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Abstract
We propose a graphene-based terahertz metamaterial approach to the detection of heavy metal ions (HMIs). Theoretical calculations and numerical simulations show that the amplitude and phase of electromagnetically induced transparency/reflection resonance of the devices depending on the concentration and type of the HMI in the solution. By changing the bias voltage, the devices can be easily adjusted to their linear working regime for enhanced response speed and performance. By adding specific functional groups to the graphene, the devices may even recognize one specific HMI out of many due to selective adsorption. The proposed concept and discussed method can be helpful to design highly sensitive, fast, and reusable HMI detectors.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Heavy metals contamination in water has become a severe issue due to industrial and agricultural activities, such as manufacture of metallurgy, chemicals and microelectronics, overuse of fertilizers and pesticides [1,2]. As heavy metal ions (HMIs) are difficult to be degraded naturally, they accumulate in organisms and environment, and then enter the human body, causing poisoning of skin, nerves and viscera, as well as various cancers [3–5]. Therefore, pollution in water caused by toxic HMIs (Hg2+, Pb2+, Cr2+, Cd2+, As2+, Ni2+, Cu2+, etc. [4]) has drawn intensive attention worldwide. Many methods and devices have been developed to detect HMIs in water, including electrochemical analysis [4,6,7], fluorescence detection [8], colorimetric method [9], inductively coupled plasma mass spectrometry (ICP-MS) [10], atomic absorption spectroscopy (AAS) [11], Fourier transform infrared spectroscopy (FT-IR) [12], X-ray photoelectron spectroscopy (XPS) [12], ultraviolet and visible (UV-Vis) spectroscopy [13], X-ray fluorescence spectroscopy (R-FS) [14], field-effect transistor (FET) [15–18], microwave sensors [19], etc. Most of them require expensive instruments and specialists to perform the analyses [2]. It is necessary to develop highly sensitive, rapid, and simple methods for HMIs detection. Electrochemical analysis and FET sensors are two common fast and simple detection schemes. Electrochemical method, however, suffers from the difficulty in determining the concentration of individual HMI in the presence of other HMIs, passivation of the electrodes due to the adsorption of different non-metallic substances, and poor reproducibility owing to the formation of intermetallic compounds [2]. The sensitivity of the FET sensor can be further enhanced by optimizing its structure using the metamaterial technique, which shows obvious advantages in high sensitivity detection, device miniaturization, and so on. Besides, the latest microwave sensor [19] implies that information such as amplitude and phase at terahertz frequencies is useful for HMIs detection, which in turn can be implemented using metamaterials, well known for free manipulation of electromagnetic (EM) waves within the sub-wavelength scale.
Recent advances in new materials, such as nanomaterials, have opened a new era of analytical techniques. In particular, graphene is one of the best transducer materials, since it exhibits extreme sensitivity, short response time, high signal-to-noise ratio and large surface-to-volume ratio thanks to its unique electrical and chemical properties [2,20,21] with great potential for detection and discriminative analysis of critically low concentrations of HMIs. Many studies have discussed the adsorption and desorption of graphene and its derivatives (for example, graphene oxide, GO; reduced graphene oxide, rGO) [1–3,5,22–29], and these capabilities have been used for HMIs sensing in some works [2,4,16–18]. Compared to other adsorbents, like rice husk, orange peel, conducting polymers, activated carbon and carbon nanotubes, graphene and its derivatives are regarded as the most promising reactants to adsorb and desorb various HMIs due to their hydrophilicity, surface hydrophobic π-π interaction, high negative charge density and the fact that they can be easily synthesized from the abundant natural graphite [24]. Therefore, by designing terahertz sensors using graphene-based metamaterials, the sensitivity and detection limit of HMIs sensing can be further improved, accompanied by the advantages of non-contact, label-free, etc.
In this study, we propose four designs of graphene-based terahertz metamaterials (GTMs), including both transmission- and reflection-types, for HMIs detection with theoretical and numerical demonstrations. The adsorbed HMIs have a consequential effect on the electronic properties of GTM [23], since the electronic state of the graphene and its derivatives e.g. Fermi energy ${E_f}$ [2,17,20] and sheet conductivity ${\sigma _s}$ [2,17] are very sensitive to ambient interaction. For instance, after cation adsorption, ${E_f}$ moves upward, reducing the hole density and ${\sigma _s}$ for FET sensors [17]. The variation of the electronic state can also lead to changes in the amplitude and phase of the EM responses of the metamaterials, which enables high resolution sensors. Moreover, the adsorption sites will be increased by adding various functional groups (-COOH, -OH, -NH2, -SH, etc.) to the graphene to form GO and rGO, thereby markedly improving the adsorption and desorption performances, and realizing selective detection to different HMIs [3,30]. Besides, by changing voltage, the device can be adjusted to its linear response region, and its adsorption speed will be accelerated. This type of HMIs sensor suggests higher sensitivity than the electrochemical method and FET sensor, while overcoming their electrode passivation and repeatability problems due to its adsorption and desorption properties.
2. Design and results
The detection process of the proposed GTM is shown in Fig. 1(a). First, the spectral information of the GTM (including amplitude and phase) is scanned using a THz time-domain spectroscopy (THz-TDS) system. Then, we drop a trace amount of HMI solution on the GTM and stand it for several minutes to ensure that the HMIs are adsorbed. Next, we detect the spectral information of the adsorbed GTM by the THz-TDS system. The EM response of the adsorbed GTM is different for various concentrations of HMIs. As for the GTM containing specific functional groups, it can only produce a strong EM response to a certain HMI while ignoring other HMIs due to selective adsorption, such as S-GQDs to Ag+ [8], N-[(1-pyrenyl-sulfonamido)-heptyl]-gluconamide to Hg2+ [16], as well as glutathione and DNAzyme to Pb2+ [18,19]. By comparing the amplitude and phase changes of the GTM before and after adsorption, the information about whether the solution contains specific HMI(s) and its (their) concentration can be obtained. Finally, we clean the adsorbed GTM several times with deionized (DI) water [31] for the next test. Because of the performance difference between ideal and actual graphene (or its derivatives), the response of the device in the desired frequency band may not be good enough. Nevertheless, this problem can be alleviated by adjusting the applied voltage to promote the adsorption.
Various HMIs have different chemical properties and valences, which cause differences in the response of graphene, even for the same solution concentration. Some works have proved the influence of various metal ions on the Fermi energy of graphene. For example, the change of Fermi energy $\Delta {E_f}$ after the adsorption of Pt2+, Cu3+ are about 0.45 eV and 0.26 eV under saturated adsorption, respectively [32,33]. Hence, different HMIs (or even the same HMI but with different valences) have different effects on the GTMs even for the same concentration. In addition, these effects can be ascribed to the change of ${E_f}$ or ${\sigma _s}$ of graphene, which macroscopically represent the number of the π electrons or anions on the graphene of GTMs combined with the heavy metal cations in solution. In other words, as long as the devices are not saturated, the concentration of HMIs is proportional to the amount of HMIs adsorbed by graphene, that is, the change of ${E_f}$ or ${\sigma _s}$ of graphene. Therefore, in order to explore the response of GTMs to HMIs more generally and fundamentally, the detection performance of the GTMs is characterized by the relationships between graphene’s Fermi energy and transmission or reflection spectrum of the GTMs, rather than the relationships between the concentration of HMIs solution and the transmission or reflection spectrum of the GTMs.
The design of the unit cell of the first type GTM (GTM-1, transmission-type) is shown in Fig. 1(b). It is composed of a gold double split ring resonator (DSRR) and a graphene strip. The graphene strip is set in between the two splits across the unit cell, which facilitates the electronic control of graphene. The geometric dimensions are optimized as l1 = 45 µm, l2 = 70 µm, t1 = 0.2 µm, t2 = 50 µm, w1 = 7 µm, w2 = 15 µm, s1 = s2 = 5 µm, and px = py = 100 µm. The relative dielectric constant of the silicon substrate is ${\varepsilon _{\textrm{Si}}} = 11.9$ [34]. The frequency domain solver of the CST Microwave Studio is employed in our simulations, and periodic boundary condition is applied in x- and y-directions. The EM plane wave propagates along the z-direction with electric field (E-field) and magnetic field (H-field) along x- and y-directions, respectively.
The electromagnetically induced transparency (EIT) is a coherent process in a three- or multi-level atomic system that makes an originally opaque medium transparent in a narrow spectral range, usually accompanied by strong dispersion [35–37]. Recently, the EIT effect has been introduced into metamaterials for sensing [38], slow light [39] and other applications. Figure 2 shows the transmission spectrum of GTM-1. It is evident that there is a high transmission (T) region at around 1.02 THz (Fig. 2(a)), together with a sharp change in the phase (${\varphi _\textrm{T}}$) (Fig. 2(b)). Namely, an EIT window forms here, which is very valuable for detection. One can see that as ${E_f}$ increases, T and ${\varphi _\textrm{T}}$ gradually decrease. And this trend is almost linear in the range of 0.05 eV - 0.3 eV (Figs. 2(c, d)). As mentioned above, ${E_f}$ or ${\sigma _s}$ of the GTM can be changed by adsorbing different concentrations of HMIs. In fact, there is a relationship between ${E_f}$ and ${\sigma _s}$ described by the Kubo formula [40,41]:
Fig. 2. (a) Amplitude T, (b) phase ${\varphi _\textrm{T}}$, (c) amplitude difference $\Delta {\textrm{T}_{\textrm{peak}}}$, and (d) phase difference $\Delta {\varphi _{\textrm{peak}}}$ of the transmission coefficient of GTM-1, and its E-field distribution at transmission resonance peaks for varying Fermi energy of graphene (e) ${E_f} = 0$ eV, (f) ${E_f} = 0.15$ eV and (g) ${E_f} = 0.3$ eV. Where peaks of amplitude and phase of the EIT resonance are marked by different symbols.
Therefore, by detecting the variation of T and $\Delta {\varphi _\textrm{T}}$ of the GTM ($\Delta {\textrm{T}_{\textrm{peak}}}$ and $\Delta {\varphi _{\textrm{peak}}}$) before and after adsorbing HMIs with different concentrations, high performance HMIs sensing can be realized at around 1.02 THz.
To better understand the EIT mechanism of the proposed structure, the E-field distributions of GTM-1 at EIT peak for different ${E_f}$ are plotted in Figs. 2(e-g). It is apparent that as the Fermi energy of the graphene rises from 0 eV to 0.3 eV, the field strengths in the left and right vertical arm regions of the splits fade out. This is attributed to the fact that the graphene strip becomes more metallic with the increase of its sheet conductivity (HMIs adsorption), which makes the graphene form an increasingly strong induced E-field that inhibits the field strength in the splits, and then impairs the field enhancement in the two vertical arms. This brings about a redistribution of the EM field in the structure, thus the destructive interference state is gradually broken. That is, the high transparency of the EIT effect deteriorates. In other words, the concentration and even type of HMI(s) solution can be characterized (due to the selective adsorption, graphene with different functional groups has different adsorption effects on different types of HMIs, and graphene can even adsorb only one specific kind of HMI by grafting it with some specific functional groups, as mentioned previously) by the variation degree of the EIT resonance of the device before and after the absorption of the HMIs.
EIT is sensitive to substructures and their relative positions, even a small change can affect its resonance, i.e., detection performance. The length of the lower horizontal arms of GTM-1 is changed to construct a second type of GTM, i.e., GTM-2. The new gap between the lower horizontal arms and graphene strip is s2 = 15 µm. As shown in Figs. 3(a, b), the EIT resonance splits into two, which is attributed to the symmetry breaking of the upper and lower horizontal arms, namely, the difference between the gaps s1 and s2. The coupling strength of the upper and lower horizontal arms becomes inconsistent due to different s1 and s2, which brings about a rebalanced destructive interference on these arms. Thus, the two EIT resonances of GTM-2 appear at around the EIT region of GTM-1. Thanks to the judicious design of the gaps s1 and s2, $\Delta {\textrm{T}_{\textrm{peak}}}$ and $\Delta {\varphi _{\textrm{peak}}}$ of the two EIT resonances are comparable in response to the concentration change of the HMIs, especially for $\Delta {\textrm{T}_{\textrm{peak}}}$ (Figs. 3(c, d)). This means both EIT resonances can be used for sensing. Moreover, despite the similar amplitude response, the phase response of GTM-2 is more sensitive to HMIs than that of GTM-1. For the same HMIs concentration (0.3 eV of Fermi energy), $\Delta {\varphi _{\textrm{peak}}}$ are 45° and 52° for GTM-2 (Fig. 3(d)) while just 26° for GTM-1 (Fig. 2(d)), indicating the superiority of GTM-2 to GTM-1.
Fig. 3. (a) Amplitude T, (b) phase ${\varphi _\textrm{T}}$, (c) amplitude difference $\Delta {\textrm{T}_{\textrm{peak}}}$, and (d) phase difference $\Delta {\varphi _{\textrm{peak}}}$ of transmission coefficient of GTM-2, (e) amplitude T, (f) phase ${\varphi _\textrm{T}}$, (g) amplitude difference $\Delta {\textrm{T}_{\textrm{peak}}}$, and (h) phase difference $\Delta {\varphi _{\textrm{dip}}}$ of the transmission coefficient of GTM-3, and (i) amplitude R, (j) phase ${\varphi _\textrm{R}}$, (k) amplitude difference $\Delta {\textrm{R}_{\textrm{peak}}}$, and (l) phase difference $\Delta {\varphi _{\textrm{dip}}}$ of the reflection coefficient of GTM-4. Where peaks/dips of amplitude and phase of the (first) EIT/EIR resonance are marked by different symbols.
Based on the above-mentioned findings, we believe that a more sensitive response to HMIs can be obtained by further modifying the DSRR structure, which results in the third type GTM, i.e., GTM-3. In GTM-3, we removed the left-right symmetry of the structure, where the substructure in the right side is replaced by a vertical gold line, and the lower horizontal arm was deleted to further increase the upper-lower asymmetry. To achieve destructive interference again, the split between the right gold line and the graphene strip is set to s3 = 5 µm, and s1 is increased to 10 µm. As expected, Figs. 3(e, f) show that an EIT window remains at around 1.03 THz. For HMIs response (0.3 eV of Fermi energy), as plotted in Figs. 3(g, h), $\Delta {\varphi _{\textrm{dip}}}$ keeps about 52° while $\Delta {\textrm{T}_{\textrm{peak}}}$ increases by about 0.36.
The above results numerically manifest that by recording transmission changes in amplitude and phase of the EIT response, HMIs and their concentration can be detected by using the GTM. This response can also be achieved on the reflection spectrum. Here we give one scheme. Figure 1(c) shows the structure diagram of the proposed reflection-type GTM-4, where l1 = 55 µm, l2 = 45 µm, t1 = 0.2 µm, t2 = 50 µm, w1 = 15 µm, w2 = 20 µm, s = 5 µm, h = 5 µm, px = 65 µm and py = 100 µm. The EM plane wave incidents obliquely at an angle of 45° with respect to the z-direction and the E-field is along x-direction. As shown in Figs. 3(i, j) (black lines), two electromagnetically induced reflection (EIR) responses appear at around 1.17 THz and 1.43 THz. EIR is a phenomenon similar to EIT but occurs in the reflection spectrum [43].
Figures 3(i-l) show the reflection response of GTM-4 to HMIs and their concentration changes, where Fig. 3(k) displays the amplitude changes $\Delta {\textrm{R}_{\textrm{peak}}}$ at two reflection peaks, and Fig. 3(l) gives the phase changes $\Delta {\varphi _{\textrm{dip}}}$ at two reflection dips after peaks. For HMIs response (0.3 eV of Fermi energy), $\Delta {\textrm{R}_{\textrm{peak}}}$ reaches about 0.27, 0.20 and $\Delta {\varphi _{\textrm{dip}}}$ are about 177°, 238° for the two EIR resonances, respectively. As the concentration of HMIs gradually increases, the response of amplitude is almost linear whereas the phase is not. Despite this, it still shows a good potential of the reflection-type GTM for HMIs detection, and the response can be optimized in the future work.
For the sensitivity of the detectors, although it can be explicitly calculated by formulas related to the refractive index unit (RIU) in some papers, it is only limited to those metamaterials-based sensors (MMBSs) that realize sensing depend on the change of environmental refractive index. The sensitivity in more MMBSs is usually expressed by $\Delta \textrm{T} - f$, $\Delta \textrm{T/T} - f$, $\Delta \varphi - f$, $\Delta \textrm{T} - {E_f}$, etc. The sensing principle in this work is not dependent on refractive index, hence the more general relationships $\Delta \textrm{T} - {E_f}$, $\Delta \textrm{R} - {E_f}$, and $\Delta \varphi - {E_f}$ are used to represent the sensitivity of the devices, as shown in Fig. 2 and Fig. 3. These results indicate the good linearity of amplitude and phase responses of the transmission-type devices before (${E_f} = 0$ eV) and after adsorption (${E_f} = 0.3$ eV), and the change in phase is more sensitive for the reflection-type device.
Quality factor (Q-factor) is also an important index to characterize the sensitivity of detector. Herein, the Q-factor is calculated by $Q\textrm{ = }{f_0}/\Delta f$ [44,45], where ${f_0}$ represents the center frequency of the EIT/EIR window in the initial state (black lines in Figs. 2(a), 3(a), 3(e), and 3(i)), and $\Delta f$ denotes the full width at half maximum of EIT/EIR window. The results are listed in Table 1, where the highest Q-factors are 53 and 852 for amplitude and phase, respectively. These high Q-factors reflect the highly sensitive response of the devices to HMIs, especially for the phase response.
Table 1. Q-factors of the presented GTMs.
3. Calculation and demonstration
The coupled mode theory and “two-particle” model are two classic models used to describe the EIT effect in metamaterials [46–52]. To theoretically demonstrate the validity and quantitatively investigate the response of the proposed HMIs detectors, the “two-particle” model for analyzing the EIT effect is introduced, which is described by the following equations [49,50]:
For this work, DSRR is the bright resonator and graphene strip is the dark resonator, namely ${x_1}$ and ${x_2}$, respectively, thereby ${\gamma _1}$ and ${\gamma _2}$ mean the corresponding losses, respectively. The resonant frequency of the graphene strip is ${\omega _2}\textrm{ = }{\omega _1} + \delta$, where $\delta$ corresponds to the detuning of the resonant frequency of the DSRR and graphene strip, E0 indicates the incident field. To simplify the calculation process, ${q_2}$ is assumed as zero due to the weak interaction with E0. Then Eq. (2) becomes [50–52]
After some algebraic calculations of Eq. (3), the transmission of the EM wave through GTM-1 can be given by the following equation [50–52]:
By combining Eqs. (4) and (5), the analytical results of GTM-1 are drawn in Fig. 4(a). It is obvious that the theoretical curves agree reasonably well with the simulated ones, which demonstrates the validity of GTM-1 for HMIs detection. For these analytical curves, the corresponding parameters are ${\omega _0}$ = 1.0208 THz, $k$ = 0.28 THz, $\delta$ = 1.508 THz and ${\gamma _1}$ = 0.07 THz. The change of the graphene strip’s loss ${\gamma _2}$ with different ${E_f}$ (i.e., the variation of HMIs adsorption amount) is shown in Fig. 4(b). It is worth noting that ${\gamma _1}$ is several times larger than ${\gamma _2}$. This is due to the significant difference in radiation losses between the DSRR and graphene strip, as displayed in Figs. 2(e-g), particularly for Fig. 2(e). Moreover, ${\gamma _2}$ increases as ${E_f}$ increases from 0 eV to 0.3 eV, which is consistent with the trend of the radiation loss in Figs. 2(e-g). These calculation results numerically indicate the physical relationship between the quantity of HMIs adsorption and the degree of the spectral response of GTM-1. For GTM-2, GTM-3 and GTM-4, similar results can be obtained by adjusting the parameter values of the two-particle model.
Fig. 4. (a) Theoretical results calculated by using the two-particle model, (b) change of graphene strip’s loss ${\gamma _2}$ with different values of Fermi energy ${E_f}$.
The future test system and experimental process are designed as follows. Measurements of the transmission and reflection spectra are to be carried out using the THz-TDS system. For the transmission-type devices (GTM-1, GTM-2 and GTM-3), the schematic diagram of system is shown in Fig. 5(a). A femtosecond laser beam is divided into a pump pulse and a probe pulse by a beam splitter (BS). The pump pulse is focused on an emitter to generate THz pulse. The THz pulse is collected by a pair of parabolic mirrors (PM) and focuses on the sample. The sample is located at the waist of the THz beam, which is much smaller than the size of the sample. Then the transmission pulse containing the sample information is collected by the other pair of PM and focused on the detector together with the probe pulse experiencing a delay stage. Thus, the transmission spectrum of the device is obtained by analyzing the detector signal. To reduce the effect of the water vapor absorption, the system should be enclosed in a box and filled with dry nitrogen gas. For the reflection-type device (GTM-4), the corresponding system schematic is drawn in Fig. 5(b). Compared with the transmission-type THz-TDS system, the position between the sample and the two PMs needs to be restructured [53,54].
Multiple measurements need to be performed. The entire experimental process in a few steps is revealed in Fig. 5(c): (i) Measure the transmission/reflection spectrum of 50 µm thick bare silicon substrate and record it as ${E_{\textrm{reference}}}$. (ii) Measure the transmission/reflection spectrum of the GTM before adsorption and denote it as ${E_{\textrm{sample }00}}$. (iii) Measure the transmission/reflection spectrum of the GTM after adsorption; clean the device with DI water; absorb the HMI solution and measure the transmission/reflection spectrum again; record results as ${E_{\textrm{sample 11}}}$, ${E_{\textrm{sample 12}}}$. (iv) Change the concentration of the HMI solution and repeat step (iii). Denote the corresponding transmission/reflection spectra as ${E_{\textrm{sample 21}}}$, ${E_{\textrm{sample 22}}}, \,{E_{\textrm{sample 31}}}\, \ldots $, until all the required concentrations are tested [55,56]. As a result, the transmission and reflection of the devices can be defined as $\textrm{T}\&\textrm{R} = {|{{E_{\textrm{sample i,j}}}/{E_{\textrm{reference}}}} |^2}$, ($\textrm{i,j} = 0,1,2\ldots $) [31].
4. Conclusion
In summary, four designs of graphene-based terahertz metamaterials for heavy metal ions (HMIs) detection are proposed, including three transmission-types and one reflection-type devices. The adsorbed HMIs have a momentous effect on the EIT/EIR resonances of the devices. The physical mechanism is explained by analyzing the E-field distribution. Then, the two-particle model is used to verify the simulation. The simulation results are in good agreement with the theoretical results, implying that the amplitude and phase of the transmission-type device change almost linearly between 0 to 0.36 and 0° to 52°, respectively, before (${E_f} = 0$ eV) and after adsorption (${E_f} = 0.3$ eV). For the reflection-type detector, the phase response is more sensitive. Moreover, by applying voltage, the devices can be easily adjusted to their linear working areas and their sensing speeds can be improved. In addition, the problem of electrode passivation in the electrochemical method and FET sensor is overcome through adsorption and desorption performance as well as judicious design. Besides, the detection sensitivity of the GTMs can be further improved by adding functional groups to the graphene strips, and even identify one specific HMI from mixed HMIs solution by the selective adsorption of specific functional groups. Therefore, this type of HMIs sensor is highly sensitive, fast and reusable. Finally, the future test system and experimental process are presented. The technical route and implementation method discussed in this paper could be useful for designing highly sensitive, fast, and reusable HMI detectors.
Funding
National Natural Science Foundation of China (61801366); Natural Science Foundation of Shaanxi Province (2020JM-078); Wuhu and Xidian University special fund for industry-university-research cooperation (XWYCXY-012020016-HT); Doctoral Students’ Short-Term Study Abroad Scholarship Fund of Xidian University.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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