1. Introduction

Metamaterials have artificial optical properties that can be tailored to design impaired terahertz sources, detectors [1] and components [2–4]. The sub-wavelength structures composing planar terahertz metamaterials are currently fabricated by photolithography. However this technique suffers from time-consuming processing steps, high capital expensures, and requires photomasks everytime the metamaterial design is changed [5].

The few microns resolution required to produce terahertz metamaterials can now be reached by various rapid prototyping techniques [6]. This offers a suitable approach to validate experimentally the optical responses of terahertz metamaterials at low cost without the need of photomasks. For instance, drop-on-demand inkjet printing of silver nanoparticles ink has been widely used for the fabrication of tunable metamaterials on flexible substrates [7–12]. However the printing resolution is limited to about $30~\,\mathrm{\mu}\mathrm {m}$, while nozzle clogging prevents the use of highly viscous inks (viscosity above 15 cP). Alternatives are currently under development to overcome these issues, such as electrohydrodynamic jetting [13,14], laser printing [15] and aerosol jet printing [16].

In addition, a microplotter technology has been used for the rapid prototyping of printed electronics [17,18] and biotechnologies [19], but to date its potential for metamaterials fabrication has not been demonstrated. The microplotter technology is based on ink ejection from a glass tip positioned typically $20~\,\mathrm{\mu}\mathrm {m}$ above the substrate, using ultrasonic excitation as the driving force. Compared to other printing techniques, the microplotter has two advantages: (i) viscous ink up to 450 cP can be ejected, and (ii) a reduced set of parameters has to be adjusted depending on the ink viscosity and the required resolution: the glass tip inner diameter (typically between $1$ and $60~\,\mathrm{\mu}\mathrm {m}$) and the voltage amplitude of the ultrasonic excitation (between $0$ and $3~\textrm {V}$).

However, three main parameters limit the spectral range accessible by the metamaterial fabricated by rapid prototyping. First, the spatial resolution of the printed structures that sets the upper frequency limit. Second, the metal thickness which has to be high enough compared to the skin depth, in order to observe the resonance behaviour, as shown on split-ring resonators (SRR) by Singh et al. [20]. Consequently, the metal conductivity has to be high enough to fulfill the latter criteria. The combination of metal thickness and conductivity thus set the lower frequency limit. In general, sub-terahertz ($0.1-1~\,\textrm {THz}$) metamaterials cannot be fabricated in a single fabrication run by rapid prototyping. The fabrication process has to be iterated several times in order to increase the deposited metal thickness at the expanse of a longer processing time [10].

In this letter, we study the ability of the microplotter technology to fabricate sub-terahertz metamaterials in a single fabrication run. A statistical analysis of the printed structures is performed in order to study the reproducibility of the printer. The spectral responses of the metasurfaces are measured by THz time-domain spectroscopy (THz-TDS) and compared with numerical simulations.

2. Design and fabrication

Figure 1(a) shows the structure of the metasurface. The metasurfaces are composed of well-known square Metal-Insulator-Metal (MIM) antennas [21]. The MIM antenna is composed of a metallic patch on top of an insulator layer and a metallic layer, thick enough to be considered as infinite. This antenna acts as a Fabry-Perot resonator for the mode propagating in the cavity formed below the metallic patch, and exhibits a nearly total absorption at its first order wavelength, given by:

 

Fig. 1. (a) Scheme of an array of square MIM antennas. The period d, and the average width w of gratings 1-4 are indicated in Table 1 - $\textrm {h}_{\textrm {Ag}} = 0.7\,\mathrm{\mu}\mathrm {m}$, $\textrm {h}_{\textrm {PI}} = 13\,\mathrm{\mu}\mathrm {m}$. (b) Computed reflectivity spectra of grating 1 for different metal thicknesses h_Ag and resistivities $\rho _{\textrm {Ag}}$. $\rho _{\textrm {bulk}}=1.59~\,\mathrm{\mu}\Omega \textrm {.cm}$ is the resistivity of bulk silver. $\textrm {w}= 319\,\mathrm{\mu}\mathrm {m}$, $\textrm {d}= 700 \,\mathrm{\mu}\mathrm {m}$. (c) Photograph of four MIM gratings printed on a polyimide film, together with optical microscope images of the gratings. (d) Reflection THz-TDS experimental setup.

Download Full Size | PDF

Table 1. Geometrical parameters of the printed gratings (experimental data).

View Table

The top metallic grating and bottom mirror of the MIM antenna were printed using a microplotter system (Sonoplot, Microplotter II) on a $13~\,\mathrm{\mu}\mathrm {m}$ thick polyimide film (Kapton HN, Dupont), purchased from Goodfellow (IM301130). A glass tip was made from a filamented fire-polished borosilicate capillary (World Precision Instr) using a glass puller (Sutter Instr, P-1000). The inner diameter of the tip typically equals $1~\,\mathrm{\mu}\mathrm {m}$. The tip was then stuck with a cyanoacrylate glue (super glue) to the piezoelectric actuator, and mounted in a cartridge attached to three motorized translation steppers ($5~\,\mathrm{\mu}\mathrm {m}$ resolution).

The tip was filled within $5$ minutes with a commercial dispersion of silver nanoparticles in diethylene glycol (Novacentrix, JS-A291) by capillary action. An automated calibration procedure is done to match the ultrasonic excitation frequency with the resonance frequency of the piezoelectric element. The calibration optimizes the ink ejection, and allows automated surface tracking on the basis of the resonance frequency shift when the tip is contacting the surface. When contacting the surface, a drop of ink was ejected without the need of an excitation of the piezoelectric element because of the low viscosity of the ink ($8-12~\textrm {cP}$). The pattern was then drawn continuously in a pencil-like fashion. The polyimide substrate was stuck by capillary adhesion to a silicon wafer in order to prevent surface curvatures that would otherwise break the glass tip. The gratings were then thermally sintered on a hot plate at $220\,^{\circ }\mathrm {C}$ for $10$ minutes, and the same procedure was performed for the bottom metallic layer. The DC resistivity was measured by a four point probe method on a printed metallic square, and equals $\rho_{\textrm{Ag}}=10.8~\,\mathrm{\mu}\Omega \textrm {.cm}$, which is about $7$ times higher than the value of bulk silver resistivity ($\rho_{\textrm{bulk}}=1.59~\,\mathrm{\mu}\Omega \textrm {.cm}$).

The printing performances of the microplotter were characterized using optical microscope images as shown in Fig. 1(c). A visual inspection of the printed features shows that the antennas are continuously filled with metal. The thickness and roughness of the structure equal $0.7~\,\mathrm{\mu}\mathrm {m}$ and $0.2~\,\mathrm{\mu}\mathrm {m}$ respectively, as measured by an atomic force microscope (AFM). We further investigated the printing performances by a statistical analysis of the antennas structure. Figure 2 shows for each grating, the width distribution of the printed antennas. The reproducibility of the printed structures was determined from their standard deviations (see Table 1), and typically equals 4 $\mathrm{\mu}$m. The linewidth of the printed structure due to ink spreading onto the substrate typically equals 15 $\mathrm{\mu}$m. The latter value determines the lowest dimensions of the structures that can be fabricated by the microplotter. The resolution can be improved by reducing further the inner diameter of the glass tip, at the cost of a higher risk of nozzle clogging.

 

Fig. 2. Normalized distribution of antennas widths of gratings 1-4.

Download Full Size | PDF

The spectral responses of the gratings were recorded by terahertz time-domain spectroscopy (THz-TDS) in reflection at normal incidence using a commercial spectrometer (Terasmart, Menlo System Gmbh). Figure 1(d) shows the reflection THz-TDS setup. A $3~\,{\textrm{mm}}$-thick high resistivity silicon substrate was used as a semi-reflective beamsplitter. The beamsplitter was chosen thick enough to delay the echoes due to the reflections on the back face. The time trace was cut before the first echo occurs ($40~\textrm {ps}$ after the main THz pulse) in order to clean the spectrum from $25~\,\textrm {GHz}$ oscillations resulting from artefact of the fast Fourier transform. In order to position accurately the reference mirror and test sample at the same location, the polymide film was attached to a silicon substrate mounted on mechanical micro-controls for a fine alignement.

We compared the results with numerical simulations using a two-dimensional rigorous coupled wave analysis (2D-RCWA) method. A Drude model with the parameters of Ordal et al. [22] was used to describe the metallic layers of the antenna, while the dielectric constant of the polyimide equals $\epsilon =3.1+0.05i$ [23,24] between $0.2$ and $2.5~\,\textrm {THz}$ [25,26]. For the sake of simplicity we neglected the cone of incidence of the THz light, and we considered that the beam arrives at normal incident on the grating. This assumption has little consequences on the final results owing to the broad angular tolerance of the Fabry Perot resonance of MIM antennas [21].

3. Results and discussion

Figure 3 shows the reflectivity spectra recorded using THz-TDS (black line). Despite some fluctuations on the reference baseline, the Fabry-Perot resonances of the MIM gratings 1-4 are clearly visible at 264, 452, 701 and 800 GHz respectively. The blue curve is the computation result of the MIM antennas of width w_avg given in Table 1. The red curve accounts for the dispersion of the size of the antennas using the following expression:

 

Fig. 3. Reflectivty spectra of the MIM gratings (1-4) measured by THz-TDS (black line) and calculated using the average width of the antennas (blue line) and accounting for the width distribution (red line).

Download Full Size | PDF

In Fig. 4(a), we calculated the reflectivity of grating 1 for silver resisitivities ranging from 1 to 15 times bulk silver resisitivity, which are typical values for silver nanoparticles inks [27]. Increasing silver resistivity gradually lowers the quality factor of the Fabry Perot cavity, and increases the skin depth $\delta =(\rho _{\textrm {Ag}}/(\pi \nu \mu ))^{1/2}$, where $\nu$ is the frequency at which the skin depth is defined, $\mu$ and $\rho _{\textrm {Ag}}$ are the permeability and DC resistivity of the metal, respectively. Obtaining low resistivity metallic film requires high sintering temperatures which are not always compatible with the printing on polymer foils having low melting point. Alternatives to the classical thermal sintering treatment aim to overcome this issue [28]. Strategies include the reduction of the sintering temperature, e.g. chemical sintering, and the selective heating of the printed patterns, e.g. photonic sintering.

 

Fig. 4. Reflectivity map of grating 1 for various (a) silver resisitivty $\rho_{\textrm{Ag}}$ normalized by bulk silver resistivity $\rho_{\textrm{bulk}}$ and (b) silver thickness h_Ag. Initial conditions: $\rho_{\textrm{Ag}}/\rho _{\textrm{bulk}}=7$, ${\textrm{h}_{\textrm{Ag}}}=0.7\,\mathrm{\mu}\mathrm {m}$.

Download Full Size | PDF

Figure 4(b) shows a reflectivity map of calculated spectra of grating 1 for metallic thicknesses ranging from $0.04~\,\mathrm{\mu}\mathrm {m}$ to $1~\,\mathrm{\mu}\mathrm {m}$. For metal thickness values approching the skin depth $\delta =321~\,\textrm{nm}$ at $264~\,\textrm {GHz}$, the MIM resonance is degraded. This is in agreement with the results of Singh et al. [20] on split-ring resonators (SRR). Therefore, metal conductivity and metal thickness both determine the lower frequency limit of the MIM antenna that can be printed by the microplotter. This frequency is a cut-off frequency for the mode confinement inside the Fabry Perot cavity formed by the MIM antenna, which can be written as follows:

This criteria assumes that the minimum operation frequency $\nu _{\textrm {min}}$ is the frequency at which the metal thickness equals the skin depth. Figure 5 shows how the cutoff frequency depends on the metal thickness and conductivity. In our conditions since the printed metal thickness equals $0.7~\,\mathrm{\mu}\mathrm {m}$, we thus estimate that the resonance frequency of the MIM antennas can be adjusted down to about $55~\,\textrm {GHz}$. Note that iterating the printing process would allow to increase the metal thickness and extend the accessible spectral range [10], at the expanse of a longer processing time.

 

Fig. 5. Cut-off frequency $\nu _{\textrm {min}}$ (GHz unit) of the Fabry-Perot mode confinement inside the MIM antenna for different metal thickness and resistivity.

Download Full Size | PDF

4. Conclusions

In summary, we demonstrated the fabrication of MIM metamaterials using a microplotter system on a flexible polyimide film in a single fabrication run. Using the microplotter we were able to produce MIM gratings exhibiting resonance frequencies in different spectral bands up to 0.8 THz. The spectral responses were recorded in reflection by THz-TDS and compared with 2D-RCWA simulations. We accounted for the size distribution of the antennas in the calculated spectra. For gratings 1 and 2 covering the spectral range from $0.25$ to $0.5~\,\textrm {THz}$, the reproducibility of the microplotter was sufficiently good to neglect the dispersion of the size of the antennas, but for gratings 3 and 4 the size distribution of the MIM antennas significantly modified the grating response. The lack of reproducibility is thus the main limitation of the microplotter to operate in the spectral range above $0.5~\,\textrm {THz}$.

We also considered the lower frequency limit that can be covered by the MIM antennas fabricated by the microplotter. We found that the high resistivity of the silver nanoparticle ink may be an issue if the thickness of the printed structure is not larger than the skin depth. In the present conditions, we estimated that MIM antennas with resonance frequency down to 55 GHz can be fabricated using the microplotter.

Therefore, the microplotter technique is a suitable low cost technique for the rapid prototyping of terahertz metamaterials, but its printing reproducibility should be further improved in order to fabricate metamaterials operating in the frequency range above $0.5~\,\textrm {THz}$.