1. Introduction

Single-layer graphene is a promising transparent conductor, owing to its unique mechanical, optical, and electronic properties [1–7]. It is regarded as an attractive platform for future effective and lightweight, photonic and optoelectronic devices. Single-layer graphene was first produced by micromechanical exfoliation of pyrolytic graphite and several approaches have been developed to provide it in large sizes and in large quantities that would be suitable for mass production [8–11]. In particular, the graphene synthesized by chemical vapor deposition (CVD) methods allows for the production of large-scale films boosting the potential use of graphenes and multilayered graphene films as advanced flexible engineering materials [12, 13]. However, the CVD-based graphene has limitation in producing optically thick films, which are required for a wide variety of optoelectronic applications, such as optical filters, waveguides, plasmonic devices, and metamaterials. Therefore, solution based suspensions of graphene could be ideal for these applications, as they enable the relatively low-cost methods of spin-coating, roll-to-roll processing and printing to be used [14–19]. In addition, highly conductive films can be produced by making networks of individual graphene oxide (GO) flakes deposited from solutions and then performing the reduction process. The conductivity of reduced graphene oxide (rGO) films has been reported to be as large as 700 S/cm [16].

Optical and ac electrical properties of various graphene films in terahertz (THz) frequency range have been of particular interests due to their great potential for broadband communications and high-speed electronics [20, 21]. More importantly, THz time-domain spectroscopy enables us to obtain information on the complex conductivities, which are crucial for inspecting and engineering the optoelectronic properties of these materials. Optical properties of graphene based materials have been studied over a wide spectral range from visible to far-infrared frequencies [22–25]. Recently, the ac conductivity has been measured by using THz spectroscopy on the single-layer graphene synthesized via CVD techniques [26–29] and GO hybrid nanostructures [30]. However, rGO films have not been considered in the THz frequency range, namely, as conductive materials. Moreover, the dc and THz conductivities of rGO films (and also their correlation) have not been studied as a function of degree of reduction.

In this study, we performed time-domain THz spectroscopy to measure the THz transmission of rGO films fabricated by spraying the GO-dispersed solution on quartz substrates. rGO films demonstrate good metallic behaviors, in terms of the THz transmission, after a reduction process from the GO films. We determined the ac conductivities and the refractive indexes of the rGO films and analyzed the frequency response in terms of the Drude free-electron model. We found that the probe frequencies are below the Drude roll-off frequency by observing the large scattering rate. In addition, we were able to manipulate the conductivities of the films by controlling the degree of reduction.

2. Experimental results and discussions

The fabrication of GO and rGO network films began with the preparation of an aqueous suspension obtained by the exfoliation of graphite oxide, based on the modified Hummers method [31]. Graphite flakes (Sigma-Aldrich) were mixed with a solution of NaNO₃, KMnO₄, and H₂SO₄ in an ice bath and reacted with a 35% aqueous solution of H₂O₂ in order to reduce the residual permanganate and oxidize the manganese. The suspension was rinsed with a 5% hydrochloric acid solution and then dried at 90 °C for further use. The dried, GO powder was suspended in water by a centrifuge process to remove unexfoliated pieces. The GO dispersion solution was coated onto a quartz substrate by the spraying methods shown in Fig. 1(a) . The pristine GO film was thermally reduced in a furnace with an Ar and H₂ mixed gas (Ar: 97%, H₂: 3%) at the typical temperature of 1000 °C [14].

 

Fig. 1 (a) Schematic of the fabrication of rGO films based on a spraying method. (b) SEM image of rGO flakes. (c) AFM image of rGO30 film. Also shown is the line profile the film thickness along the dashed line in the AFM image.

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Figure 1(b) shows a scanning electron microscopy (SEM) image for the individual GO flakes deposited on a quartz substrate from the diluted dispersion solution. The average size of GO flakes synthesized in this manner is sufficiently large (average diameter of ~50 μm) to form a thin network layer with a relatively large conductivity. The thickness of the individual GO flakes was 1.1 nm. An atomic force microscopy (AFM) image of a typical rGO film, taken after the reduction process, is shown in Fig. 1(c); the film exhibits a flat surface (rms roughness of 2.5 nm) with a 30 nm thickness. The film is partially etched to allow for the measurement of the film thickness. In addition, the etched area is used to record the reference transmission for the individual rGO samples.

A plot of sheet resistance is shown in Fig. 2 for the series of the rGO samples for different numbers of spraying times (N_sp) from 5 to 30 (denoted by rGO5 – rGO30). Open and filled squares show optical transmission at 550 nm as a function of the thickness for the GO and rGO films, respectively. The thickness of the rGO layers increases linearly in accordance with the increasing N_sp, and that of rGO30 becomes roughly 30 nm after the annealing process. The monotonic increase in rGO thickness results in the gradual decrease in the visible-range transparency. We also note that the dc conductivity (extracted from the sheet resistance in Fig. 2 and the thickness) does not change significantly as we increase N_sp, from the rGO5 (620 S/cm) to rGO30 (970 S/cm) samples. However, the small increase in conductivity with increasing thickness is likely due to the vacancy filling from the repeated coating of GO flakes, which could lead to the improved, electrical percolations [32].

 

Fig. 2 Plot of sheet resistance for the series of the rGO samples with different thicknesses, from rGO5 (5 nm) to rGO30 (30 nm) films (red circles). Open and filled squares show optical transmission at 550 nm as a function of the thickness for the GO and rGO films, respectively.

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Transmissions through the films were measured by THz time-domain spectroscopy using an electro-optic sampling technique. We used a photoconductive antenna as an emitter and a ZnTe crystal as a detector, as described in previous studies [32, 33]. A femtosecond laser pulse at λ = 800 nm was used to generate and detect the transmitted pulses by using electro-optic sampling techniques. GO and rGO films were placed at the focus position of the THz field (focal spot size of ~1 mm). The frequency-dependent transmittance and dispersion of the rGO films can be obtained through a Fourier analysis of the transmitted pulses.

The GO and rGO films with different thicknesses were investigated at room temperature in a nitrogen-purged environment. We measured the time-dependent electric fields of the THz pulses transmitted through the thin film on the substrate (E_{rGO + sub}) and through the uncoated area of the substrate as a reference (E_sub), as illustrated in the inset of Fig. 3(a) . Figure 3(a) shows the time-dependent field amplitudes transmitted through the GO and rGO films, for N_sp = 30. The time trace was normalized to the transmission peak of the uncoated area (dashed line). The peak amplitude of the transmitted field through the GO30 film does not change significantly (blue line). In contrast, the transmission through the rGO30 which has undergone the reduction process decreases considerably (red line). This result validates formation of conducting channels in the rGO films after the annealing process which is in accordance with the sheet resistance measurement results shown in Fig. 2. The peak amplitudes range from 96% to 73% in terms of the reference THz field for rGO5 – rGO30.

 

Fig. 3 (a) THz time-domain transmission amplitudes for rGO30 (red line) and GO30 (blue line) films, respectively, normalized to the reference transmission (dashed line) (b) THz transmission amplitude spectra, from rGO5 to rGO30 films.

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Figure 3(b) shows the normalized transmission amplitude spectra for a series of rGO films with different thicknesses. The spectra show that the transmission decreases over the entire frequency range in response to the increase in the number of spraying times (i.e., with the increasing thickness of the rGO layers). This demonstrates that our method, based on spraying techniques, can provide an easy-to-control method of fabricating the conductive films with variable THz shielding capabilities. Therefore, these films can be used as density filters for THz applications. In addition, rGO films are also good candidates for electromagnetic interference (EMI) shielding materials. The EMI shielding effectiveness (SE) for rGO30 is 2.7 dB, where SE is defined as SE(dB) = −20 log(E_{rGO + sub}/E_sub). The shielding efficiency can be improved further by simply increasing the number of spraying times. The SE, as a function of the thickness can be expressed as SE = 0.096 × d at 1 THz, where d is the film thickness in nanometers. The value of SE is considerably larger than that of the graphite powder composite films (~10⁻⁴ × d (nm)) [34] and close to that of the virtually free-standing, conductive nanotube films [33].

The complex optical constants can be extracted from both the amplitude and the phase of the transmission obtained in the THz time-domain spectroscopy. The complex Fourier transforms of the time-dependent fields give the complex ac conductivity, $\tilde{\sigma }(\omega )$, directly by the thin film equation. In the thin film limit, i.e., for $\left|n\omega d/c\right|\ll 1$, we have

The ac conductivities for the rGO30 sample are plotted in Fig. 4(a) . It is clear that the real part of the conductivity is relatively uniform over the entire frequency range from 0.2 to 2.0 THz. On the other hand, the imaginary part of the conductivity increases with the increasing frequency, showing a dispersive behavior. The frequency-dependent complex conductivity of the rGO film is analyzed in terms of the Drude free-electron model by simultaneously fitting both the real and the imaginary parts of the conductivity as follows:

 

Fig. 4 (a) Real (open squares) and imaginary (open circles) parts of the THz conductivity of rGO30 film. Red and blue solid lines are fits to the data by Drude free-electron model. (b) Real (blue line) and imaginary (red line) parts of the refractive indexes for the rGO30 film extracted from complex conductivity in (a).

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Finally, we present the THz transmission characteristics for rGO samples with different reduction temperatures. Here, we monitor the continuous transition from the insulating GO to the conductive rGO films. Figure 5(a) shows the real part of the ac conductivities for the series of films with N_sp = 60, at the different reduction temperatures of 120−1000 °C. The ac conductivities show a similar spectral response, regardless of temperature, while the conductivities increase gradually as the reduction temperature increases. In Fig. 5(b), we show both the dc conductivity (extracted from the four-probe sheet resistance measurements) and the ac conductivity measured at 1 THz, as a function of the reduction temperature. It is clearly observed that for T_R > 200 °C, the measured ac conductivities are very close to the dc conductivities, both gradually increasing with T_R. Importantly, we would like to point out that the conductivities (and hence, the dielectric constants) of the rGO films can be manipulated by controlling the reduction process. This will be useful for fabricating various plasmonic devices and metamaterials, whose characteristics will be possible to control by adjusting the dielectric constants of the materials, or in applications where finite dielectric constants are required in the THz frequency region.

 

Fig. 5 (a) Real part of the ac conductivities for the series of the films with N_sp = 60, at reduction temperatures ranging from 200 to 1000 °C. (b) THz conductivities at 1 THz as a function of reduction temperature (red). Shown together are dc conductivities extracted from the four-probe measurements (black). Inset shows conductivities ($\sigma \approx {\sigma }_r$) at visible to near-IR range for the rGO films with different T_R values extracted from the transmission spectra and the thin film equation.

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Below 200 °C, the dc conductivity dropped sharply and was not measured for temperatures lower than 160 °C. This is because the samples with T_R < 200 °C are below the percolation threshold for conductive films [39]. It is interesting, however, that the ac conductivity still shows nontrivial values for T_R < 200 °C. This is likely because THz spectroscopy probes the ac conductivity locally, whereas the dc conductivity measurements require conduction channel formation over an extended area. This is consistent with the visible and near-IR conductivity measurements, which are shown as a log-log plot in the inset of Fig. 5(b). We extracted the ac conductivities for the rGO films with different T_R values from the transmission spectra (T) measured by a spectral photometer. Again we used the thin-film Eq. (1) and the assumption of $\sigma \approx {\sigma }_r\gg {\sigma }_i$, which yielded $T\approx {\left|(1+n_{sub})/(1+n_{sub}+Z_0\sigma d)\right|}^2$ [40]. Although the conductivity values were obtained on the basis of the crude assumptions (which do not hold precisely in the visible-UV range), the frequency responses clearly demonstrate the sharp transition from below to above the percolation threshold (T ~200 °C). In other words, the ac conductivity increases sharply with frequency for the low T_R case (i.e., with low percolation) in accordance with the universal dynamic response, as found in the literature [39]. Our results for the partially reduced rGO films will provoke future investigations on the spectral responses which are unique for the disordered systems with localized conducting domains [35].

3. Conclusions

In conclusion, we performed time-domain THz spectroscopy to measure the optical and electrical properties of reduced GO films. These films demonstrated good shielding of electromagnetic waves with the conductivity of ~10³ S/cm in the THz range and were obtained by applying the reduction process to GO films from the solution process. The frequency dependent conductivities were studied in terms of the Drude free-electron model, whereas the spectral range was below the Drude roll-off frequency due to the large scattering rate. We found that the conductivities can be manipulated by using the reduction process. In other words, the dc and THz conductivities increase gradually with increased reduction temperature. We believe that the rGO films with variable dielectric constants and conductivities will provide a novel platform for various functionalized optoelectronic devices.