain Spectroscopy and Kramers–Kronig Analysis

We propose and experimentally demonstrate an original method, combining terahertz time-domain spectroscopy (THz-TDS) and Kramers–Kronig relations (KKR), in order to characterize in transmission materials exhibiting high absorption peaks. At these frequencies, the modulus of transmittance of a sample could be null, or at least smaller than the detector noise, and consequently the signal phase is lost, not only at the peak frequency, but also at higher frequencies. Thus, for these high frequencies, the value of the refractive index estimated from the measured THz-TDS data could be strongly erroneous. Using an optimized version of KKR, namely singly subtractive KKR, we are able to retrieve the phase of the THz transmittance over the whole studied bandwidth and thus to correct the THz-TDS data to precisely determine the refractive index as well as the absorption coefficient of the material over almost the whole THz range.

Quantitative Analysis of Hexahydro-1,3,5-trinitro-1,3,5, Triazine/Pentaerythritol Tetranitrate (RDX-PETN) Mixtures by Terahertz Time Domain Spectroscopy.

Absorption spectra of explosives such as hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), pentaerythritol tetranitrate (PETN), and mixtures of both were measured by terahertz time domain spectroscopy (THz-TDS). Chemometrics was applied to quantitative analysis of terahertz absorbance spectra obtained in transmission mode to predict the relative amounts of RDX and PETN in samples containing pure components or their mixtures. This analysis was challenging because significant spectral overlap prevented identification of each product fingerprint. Partial least squares (PLS) regression models were thus applied to the terahertz spectra. A comparison between the so-called PLS1 and PLS2 algorithms was performed to predict the PETN concentrations in mixture samples. PLS2 demonstrated better predictive ability than PLS1 with RMSE value lower than 3.5 mg for 400 mg total weight pellets. Moreover, the influence of the highly overlapping spectral frequency band was investigated by reducing the original 0.2-3 THz (6-100 cm(-1)) spectral band to 1.8-3 THz (60-100 cm(-1)). The predictive ability was quite similar in both cases, highlighting the excellent ability of chemometrics to perform quantitative analysis when applied to THz-TDS data, even in the case of highly overlapping spectra.

Sample Thickness Measurement with THz-TDS: Resolution and Implications

The accuracy of any measurement with terahertz time-domain spectroscopy (THz-TDS) depends strongly on knowing and supplying the precise sample thickness when processing the raw terahertz data. Sample thickness usually is estimated using other (non-THz) metrology and invariably involves some degree of uncertainty. It turns out that the terahertz data itself typically also contains information regarding sample thickness. However, there is limited systematic work addressing the following questions: What is the best method for extracting sample thickness from THz-TDS data? And, what is the thickness resolution obtainable with THz-TDS? In this study we demonstrate how these questions can be answered in general by answering them for a specific example: undoped silicon wafers. We determine the accuracy with which the exact thickness of nominally 500 μm silicon wafers can be measured using transmission mode THz-TDS. We analyze and compare the resolution of 5 different approaches for determining sample thickness using THz-TDS data, including two new methods and three methods proposed in the literature. The quantitative results and analyses of methods we present will be useful in developing far-infrared optical metrology. Conversely the quantitative results presented can be used to relate uncertainty in sample thickness to uncertainty in the measured terahertz data both in the time domain and frequency domain (phase and amplitude). Finally, a precise understanding of the relationship between sample thickness and THz-TDS data can be used to formulate superior THz-TDS data work-up methodologies.

Optical properties of borate crystals in terahertz region

In this paper we study the optical properties of a family of borate crystals comprising alpha and beta barium borates, barium fluoroborate, lithium triborate, and lithium tetraborate in the frequency range from 0.3 to 2.0THz. We extract the refractive indices and absorption coefficients for both ordinary and extraordinary beams from terahertz time-domain spectroscopy data. All of the investigated crystals exhibit substantial birefringence and dichroism, which qualifies them as potential materials for terahertz polarization-optical devices. We also find an additional absorption band in barium borate crystals, which is not defined by the group of phonon modes lying above 2THz. We argue that this phenomenon may be caused by excessive sodium atoms and ions in the crystal lattice.

Extracting accurate optical parameters from glasses usingterahertz time-domain spectroscopy

Terahertz time-domain spectroscopy (THz-TDS) can be used to characterize the optical properties of glasses in a frequency regime that is barely accessible by other techniques. It can be used to measure the electric field of a pulse of broadband terahertz radiation with frequency components between 0.1 and 4.5 THz propagating through the material of interest. Data processing is required to transform the information from the raw time-domain waveform data into the absorption spectrum. While most crystalline materials exhibit a number of distinct spectral features, amorphous materials show an almost featureless frequency response in the terahertz range and very accurate measurements of the absorption coefficient are required to characterize the materials. The accuracy of existing data processing techniques is limited as a result of truncating the time-domain data to remove multiple reflections of the terahertz pulse within the sample material and by neglecting scattering losses at the surface of the sample material. Using the experimental THz-TDS data of As 2 S 3 we present a new approach to extract accurate optical parameters from THz-TDS experimental data.

Fast and Accurate Thickness Determination of Unknown Materials using Terahertz Time Domain Spectroscopy

We present a fast and accurate time domain based algorithm which extracts simultaneously the thickness and refractive index of highly transparent samples from terahertz time domain spectroscopy data. The utilized transfer function considers the Fabry-Perot oscillations of the sample and enables to analyze data with multiple reflections. The algorithm can also be applied to signals corrupted by vapor absorption lines. Since the data extraction takes only fractions of a second, this computation method is well suited for real-time monitoring of industrial processes. We show that the accuracy of the new algorithm is comparable to that of sophisticated, highly accurate and time consumptive frequency domain algorithms.

Uncertainty in terahertz time-domain spectroscopy measurement

Measurements of optical constants at terahertz—or T-ray—frequencies have been performed extensively using terahertz time-domain spectroscopy (THz-TDS). Spectrometers, together with physical models explaining the interaction between a sample and T-ray radiation, are progressively being developed. Nevertheless, measurement errors in the optical constants, so far, have not been systematically analyzed. This situation calls for a comprehensive analysis of measurement uncertainty in THz-TDS systems. The sources of error existing in a terahertz spectrometer and throughout the parameter estimation process are identified. The analysis herein quantifies the impact of each source on the output optical constants. The resulting analytical model is evaluated against experimental THz-TDS data.