Terahertz (THz) electromagnetic waves are regarded for use in novel nondestructive testing techniques and noninvasive medical sensing methods [1–6]. THz waves are electromagnetic waves corresponding to wavelengths of 3 mm to 30 µm, frequencies of 0.1 to 10 THz, and energy levels of 4 to 40 meV. This band is located between microwaves and infrared waves and bears characteristics of both. Radio and microwaves easily penetrate nonmetallic materials such as ceramics and semiconductors, and their low energy levels make nondestructive testing of concealed objects possible [1–3]. Infrared and visible light have been used for vision testing of various products. Positioned between the microwave and infrared bands, THz waves carry the advantages of both, enabling nondestructive imaging of concealed objects. Active research is underway to commercialize next-generation nondestructive imaging techniques applicable to a range of subjects, including food, semiconductor packaging, and security scanning [4–6]. The energy of THz waves corresponds to weak hydrogen bonds. According to the International Commission on Non-Ionizing Radiation Protection (ICNIRP), THz waves are considered safe for the human body at intensities of a few mW/cm² [7]. Therefore, applications of THz wave technologies are expanding, including nondestructive testing safe for the human body, and next-generation medical devices. THz time-domain spectroscopy (THz-TDS) based on THz pulses with amplitude and phase information is able to reveal the complex optical constants, conductivity, and dielectric constant of a material. THz-TDS can provide time-of-flight information, making it possible to measure film thickness and analyze multilayer structures. Thus, THz-TDS technology has been used for measuring the thickness of coatings in automobiles and airplanes, and for analyzing thin films of graphene and other two-dimensional materials [8–12]. THz-TDS is useful for analyzing both the doping of semiconductors and the conductivity and thickness of metal films, which find widespread use in industry. Metal films are widely used as electrodes in semiconductor and display devices, and for enhancing the aesthetic design of electronic products. They are also employed in encapsulating substances that are sensitive to moisture and oxygen, such as OLEDs and perovskites [9, 10]. The thickness and electrical characteristics of these metal films determine the lifetime and performance of semiconductors and displays, so accurate measurements of film thickness and electrical characteristics are required. Various commercial methods, such as haze meters, spectrophotometers, surface resistance meters, and microgloss meters, have been employed to analyze metal films coated on polymers. These methods indirectly measure the electrical characteristics of a film based on its transmittance. However, they have limitations, such as inability to determine the film’s thickness and complex electrical parameters like real and imaginary conductivity and permittivity. For thickness measurement, methods using alpha step and ellipsometry, for example, are available. Methods using visible light or ellipsometry have difficulty measuring the thickness of materials with skin depths above a certain threshold, because the skin depth is inversely proportional to the square root of the frequency of the wave. The THz-TDS method can accurately measure the complex optical and electrical coefficients of materials, unlike Fourier-transform infrared spectroscopy which could obtain both coefficients of materials using fitting. Therefore, THz-TDS is a very useful method for characterizing nickel-chromium (Ni-Cr) films deposited on polymers. In this paper we measure the optical and electrical constants of Ni-Cr films deposited on polymer films using Thz-TDS, and thus measure the thickness of Ni-Cr films. We also compare this method to existing methods that use visible light.

2.1. Ni-Cr Metal Film on Polyethylene Film

We characterize the Ni-Cr films that are deposited on a polyethylene (PE) film using a sputtering technique. The Ni-Cr films used in this study are coated at a constant roll-to-roll speed of 5 m/min in a vacuum chamber, utilizing a machine (Rinopak Co., England, UK). In the chamber are installed six cathodes, onto which nickel and chromium sources are mounted in an 8:2 ratio. Different film thicknesses are achieved by applying varying voltages and currents to each Truplasma DC 4020 power supply, monitored by an external system. The thickness of Ni-Cr films are acquired by multiwavelength ellipsometer measurements.

2.2. THz Time-domain Spectroscopy

THz time-domain spectroscopy here is based on a femtosecond laser with a pulse width of 100 fs and a center wavelength of 800 nm. This laser is focused on a p-InAs wafer to generate the THz pulse. The surface current and the photo-Dember effect, induced on the p-InAs wafer by the irradiation of the femtosecond laser, can be used to generate THz pulses. These pulses are guided into the sample using parabolic mirrors, then focused onto the detector antenna. The photoconductive antenna (PCA) used as a detector is a dipole antenna fabricated on a low-temperature-grown gallium arsenide (LT-GaAs) wafer. The pump-probe sampling method is used for measurement of THz pulses. The convolution signals of the THz pulse and laser pulse, which is split by a beam splitter and delayed by a mechanical delay stage, are acquired using lock-in detection. The THz beam path is maintained in a dry chamber, to avoid the effects of water vapor in the air.

3.1. THz Waveforms

We measure the THz time-domain waveforms of five Ni-Cr films, as well as the PE film used as substrate for the Ni-Cr film, as depicted in Fig. 1(a). Consistent with results from haze-meter and transmission-densitometer measurements, the peak-to-peak values of the THz time-domain waveforms decrease as the thickness increases. These time-domain waveforms are then transformed into frequency-domain waveforms using the fast Fourier transform (FFT), as shown in Fig. 1(b). Like the time-domain waveform results, the amplitude level across all frequency ranges reduces as the thickness increases.

Figure 1. THz waveforms of Ni-Cr films: (a) Time-domain waveforms, (b) frequency-domain waveforms.

3.2. Transmissivity of Ni-Cr Film

We obtain the THz transmissivity spectrum of several Ni-Cr films by dividing the measured intensity of the THz signal passing through the Ni-Cr film by that passing through the PE film, as shown in Fig. 2. The transmissivity is found to be frequency-dependent.

Figure 2. Transmissivity of Ni-Cr films at THz frequencies.

As the frequency increases, so do the transmissivity values within the THz frequency range. These transmissivity values decrease as the thickness of the Ni-Cr film increases. We use the transmissivity values at 1 THz for comparison to results from other quality-control test methods. As depicted in Table 1, our THz transmissivity results are consistent with the results obtained from haze-meter and transmission-densitometer measurements.

TABLE 1. Transmissivity of Ni-Cr films by different methods. NDH-7000 is a haze meter, and X-rite 361T is a densitiometer.

Thickness (nm)	NDH-7000	X-rite 361T	THz-TDS (1 THz)
49	2	5	5
23	13	19	15
16	20	25	22
10	33	40	35
7	41	49	50

3.3. Electrical Properties of Ni-Cr Film

The transmissivity spectrum has been utilized for the quality control of metallic films, such as Ni-Cr films, but its capacity to measure film thickness is limited. The thickness of a metallic film can be extracted from its electrical parameters, such as complex conductivity or permittivity. For very thin films with thickness significantly less than the skin depth, the complex transmissivity is given by [13, 14]

where ${\tilde{E}}_{\text{film}}$ and ${\tilde{E}}_{\text{sub}}$ is the electric field intensity of the THz pulse through the film on PE and through PE respectively, n_sub is the index of refraction of PE in the THz range, Z₀ is the impedance of free space (377 Ω) and $\tilde{\sigma }$ is the complex conductivity of the film.

We measure the complex conductivity for the thickest and thinnest Ni-Cr films in our study, as depicted in Fig. 3, and then use the results to estimate film thickness.

Figure 3. Complex conductivity of Ni-Cr films: (a) Real conductivity, (b) imaginary conductivity. The open circles are experimental data; The lines are Drude fitting data.

The frequency-dependent complex conductivity denoted as $\tilde{\sigma }\left(\omega \right)$ is related to the complex refractive index $\tilde{n}$, as shown in Eq. (2). Figure 4 displays the complex optical constants. ϵ₀ represents the vacuum permittivity.

Figure 4. Complex refractive index of Ni-Cr films: (a) Index of refraction, (b) absorption coefficient. The open circles are experimental data; The lines are Drude fitting data.

The metal films conform to the Drude model of Eq. (3), a free-electron model that has been used to characterize the electrical properties of conductive materials [15, 16].

The Drude weight, denoted as σ₀, and the carrier scattering time, denoted as τ_DS, are obtained by numerical fitting methods, σ₀ and τ_DS as 6,830 Ω cm⁻¹ and 127 fs respectively. The best fitting curves are shown as black solid lines in Figs. 3 and 4. The THz-frequency results shown in Figs. 3 and 4 align well with the Drude model, indicating that our electrical and optical constants for Ni-Cr films are reliable. The results for the thinnest Ni-Cr film are almost identical to those for the thickest one. These results imply that a homogeneous Ni-Cr film has already formed at a thickness of 7 nm, consistent with the findings for Cr films by Walther and Lourens [8, 17].

3.4. Evaluation of Thickness of Ni-Cr Film

We obtain the thickness for each of three Ni-Cr films using the transmissivity. The Tinkham formula is employed to extract the thickness of Ni-Cr film. Figure 5 depicts the frequency-dependent transmissivity and fitting graphs. The thickness values are obtained by fitting of transmissivity with the complex conductivity in the range of 0.2–1.8 THz.

Figure 5. Thickness of Ni-Cr films from THz time-domain spectroscopy (THz-TDS) measurements.

The thickness values extracted from THz-TDS are almost identical to those acquired from the multiwavelength ellipsometer measurements, as shown in Table 2. These results show that THz-TDS is a suitable technology for measuring both the thickness and electrical properties of Ni-Cr films.

TABLE 2. Thickness of Ni-Cr films from two methods.

Measured Thickness (nm)	Estimated Thickness (nm)
49	48.7
23	23.0
16	16.1
10	10.6
7	6.8

Our study has demonstrated that THz-TDS is an effective and accurate method for measuring the thickness and electrical properties of Ni-Cr films. THz-TDS not only aligns with traditional methods like haze-meter and transmission-densitometer measurements, but also provides a more comprehensive analysis by taking into account the complex conductivity constants. We have shown that these constants can be used to accurately estimate the thickness of a Ni-Cr film. The optical and electrical coefficients of Ni-Cr thin film were extracted using the Tinkham formula. Moreover, the frequency-dependent complex conductivity values closely followed the Drude model. The thickness of Ni-Cr was estimated using the complex conductivity, and our results were almost identical to those obtained from multiwavelength ellipsometer measurements. These results underscore the potential of THz-TDS for broad application in the quality control of metallic films, as it provides both thickness and electrical property-measurements in a nondestructive test.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Research data are not shared.

Institute of Information & Communications Technology Planning & Evaluation (IITP) grant, funded by the Korea government (MSIT) (Grant No. 2022-0-01044, Development of terahertz wave-based real-time intelligent brain tumor diagnosis system and technology).